WINTER OPERATIONS OPTIMIZATION AND ASSET MANAGEMENT FOR THE STATE OF OHIO. A Dissertation Presented to The Graduate Faculty of The University of Akron

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1 WINTER OPERATIONS OPTIMIZATION AND ASSET MANAGEMENT FOR THE STATE OF OHIO A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy William A. Holik August, 2015

2 WINTER OPERATIONS OPTIMIZATION AND ASSET MANAGEMENT FOR THE STATE OF OHIO William A. Holik Dissertation Approved: Advisor Dr. William Schneider Committee Member Dr. Christopher Miller Committee Member Dr. Qindan Huang Committee Member Dr. Arjuna Madanayake Accepted: Department Chair Dr. Wieslaw Binienda Interim Dean of the College Dr. Rex Ramsier Interim Dean of the Graduate School Dr. Chand Midha Date Committee Member Dr. Richard Einsporn ii

3 ABSTRACT One of the most difficult challenges facing agencies is the rising costs of winter maintenance. With the current economic climate, winter maintenance personnel have been tasked with providing an adequate level of service to the motoring public while simultaneously reducing their expenditures. This research specifically addressed several winter maintenance issues ODOT faces with the goal of decreasing winter maintenance expenditures while improving or maintaining the level of service. The areas evaluated in this research include: 1) snow plow routing and optimization, 2) the implementation of specialty equipment into winter maintenance vehicle fleets, 3) the management and distribution of winter maintenance materials throughout the State of Ohio, and 4) automated vehicle and material tracking. The snow plow route optimization is developed in two stages, one with county and district borders and one without the borders. A cost savings of greater than $800,000 is realized by removing the border restrictions. Specialty winter maintenance equipment are modeled to determine the benefits of the equipment. The specialty equipment are implemented in a route optimization model and the results of that model are combined with field data to estimate the cycle time reductions and cost increases of the specialty equipment. Cost curves are developed to determine the payback period of the specialty equipment. The vulnerability of salt supplies to depletion during winter operations are investigated. Cost analysis is conducted to determine the risk costs and total costs iii

4 associated with the salt supply in Ohio counties. These curves may be used as a guide to determine how much material to keep on hand. Automated vehicle and material management sensors are investigated to determine the reliability and calibration requirements of several types of sensors. The results indicate a significant cost savings associated with calibrating sensors. As plow truck sensors become more prevalent, winter maintenance personnel must commit more time to maintaining and calibrating sensors. Focus needs to shift from solely worrying about the maintenance of the plow trucks to including ensuring the accuracy of the sensor data as agencies rely more heavily on this data for their analytical assessment and daily operations. iv

5 ACKNOWLEDGEMENTS I would like to thank Dr. Schneider for his guidance and support throughout my graduate studies. Dr. Schneider has provided pivotal guidance for all the projects I worked on during my studies including this research. I would like to thank the member of my committee: Dr. Miller, Dr. Huang, Dr. Madanayake, and Dr. Einsporn for their help and insight into my research. Additionally, I would like to thank my family and friends for their support during my academic studies. I am very grateful for the support and suggestions from the research team, specifically Alexander Maistros, Brandon Stackleff, and Mallory Crow. Additionally, I would like to thank the Ohio Department of Transportation for their guidance and availability for data collection. I would like to thank the United States Department of Transportation for their support for our research projects. v

6 TABLE OF CONTENTS vi Page LIST OF TABLES...x LIST OF FIGURES... xi CHAPTER I. INTRODUCTION...1 Benefits of this Research...2 Organization of the Dissertation...3 II. BACKGROUND...4 Equipment...6 Traditional Equipment...10 Innovative Equipment...13 Materials...20 Traditional Materials...20 Innovative Materials...21 Conclusions...22 III. QUANTIFYING THE FINANCIAL IMPACTS OF MAINTENANCE ZONES FOR SNOW PLOWS...23 Introduction...23 Methodology...26 Ohio Department of Transportation Study Area...26 Route Optimization Model Development...27 Cost Analysis Methodology...29

7 Results and Discussion...31 Route Optimization...32 Cost Analysis...33 Conclusions...36 IV. WINTER MAINTENANCE FLEET SAVINGS FROM IMPLEMENTING SPECIALTY WINTER MAINTENANCE EQUIPMENT...38 Introduction...38 Research Objective...42 Study Area...43 Methodology...45 Change in Lane Miles Maintained...46 Cycle Time Failure Probability...48 Costs Analysis...50 Analysis and Discussion...53 Failure Probability...54 Annual Benefit to Garage...57 Conclusions...59 V. ASSESSING THE VULNERABILITY OF WINTER MAINTENANCE MATERIAL STORAGE FAILICITIES...62 Introduction...62 Methodology...64 Performance of Storage Facilities...65 Facility Material Capacity...66 Material Usage...67 Reliability Analysis, Sensitivity Measures, and Importance Measures...71 Annual Risk Costs...73 vii

8 Results and Discussion...74 Conclusions...81 VI. PLOW TRUCK SENSOR FAILURE AND CALIBRATION...83 Introduction...83 Data...85 Methodology...88 Sensor Reliability and Calibration...88 Sensor Costs...90 Results and Discussion...91 Sensor Analysis...91 Sensor Failure Costs...98 Conclusions VII. CONCLUSIONS Introduction Snow Plow Route Optimization Implementation of Specialty Equipment Salt Storage Facility Management Automated Vehicle and Material Tracking Future Work Optimal Facility Location Equipment Optimization Salt Storage Facility Optimization Vehicle Sensor Data Conclusion REFERENCES viii

9 APPENDICES APPENDIX A. SALT STORAGE FACILITY DATA APPENDIX B. SALT DOME FAILURE PROBABILITY AND SENSITIVITES AND IMPORTANCE MEASURES ix

10 LIST OF TABLES Table Page 2.1 Equipment and Material Evaluations Average and Standard Deviation for Cost Analysis Variables Time and Distance Differences, Number of Events, and Cost Savings Correlation Coefficients for Parameters Related to Annual Savings Lane Miles Maintained before and after Specialty Equipment are Implemented Average and Standard Deviation of Parameters used in Cost Analysis Example of Salt Storage Facility Data Collected Sensitivity and Importance Measures for Several Counties in Ohio Average Snowfall and Number of Events in Regions of Ohio Sensor Failure Percentages and Percent Drift Costs per Truck Associated with Sensor Failures and Calibration in Each Region of Ohio...98 x

11 LIST OF FIGURES Figure Page 2.1 Winter Maintenance Decisions for ODOT Traditional ODOT Tandem Axle Plow Truck Traditional ODOT Plow Truck with Front Plow and Wing Plow Epoke Sirius AST Combi S4902 Spreader Diagram of Epoke System Process Salt Consistency after Crushing by Epoke (left) and Standard Salt Used by ODOT (right) Dry Material Spreader and Liquid Nozzles on an Epoke Fully Deployed TowPlow Partially Deployed TowPlow Hydraulic Controllers for TowPlow Snow Plow Routes and Facility Locations Maintained by ODOT Specialty Hopper (left) and Specialty Plow (right) Ohio Average Annual Snowfall Distribution of Events in Each Region for (a) Light, (b) Moderate, and (c) Heavy Snowfall Failure Probability of a Garage if any of the Trucks Exceeds the Cycle Time in (a) Region I, (b) Region II...54 and (c) Region III Failure Probability of a Garage if the Total Time used by all the Trucks Exceeds the Total Cycle Time in (a) Region I, (b) Region II, and (c) Region III Cumulative Benefit Costs of Implementing One Specialty Hopper (left) and One Specialty Plow (right) in (a) Region I...57 (b) Region II, and (c) Region III...58 xi

12 5.1 Number of Light, Moderate, and Heavy Snowfall Events in Cleveland (left) and Cincinnati (right) Salt Application (left) and Brine Application (right) during (a) Light...70 (b) Moderate, and (c) Heavy Snowfall Events Probability of Exceeding Salt Supply for Each County in Ohio Normalized Expected Risk Costs over the Price of Salt versus Material Supply in the Three Regions of Ohio Normalized Expected Total Costs over the Price of Salt versus Material Supply in the Three Regions of Ohio Constant Bed Scale Weight Reported on January 29, Bed Scale Sensor that Failed and Reported an Erroneous Value on December 18, Bed Scale Data from January 30, 2015 (a) Raw and (b) Cleaned Bed Scale Weight Noise when Driving over Bridge Joint in Summit County, Ohio on February 3, Total Sensor Related Costs for Each Region Based on the Fleet Size...99 xii

13 CHAPTER I INTRODUCTION One of the toughest challenges faced by motorists and state Departments of Transportation (DOTs) is winter weather. For motorists, winter weather causes decreased friction between their vehicle and the roadway as well as decreased visibility. While for DOTs, winter weather must be combated to keep the roadways clear of ice and snow. DOTs in northern climates, where winter storms are unavoidable, must expend a considerable amount of time and money to maintain a passable level of service of their roadways. Recently, advances have been made in winter maintenance operations, materials, and equipment. These include the implementation of new equipment and practices for agencies to better handle winter storms. While a DOT may incorporate various practices in different areas, a unified system balancing all of the standard equipment with strategically placed specialty equipment presents the most financially beneficial system. Ohio presents a unique and challenging aspect to this balance because of the variation in the amount of snowfall in areas throughout the state. Lake effect snow occurs mostly in the northeastern region of Ohio, and the snowfall ranges from over 100 1

14 inches annually in the northern portions to less than 20 inches annually in the southern regions of the state (The Ohio Department of Transportation, 2011). Operating a vehicle during a winter event, whether it is snowfall, ice, or freezing rain, is a difficult and dangerous task. According to the Federal Highway Administration (FHWA) between 2002 and 2012, over 211,000 crashes occurred each year during snow or sleet, resulting in 769 fatalities per year (USDOT a). During the same time frame, nearly 330,000 crashes occurred each year on snow, slush, or ice covered pavement, which resulted in 1,152 fatalities per year (USDOT a). The cause of these crashes is mostly attributable to the decreased friction between the vehicle and the road and the decreased visibility during snowfall. These crashes do not represent a large percentage of overall crashes and fatalities with 4% of crashes and 2% of fatalities occurring during snow or sleet weather and 6% of crashes and 4% of fatalities occurring on snow, slush, or ice covered pavement. However, nearly 20% of all state s highway and traffic services budget is spent on snow and ice removal (USDOT b). This shows how much of an emphasis that states place on keeping their roads clears of snow and ice. 1.1 Benefits of this Research The research described within this dissertation will have immediate as well as long-term benefits to practitioners and researchers. This research works describes a plan to solve some of the most challenging problems faced by state DOTs. Many new and emerging technologies are employed to tackle various obstacles faced and to help in maximizing the return on investment for winter maintenance operations. Known algorithms will be applied to new datasets to analyze winter maintenance operations in a unique fashion and new methodologies will be developed throughout this research. 2

15 The immediate benefits include route optimization techniques that may be implemented by ODOT immediately. Additionally, Counties susceptible to depleting their salt supply, as identified in this study, may add temporary salt storage locations. As automated vehicle tracking and reporting become more prevalent in the state, the algorithms developed herein may be implemented. The salt vulnerability results may be used as part of ODOT s long-term facility planning process when deciding on the size of new storage facilities. 1.2 Organization of the Dissertation This dissertation is divided into seven chapters. Chapter I is this introduction to the dissertation. Chapter II provides a background on the projects used to gather much of the data used in this research. Chapter III describes the development of route optimization models to determine the financial impacts of removing county and district borders typically used for winter maintenance operations. Chapter IV describes the benefit of reduced cycle times compared to the increased costs of implementing several types of specialty equipment into a winter maintenance fleet. Chapter V assesses the vulnerability of winter maintenance material storage facilities to depletion using risk analysis. Chapter VI evaluates GPS/AVL sensor failure and calibration requirements as well as the costs associated with the loss of sensor data. Chapter VII presents the conclusions and summarizes the research conducted. 3

16 CHAPTER II BACKGROUND Based on the amount of snowfall received in northern climates and the rising costs of winter maintenance operations for state DOTs, agencies have several options to consider when maintaining roads. Essentially, there are two options available to winter maintenance decision makers: the traditional or standard equipment option or the innovative option. Figure 2.1 shows the options currently available to ODOT and the pros and cons of each selection. 4

17 Winter Maintenance Decisions Traditional Option Innovative Option Pros and Cons of Options Equipment Single or tandem axle truck Front plow, variable width Wing plow Salt spreader with prewet capabilities Epoke hopper Epoke tanker TowPlow Hi-Way Xzalt Epoke and TowPlow are more expensive Innovative equipment requires more training Epoke and TowPlow clear roads faster Operators may perform other tasks if treatment is accomplished more quickly Materials Salt Liquid brine Application equipment Specialty deicers Crushed salt Salt/Deicer blends Specialty deicers are more expensive Specialty deicers last longer and are more durable Innovative option may reduce the amount of treatment required Managerial Tool for Deployment Strategy Figure 2.1. Winter Maintenance Decisions for ODOT The standard options are what ODOT currently uses to maintain roadways, while the innovative option includes equipment and materials that ODOT is evaluating to consider for use within their operations. The negative consequence of the innovative equipment is that it typically costs much more than the traditional equipment. In addition to the 5

18 increased capital costs, when implementing new equipment there is a need for proper training for the users to ensure that a cost savings will be realized. If the equipment is not utilized properly, its full capabilities may not be realized. When using innovative equipment, typically there are fewer units of these types of equipment and materials within a fleet. If an innovative piece of equipment breaks down, this may have a larger impact than if a traditional piece of equipment is no longer useable. Moreover, innovative equipment may only be compatible with a certain truck, and if that truck breaks down, the equipment is no longer able to be used even though it is fully functional. To describe some of the available innovative and traditional equipment, this section will be divided into three sections as shown in Figure 2.1: Traditional and innovative equipment, Traditional and innovative materials, and Managerial tools used as a deployment strategy for the most economic implementation of the available equipment. 2.1 Equipment This section describes the traditional and innovative equipment available to ODOT for winter maintenance operations. In addition to the recent research conducted in conjunction with ODOT, several other research projects have included evaluations of innovative and traditional equipment and material. Table 2.1 presents a summary of evaluations that have been completed. 6

19 Table 2.1. Equipment and Material Evaluations Equipment/Material Evaluated Evaluation Application Findings Reference Equipment Evaluations Epoke Bulk Spreader Evaluated the Epoke hopper and tanker on Interstates in Summit County, Ohio. Determined salt savings and LOS impacts as compared to standard plow truck. Epoke hopper resulted in 12% salt savings per year and the payback period would occur in year eight based on current salt usage and prices. The LOS impacts were similar between the Epoke and standard trucks. Schneider et al., 2013 Viking-Cives TowPlow. Used TowPlow on SR-11, I-90, and US-20 in Ohio. Collected driver feedback. TowPlow was a valuable addition to ODOT s fleet for snow and ice removal. Reduced usage of fuel, labor, and material while still providing adequate LOS. Griesdorn, 2011 Various equipment and techniques used for winter maintenance. Conducted survey with maintenance professionals. Developed a cost benefit toolkit of most widely used techniques and equipment. Veneziano et al.,

20 Equipment/Material Evaluated Evaluation Application Findings Reference Automatic vehicle location (AVL) equipment. Evaluated the cost benefit ratio of a statewide deployment. Using the cost of the system and the annual maintenance cost while quantifying the expected benefits such as timely responses, reduced legal costs, improved efficiency, reduced crashes, etc. Determined expected benefits of using AVL equipment. Meyer and Ahmed, 2003 Zero velocity deicer spreader and salt spreader protocol. Used a visual evaluation of the spreaders to determine if the zero velocity spreader kept salt on roads better than the standard spreaders. Too many other variables, i.e. truck speed, were present to determine if the zero velocity spreader is more beneficial. Visual evaluation is not enough to draw a conclusion. Nantung, 2001 Winter maintenance activities in Utah, which includes labor, material, and equipment. Developed winter maintenance metric to compare the price of winter maintenance to the storm severity and amount of lane kilometers maintained. An effective performance measurement and management system links individual and teamwork behaviors to business goals. Decker et al.,

21 Equipment/Material Evaluated Evaluation Application Findings Reference Epoke models 3500 and Purchased several Epokes and evaluated salt savings compared to standard spreader with dry material. Conducted cost benefit analysis after each winter season. Data shows that Epoke is a costeffective system that pays off in two seasons. The agency equipped their entire fleet with Epoke. Cuyahoga Falls, 2013 (Personal Conversation) Anti-/De-Icing Evaluations Chloride-based ice control products for antiicing and de-icing. Evaluated reports providing information on effectiveness of chloride-based ice control products. Reports include reported savings, reduced crashes, and benefits to motorists. Shi et al., 2013 Fixed anti-icing tracking systems for snow removal and ice control. Monitoring and documentation of system placement and construction, data collection of system operations, both during and subsequent to actual inclement winter conditions. When properly functioning, the system is an impressive winter management tool. Improved road/travel conditions in ice and snow. Hurst and Williams, 2003 Chloride-based deicers, acetate-based deicers, and sanding materials. Conducted literature review of various de-icing and sanding materials and their impacts on health, the environment, performance, and costs. Surveys to determine health impacts. List the different advantages and disadvantages of each deicer tested. Fischel,

22 Equipment/Material Evaluated Evaluation Application Findings Reference Physical pavement modifications to prevent ice bonding by traffic action or other external energy. Investigated the possibility of developing a curved, optimized, cutting edge profile to remove a bonded ice layer from highway pavements. Improved geometry of cutting edge (15º to 30º rake angle) with result in significant energy savings in cutting ice from pavement. Wuori, Traditional Equipment ODOT has several types of traditional equipment within their fleet. The typical truck is either a single or tandem axle dump truck outfitted with a front plow and salt hopper. The front plow is either 11 or 12 feet in length, and the salt hopper is a center mount and applies brine at the point of application of salt from the hopper. An example of a tandem axle dump truck is shown in Figure

23 Figure 2.2. Traditional ODOT Tandem Axle Plow Truck No plow is attached to the truck in Figure 2.2, but the hopper with liquid tanks and the spreader are shown. Figure 2.3 shows two traditional ODOT plow trucks: one with a front plow and the other with a front plow and a wing plow. 11

24 Figure 2.3. Traditional ODOT Plow Truck with Front Plow and Wing Plow The wing plow is mounted to the passenger side of the plow truck and when used, it allows the truck to plow the center line or shoulder in addition to the lane of travel. ODOT often plows with two trucks in this manner, a process referred to as gang plowing (as shown in Figure 2.3), to treat both lanes of the highway in a single pass. During snowfall, ODOT combines plowing with the application of materials to remove ice and snow from the roadways. Due to the rising costs of winter maintenance and the current economic climate, it is imperative for agencies to determine cost saving methods. As a result, many agencies are evaluating techniques that allow them to perform more work while committing fewer resources. One way to accomplish this is to implement innovative equipment that is 12

25 capable of reducing maintenance times, potentially reducing the number of operators required for maintenance activities Innovative Equipment Recently, ODOT has evaluated two types of innovative equipment to aid with snow and ice removal. The first evaluation was of an Epoke, which is a specialty salt spreader and hopper capable of spreading material into three lanes at once and is shown in Figure 2.4. The second evaluation was of a TowPlow, which is a tow behind trailer that is capable of swinging out and plowing a second travel lane, and is shown in Figure 2.8. While both types of equipment cost significantly more than the standard equipment, they have the capability to treat roadways more quickly, providing users with faster travel times. The Epoke Sirius AST Combi S4902, the spreader utilized for evaluation by ODOT, is capable of spreading dry material, liquid, or both in combination over multiple lanes. An image of the spreader as installed on an ODOT truck is shown in Figure

26 Figure 2.4. Epoke Sirius AST Combi S4902 Spreader The grey tanks on the Epoke are used for storing liquid material, which for ODOT is typically brine, while the orange hopper stores the salt. The Epoke is placed on a tandem axle hook lift truck equipped with a front plow. The concept of the Epoke system, which was developed in the 1950s, is to crush salt into fine grains and apply a liquid that allows it to stick to the road. The salt is loaded into the hopper as with a typical ODOT plow truck. Within the hopper is an agitator used to keep the material loose so that it will flow down into a roller, which crushes the salt into a powder. After the material is crushed, it falls onto a conveyor belt, where it is metered and fed into the salt spreader. The Epoke is equipped with tanks for storing liquids, which feed into the liquid spray nozzles. When the salt is spread, it is either covered with liquid to create a material with a paste-like consistency or it may be pre-wetted, where 30% by weight of the salt is replaced with liquid. By mixing the salt with liquid, the amount of 14

27 salt applied may be reduced. Figure 2.5 presents a diagram that shows the process taking place in the Epoke. Note: This figure is provided by Epoke and All spreaders refers to all spreaders that are a part of the Epoke product line. Figure 2.5. Diagram of Epoke System Process The Epoke process crushes the salt at the roller and drops it onto the conveyor belt, which delivers the salt to the spreader. Figure 6 shows photographs of the crushed salt that is spread by the Epoke and the standard salt found in an ODOT stockpile. 15

28 Figure 2.6. Salt Consistency after Crushing by Epoke (left) and Standard Salt used by ODOT (right) Figure 2.6 shows the difference in the consistency of salt from the Epoke and the stockpile. After the salt travels through the Epoke and is dispensed, it is finer and consists of smaller grains than the salt dispensed by the standard truck. The finer consistency reduces the amount of bounce and scatter, so that more salt remains on the roadway. However, by reducing the particle size, the salt may also be absorbed more quickly and stay on the roadway for a shorter period of time. The Epoke is also capable of spreading material over multiple lanes. It will spread up to three lanes and may be adjusted to spray behind, to the left, or to the right of the truck. Figure 2.7 shows an image of the spreader on the rear of the Epoke with the liquid nozzles and salt spreader. 16

29 Liquid Nozzles Dry Material Spreader Figure 2.7. Dry Material Spreader and Liquid Nozzles on an Epoke When selecting to spray material to the left or right, the material is also being spread in the lane the truck is traveling. An onboard display for the Epoke reports the application rates of salt and liquid in metric units. The application rate for the dry material is reported in grams per meter-squared (g/m 2 ), while the liquid rates are reported in milliliters per meter-squared (ml/m 2 ). These values are easily converted to pounds per lane mile (lbs/ln-ml) and gallons per lane mile (gal/ln-ml) for the dry and liquid application rates, respectively. The second type of innovative equipment analyzed by ODOT is the Viking-Cives TowPlow. The concept of the TowPlow is to swing the trailer out into the second travel 17

30 lane to maintain two lanes at once. An image of the fully deployed TowPlow is shown in Figure 2.8. Figure 2.8. Fully Deployed TowPlow The TowPlow is a tow behind trailer unit equipped with a 24 foot snow plow and either a salt hopper or a brine tank. The trailer is capable of rotating out to any angle up to 30 degrees, allowing the plow the ability to clear a second travel lane when used in combination with a front plow. Additional general specifications suggest the TowPlow is capable of operating at 55 mph and requires a 90,000 pound pintle hook, one double and one single acting hydraulic remote, a 7-wire trailer plug with ABS, a 6-wire trailer plug for plow lights, a standard trailer air package, and two tow eyes for the vehicle towing the TowPlow (Viking-Cives Group, 2009). A picture of the TowPlow partially deployed is shown in Figure

31 Figure 2.9. Partially Deployed TowPlow The TowPlow does not have to be swung fully out to be used. This figure shows the TowPlow partially swung out to plow a narrow shoulder with a guardrail. To control the TowPlow and the regular plow separately, two hydraulic controllers must be installed in the truck. Figure 2.10 shows the two controllers installed inside the cab of the TowPlow truck. Figure Hydraulic Controllers for TowPlow 19

32 While it is possible to operate the TowPlow and truck salt spreader with one controller, the negative of doing so is that the salt spreader on the TowPlow and the truck are linked to the same controls. This means that any time the spreading option is activated, both spreaders will turn on. The downside of this is that the spreader on the TowPlow will be used when the trailer is directly behind the truck. One main advantage of the TowPlow may be found by comparing the ability to treat two lanes in a single pass to the configuration presented in Figure 2.3, where two trucks are required. By using the TowPlow, one truck and operator are capable of maintaining both lanes while the second truck and operator are free to focus on maintaining another area. Several types of innovative equipment that ODOT is currently using or evaluating have been presented in this section. In addition to these types of equipment, there are several other types of innovative equipment available. The Hi-Way Xzalt is similar to the Epoke in that it spreads material over multiple lanes. Some of these types of innovative equipment may be used in conjunction with innovative materials, which presents an opportunity for greater cost savings. 2.2 Materials This section describes the traditional and innovative materials available to ODOT for winter maintenance operations Traditional Materials The traditional materials used by ODOT for winter maintenance include salt and brine. ODOT places salt out to bid every year, and the county average for all 88 counties was $38.77 in fiscal year 2014 (ODOT, 2014). However, at the end of last season, those 20

33 prices rose to nearly $100/ton due to diminishing supplies during the harsh winter. With prices on the rise, it becomes more prudent to evaluate innovative materials and equipment. In the past, traditional rock salt was applied as a dry material, and much of the material bounced off of the roadway. This resulted in wasted material and detrimental effects to the surrounding environment. To help limit the amount of salt that bounced off roadways, new products were developed. One such product was a zero velocity spreader, which spreads salt at the rate equivalent to the velocity that the truck is traveling. This is done to lay the salt straight down onto the road rather than spreading it at the speed the truck is moving. These spreaders were short lived, as they were found to be ineffective. After agencies moved on from evaluating different types of spreaders, they began to use more liquid materials. These include a brine solution produced in-house by ODOT that is 23% salt. By prewetting salt with brine, the amount of salt applied is reduced. Additionally, when salt is applied with brine, it does not bounce and scatter as much as pure rock salt. In addition, by prewetting the salt, it activates faster and begins melting snow sooner after application than rock salt. When using prewet salt, most agencies use a lower application rate than they would for dry material, further reducing the amount of salt required for treating a route Innovative Materials In response to the rising salt prices, ODOT has evaluated innovative deicing chemicals. Deicers have become more popular in recent years, as they may be used by themselves in lighter snowfall events, or in concert with plowing. There are a plethora of liquid deicers 21

34 commercially available, and many of the new deicers to come on the market are byproducts of an unrelated process such as oil refining, food manufacturing, and the manufacturing of agricultural products. Determining which deicers will have minimal environmental impact, low corrosiveness, high melting capacity, high longevity and will be compatible with ODOT s existing equipment and materials is an intensive process. The innovative deicers are more expensive than salt and brine, but they present several benefits including increased effectiveness and longevity. Similar to the innovative equipment, the goal of using innovative materials is to reduce the overall costs of winter maintenance operations. Since they have greater longevity and effectiveness, use of innovative materials may result in fewer treatments, which allows for operators to accomplish other tasks or for an agency to reduce the man-hours required for winter maintenance operations. 2.3 Conclusions This chapter provided a brief overview of some of the data that will be utilized in this research as well as a literature review. Generally, the costs for winter maintenance are increasing while agencies are attempting to reduce their budgets. There are several options available to aide with reducing these costs including innovative equipment and materials. However, studies must be conducted to determine the cost effectiveness of implementing thse as well as determining where and when the innovative equipment and materials should be implemented. This research work will address some of the pertinent issues facing agencies. A more in-depth literature review is included with each chapter as it pertains to the specific research undertaken. 22

35 CHAPTER III QUANTIFYING THE FINANCIAL IMPACTS OF MAINTENANCE ZONES FOR SNOW PLOWS 3.1 Introduction In cold weather climates, snow removal is paramount to the efficient transportation of goods and people. The combination of plowing and material application is the most common method utilized for snow removal. In the United States, state and local agencies are typically responsible for winter road maintenance, and the associated costs total more than $2.3 billion annually (FHWA, 2013). This represents a significant investment made by these transportation agencies to reduce the number of vehicle crashes and increase mobility on the nation s roadways during winter events. In the current economic climate, agencies are attempting to implement processes and procedures to reduce expenditures whenever possible. One such avenue that agencies are considering for reducing expenditures is the evaluation of routes for plow trucks conducting snow and ice removal. Larger state agencies are 23

36 generally divided into districts and counties, which are responsible for the maintenance operations within their jurisdictions. As a result of the separation of responsibilities, the snow and ice routes typically end at the county or district border, which may not be the most efficient route for every truck. This research determines the cost savings that would be realized for the State of Ohio if the county and district border restrictions were removed for the snow plow maintenance routes defined by the Ohio Department of Transportation (ODOT). The optimization of snow plowing routes and vehicle fleets has become a topic of interest for agencies in recent years and, as a result, many route optimization models have been developed. Several types of models have been developed to predict costs of snow and ice removal and to allocate the available resources of an agency (Duaas et al., 1994; Adams et al., 2006). One method commonly used for optimizing routes is arc routing, which is defined as a network of interconnected routes with each having an associated service time. The objective of route optimization is to divide the links into areas with similar service times (Bodin and Levy, 1991; Salazar-Aguilar et al., 2012; Marks and Striker, 1971). Another common method for solving route optimization problems is known as the traveling salesperson problem (TSP), in which a road network is dived into arcs that connect to nodes. Input parameters are used for vehicle properties, roadway and network properties, and various costs such as travel times or distance traveled (Gupta et al., 2011). In addition to optimizing the snow plow routes, several studies have looked into optimal fleet sizing and the ideal location of salt storage depots (Kandula and Wright, 1995; Kandula and Wright, 1997). Perrier et al. conducted a comprehensive four-part survey of route optimization methods and algorithms covering a wide variety of winter 24

37 maintenance topics including vehicle routing, fleet sizing, and depot locations (Perrier et al., 2006a; Perrier et al., 2006b; Perrier et al., 2007a; Perrier et al., 2007b). With advances in computing power, researchers began to develop more complex models that considered a larger number of factors in the route optimization model. Accordingly, researchers have evaluated snow plow routing problems with multiple depots and time windows, in which the problem routes the snow plows from a start depot, covers every route once, and returns to the same depot, essentially simulating one cycle of a plow truck (Golbaharan, 2001; Razmara, 2004; Sochor and Yu, 2004). Recently, research has evolved to consider priority routing, which includes the fact that the travel time on plowed streets is shorter than on unplowed streets (Dussault et al., 2013). Other researchers have developed models that utilize real-time data to optimize vehicle dispatch schedules and winter maintenance operations (Fu et al., 2009). Research has been carried out to determine the sustainability of winter road maintenance by identifying areas of improvement by optimizing routes and fleets (Gudac et al., 2014). Work has been conducted in the realm of simulating maintenance routes for snow plow trucks in order to aid transportation planners, resulting in more efficient routes and in turn reducing the operating costs for agencies (Rao et al., 2011; Xie et al., 2013). The majority of the route optimization work completed to date has been conducted over a small area, such as the maintenance routes for a city, rather than for a large geographical area that includes hundreds of depots and thousands of lane miles. 25

38 3.2. Methodology This methodology is divided into two subsections which describe the study area utilized and the route optimization process undertaken Ohio Department of Transportation Study Area Typically, route optimization is conducted using complex algorithms and matrix mathematics. These methods are suitable for small-scale route optimization, such as city maintenance routes. For the purposes of this research, which is conducted for the entire state of Ohio, the route optimization is conducted using the ArcGIS software platform. ArcGIS has an extension designed to determine the optimal routing for discrete locations, which is modified to work with continuous routing needed for snow plows. The program uses the Dijkstra algorithm to determine the shortest path of the network and a tabu search meta-heuristic as the vehicle routing problem-solving method; the program provides results comparable to or better than other optimization methods (Karadimas et al., 2008; Zsigraiova et al., 2013). By using this software platform, it is possible to conduct route optimization for a large number of trucks covering a vast geographical area, and the results may be easily incorporated into ODOT s extensive GIS database. ODOT is responsible for maintaining over 43,000 lane-miles of road, employing a fleet of 1,700 trucks and a total of 200 maintenance facilities (ODOT, 2011). Maintenance operations are the responsibility of each county garage, with snow plow trucks typically stopping at the county borders. Figure 3.1 shows the routes that ODOT is responsible for maintaining and the location of all ODOT facilities within the state. 26

39 Figure 3.1. Snow Plow Routes and Facility Locations Maintained by ODOT ODOT divides the state into 12 districts, and these districts are responsible for maintaining the interstates, US routes and state routes within their jurisdictions. ODOT has several maintenance garages within each of Ohio s 88 counties; some of the garages have trucks based out of the location, while other garages only consist of a salt storage facility. Since ODOT is a single organization, it is feasible to optimize the routes without restrictions for the 88 counties and 12 ODOT districts in order to determine the resulting cost savings, if any Route Optimization Model Development Initially, a road network relevant to the study area needs to be set up. In this case, a national road network with every level of road defined is trimmed for the state of Ohio. 27

40 Once the roads are input, a network dataset is created and the road network is transformed into edges with elevation differences applied; these elevation differences allow the model to distinguish between intersections and overpasses. The network dataset determines the length of each edge and calculates a travel time based on the length and speed limit associated with each edge. Network attributes used in the route optimization are added to indicate road hierarchy, one-way restrictions, and any cost attributes that are associated with a route (such as travel time and distance). The next step of the model is to begin the vehicle routing problem, which includes inputting the facility locations and setting up the truck routes. The plowing locations must be input for the entire state, and successive locations are input on roadways to route the snow plow trucks along the roads. These locations allow a simulation of the delivery of salt to each point on the route, and the amount of salt delivered is calculated from the desired application rate, length of the route, and number of lanes. This information provides the model with the capability to account for diminishing loads, and the model will route a truck to a salt depot before the truck exceeds its capacity to apply material; a delay is applied at the depot to account for the time required to reload the truck with material. When inputting the routes to the model, a start and finish depot must be defined for each route, as well as the depots each truck is allowed to visit for refilling. The model is capable of incorporating route zones, applying restrictions to cause the routes to remain within a user-defined area. For the purposes of this analysis, a route zone is created for each route that follows the border of the county in which the truck is based. This feature allows the model to be run in two stages: the first with no border restrictions and the 28

41 second with the trucks restricted so that they will remain in the county in which they are based Cost Analysis Methodology After the vehicle routing problem is created, it is solved to optimize the routes based on travel time, travel distance, and the material capacity of the trucks. The output includes the optimized routes for every truck or garage input as well as specific information such as the travel time and distance. The difference in the travel time and distance between the models with county border restrictions (the closed model) and without restrictions (the open model) will be used to determine the cost savings associated with opening the county borders for winter maintenance purposes. The resulting savings are related to the time and distance differences between the two models. The time savings includes the wages paid to operators while the distance savings includes the fuel costs and fuel efficiency of the trucks. The time savings may be determined using Equation (3.1): C Time,i = Time,i αc d (3.1) where C Time,i is the dollar value of the time savings at the i th county, Δ Time,i is the difference in total cycle time between the open and closed border models, α is a conversion factor equal to 1/60, and C d is the hourly wages paid to operators. The distance savings may be formulated as follows: 29

42 C Dist,i = Dist,i C f E f (3.2) where C Dist,i is the dollar value of the distance savings as the i th county, Δ Dist,i is the difference in total distance traveled between the open and closed border models, C f is the cost of fuel, and E f is the fuel efficiency of the snow plow trucks. These savings correspond to one cycle of winter maintenance operations. Typically, operators will treat their assigned maintenance area multiple times during a winter storm event. To capture the total annual savings of optimizing the snow plow routes without border restrictions the following equation is developed: C ann,i = S tot,i L (C Time,i + C Dist,i ) (3.3) where S tot,i is the total number of snow events and L is the number of treatment cycles per event in the i th county. The resulting savings will correspond to the annual savings that are expected for relaxing the county border restrictions. There is uncertainty associated with each of the variables included in the cost savings analysis. As a result, the research team has collected several years of data on the hourly wages, fuel costs, fuel efficiency, number of cycles per event and the number of events per year for winter maintenance in Ohio. The average and standard deviation of each variable are presented in Table

43 Table 3.1. Average and Standard Deviation for Cost Analysis Variables Variable Symbol Average Standard Deviation Hourly Wages ($) C d Fuel Cost ($/gallon) C f Fuel Efficiency E f (miles/gallon) Cycles per Event L 3 1 Events per Year * S tot 39 8 Note: * The statewide values are presented in this table; actual values for each district are used in the analyses. The number of winter events per year varies throughout the state of Ohio. The statewide average and standard deviation are shown here and will be used in the final cost analysis, while the values for each district are used accordingly in the individual analyses. To include the variability of the field data in the cost analysis, the average and standard deviation of each variable will be included, and the cost savings will be estimated using Monte Carlo simulations. By modeling the cost analysis in this manner, the uncertainty will be captured and a more accurate average cost savings will be determined. 3.3 Results and Discussion The route optimization models were run in two scenarios, one with county border restrictions in place (the closed model) and one without county border restrictions (the open model). The resulting time and distance differences between the two models are analyzed to determine the cost savings associated with optimizing the maintenance routes with no county border restrictions. It should be noted that when the county border restrictions are implemented, the trucks are permitted to drive beyond the border when adequate turn-around locations are not available within the county. Since the trucks used 31

44 for winter maintenance are large snowplows, U-turns are not possible in most cases, and the operators will typically use intersections or crossovers on divided highways to turn around the trucks Route Optimization Route optimization was conducted for all ODOT maintenance garages. This included the optimization of truck maintenance routes originating at 160 locations (which represent the garages at which trucks are stored) and over 22,000 delivery locations (which were created to route the trucks and to account for salt application during maintenance operations). Part of the model output includes the total time and distance for each route. The total time and distance of the routes are summed for each county for the open and closed county border restriction models. The total time and distance are calculated from the time and point the truck leaves the garage until it returns, and this includes deadheading, which is the time and distance the truck travels while not maintaining its routes (such as travel to/from the maintenance area or a salt storage facility). Generally, as the number of lane miles maintained increases, the total maintenance time increases. The districts with a high number of lane miles and low total maintenance times have a higher number of garages, which results from the trucks being based closer to the areas they are treating. Conversely, districts with high total maintenance times typically have trucks that need to travel a greater distance from their garages to their assigned maintenance areas. 32

45 3.3.2 Cost Analysis Using the results of the route optimization and Equations (3.1) to (3.3), the cost savings are determined for each district and for the entire state. The time and distance differences, number of events, and cost savings are shown in Table 3.2. Table 3.2. Time and Distance Differences, Number of Events, and Cost Savings Difference due to Opening Borders Number of Events District Time (minutes) Distance (miles) Average Standard Deviation Lane Miles Maintained Annual Savings 1 2, ,301 $ 152, ,260 $ 38, , ,918 $ 11, ,628 $ 106, ,952 $ 57, , ,174 $ 114, , ,626 $ 135, ,846 $ 19, , ,667 $ 59, ,994 $ 23, ,179 $ 43, , ,118 $ 76, Statewide 13, ,663 $ 838, Note: The number of events in each district is found by using data from 56 weather stations in Ohio that are maintained by the National Oceanic and Atmospheric Administration. The total savings for the various ODOT districts ranges from $11,392 (in District 3) to $152,220 (in District 1) with an average of $69,900. The total savings ODOT would realize by removing the county and district border restrictions is $838,802 annually. These savings are attributed to the reduced time and distance required to complete the maintenance activities. Removing county border restrictions will result in decreased 33

46 winter maintenance expenditures and increased time for employees to conduct other work. This is a rather large cost savings that does not require the purchase of additional equipment or a reduction in staffing levels. In addition to determining the average cost savings for each district, it is important to know what factors influence the potential cost savings. Correlation coefficients may be determined for two variables using the Pearson s correlation coefficient (Mudelsee, 2003). The Pearson s correlation coefficient describes the relationship between two variables and rates them as strong, moderate, or weak based on the absolute value of the correlation. A correlation greater than 0.5 is considered a strong correlation, 0.3 to 0.5 is considered to be a moderate correlation, and less than 0.3 is considered to be a weak correlation (Cohen, 1988). Since not every ODOT district has the same number of counties, the savings per county is compared to several factors to determine which factors have an influence on the cost savings. Table 3.3 presents the correlation coefficients and the strengths of correlation for several variables to determine which are correlated to the annual cost savings per county. Table 3.3. Correlation Coefficients for Parameters Related to Annual Savings Parameters Pearson s Correlation Strength Time Savings per County 0.43 Moderate Distance Savings per County 0.33 Moderate Events Savings per County 0.59 Strong Percent Urban * Savings per County 0.35 Moderate Lane Miles Savings per County Strong Lane Miles per Truck Savings per County Moderate Note: * The Percent Urban parameter is based on the United States Office of Management and Budget definition of metropolitan counties. 34

47 The savings per county is used in this comparison to control for the number of counties in each of ODOT s 12 districts, since the districts vary in size. A moderate correlation is found to exist between the savings per county and the time and distance differences between the open and closed route optimization models. The time difference has a slightly greater correlation than the distance traveled differences, indicating that larger benefits are obtained from reducing the amount of time committed to maintenance operations rather than reducing the distance traveled by the plow trucks. A strong correlation exists between the number of snowfall events and the savings per county, indicating that areas receiving more snowfall are likely to see a greater annual savings. In addition to evaluating the influences of the differences between the models and the weather, some tangible attributes of the districts are evaluated to determine their influence on the cost savings. The percentage of each district that is considered by the United States Office of Management and Budget as an urban area is found to have a moderate correlation with the savings per county. The number of lane miles maintained has a strong correlation, albeit a negative one, meaning that the savings decreases as the number of lane miles increase. This negative correlation is likely a result of the truck being required to travel a longer distance without treating to reach the maintenance area when the number of lane miles in rural areas of a county is greater. In urban areas, highways may consist of multiple lanes in each direction, resulting in trucks having to travel greater distances when treating the additional lanes and with no possibility of shortening the total distance traveled. Since the number of trucks also varies between the garages in each county, the lane miles maintained per truck is compared to the savings 35

48 per county, and a moderate correlation was found. Similar to the total lane miles, the lane miles maintained per truck has a negative correlation. 3.4 Conclusions Currently, ODOT divides their maintenance areas into countywide subgroups, and winter maintenance activities stop at the county borders. Since ODOT is a single organization, it is feasible to consider removing the county border restrictions of the maintenance garages in each ODOT district. This research work quantifies the cost savings that result from removing the county border restrictions by developing two route optimization models, one with the county border restrictions and one without. The cost savings are related to the difference in time and distance traveled. The savings come from reducing the operator s time working on the route and the reduced amount of fuel used. Data are collected over several years, and Monte Carlo simulations are used to determine an annual savings associated with the removal of the county border restrictions. The total travel time and distance are grouped for each of ODOT s 12 maintenance districts to determine the cost savings for each. It was found that by removing the county border restrictions, the districts would realize a savings of $11,392 to $152,220 (with an average of $69,900). The total savings ODOT would realize by removing the county border restrictions throughout the entire state is $838,802 annually. The savings per county are compared to several factors to determine what factors influence the cost savings. The number of snowfall events in a winter season is found to be strongly correlated with the savings, indicating that areas receiving more snowfall events are likely to realize greater savings. Additionally, the lane miles maintained is strongly correlated to the savings per county, but the correlation is negative. This negative 36

49 correlation is likely influenced by different factors in urban and rural areas. In rural areas, as the number of lane miles maintained increases, the trucks are required to travel farther to reach the maintenance area. In urban areas, highways may consist of multiple lanes that require multiple passes, resulting in the trucks traveling greater distances with no possibility of shortening the total distance traveled. The labor cost savings found by opening the county borders will not be refunded to ODOT, but rather will provide additional time where employees are able to perform other tasks. Also, by decreasing the amount of time each maintenance cycle takes, the roads may be cleared of snow more quickly, resulting in better driving conditions for the motoring public. By decreasing the distance traveled, fuel costs will be lowered. Additionally, the maintenance costs and corrosion damage to trucks may decrease due to fewer miles being traveled. In addition to the immediate cost savings, there is the potential for an increase in the life span for winter maintenance equipment. 37

50 CHAPTER IV WINTER MAINTENANCE FLEET SAVINGS FROM IMPLEMENTING SPECIALTY WINTER MAINTENANCE EQUIPMENT 4.1 Introduction With the rising costs of winter maintenance, agencies are evaluating specialty equipment, optimizing routes, and developing innovative methods to analyze the benefits of equipment and materials by taking advantage of the increased prevalence of GPS/AVL technology. The general goal of transportation agencies is to increase the efficiency of maintenance operations, while decreasing their overall costs. As a result of the increased demands on the transportation system and the increased winter maintenance costs, much research has focused on improving the efficiency of winter maintenance fleets. Some research has focused on assessing the benefits and level of service provided by winter maintenance operations. A recent study evaluated the benefits and costs of weather information for winter road maintenance and found that winter maintenance costs could be reduced by improving the accuracy of weather prediction information (Ye 38

51 et al., 2009). Researchers have developed speed recovery durations for the length of time required to return vehicle speeds to a baseline condition after a winter event (Lee and Ran, 2004). Carmichael et al. (2004) developed a weather index to estimate winter severity, and when combined with measures of transportation department infrastructure, the authors estimated the expenses that correlated with reported costs more accurately than other models (Carmichael et al., 2004). Recently, many agencies, including the Ohio Department of Transportation (ODOT), have been evaluating specialty equipment such as specialty hoppers capable of spreading material in up to three lanes and specialty plows capable of plowing two lanes in a single pass (Schneider et al., 2013; Schneider et al., 2014). The specialty hopper, as shown in Figure 4.1 (left), reduces the salt usage but increases the amount of liquid applied. Specifically for this hopper, the salt is crushed into fine grains and liquid is added to reduce bounce and scatter compared to rock salt. Additionally, the unit tested by ODOT was capable of spreading material directly behind the truck, on either side of the truck or on both side of the truck. This allows the specialty hopper to treat up to three lanes in a single pass. The specialty plow, as shown in Figure 4.1 (right), is a tow behind trailer that can swing out a plow a second lane in a single pass. The trailer also includes the possibility to apply dry and liquid material so that two lanes may be plowed and treated simultaneously. 39

52 Figure 4.1: Specialty Hopper (left) and Specialty Plow (right) While the material reduction and efficiency benefits of both types of specialty equipment are apparent, the impacts on an entire fleet and the cost benefit need to be evaluated quantitatively. Determining where to implement the specialty equipment is a difficult task faced by winter maintenance personnel, and this research will aid with determining the efficiency increases and cost savings of specialty winter maintenance equipment. This research evaluates the efficiency benefits and cost increases of implementing specialty winter maintenance equipment using reliability analysis and robust cost estimation. This research work determines the fleet savings associated with implementing specialty winter maintenance equipment by evaluating the route changes obtained from route optimization, the probability of exceeding a given cycle time through reliability analysis, and cost-benefit considering uncertainties. When implementing specialty equipment to increase efficiency in winter maintenance operations, the routes maintained should be evaluated before and after the implementation. This is because the specialty equipment is capable of maintaining a larger number of lane miles than the standard plow truck. Determining the increase in lane miles is necessary to estimate the cost savings of the specialty equipment. To determine the routes maintained, one can use snow plow route optimization, which has 40

53 become a topic of interest for many agencies in recent years. A common method for optimizing routes is known as arc routing, where a network of routes are divided into areas with similar service times (Bodin and Levy, 1991; Salazar-Aguilar et al., 2012; Marks and Striker, 1971). Another common route optimization method is known as the traveling salesperson problem where a road network is divided into arcs and nodes and the input parameters include the types of vehicles, roadway attributes, and cost functions (such as travel time and distance) (Gupta et al., 2011). Perrier et al. (2006a; 2006b; 2007a; 2007b) conducted a comprehensive four part survey of route optimization methods and algorithms for vehicle routing, fleet sizing, and depot locations. Several researchers (Golbaharan, 2001; Razmara, 2004; Sochor and Yu, 2004) have evaluated snow plow routing problems with multiple depots and time windows, in which the problem routes snow plows from a start depot, covers every route once, and returns to the same depot, or essentially simulating one cycle of a plow truck. ODOT sets a cycle time of 120 minutes for every truck in their fleet. This means that when a vehicle leaves the garage, it should be able to maintain the assigned route and return to the garage within two hours. Having a cycle time of two hours allows ODOT to know that a road segment will be treated roughly every two hours during a snow event. Depending on the severity of snowfall and type of treatment performed, snowfall may not accumulate on the road. The principle of setting a cycle time is to diminish the impacts of snowfall on traffic, such as vehicle delay. With the consideration of uncertainties, one of the methods to quantitatively assess the benefits of incorporating the specialty equipment on the maintenance fleet is to evaluate the probability of exceeding a certain cycle time (or failure probability). Specifically, considering the probability of one truck exceeding a 41

54 cycle time as a component failure, two types of system failure are assessed: parallel system failure and series system failure. Particularly, we will compare four cases: no implementation of specialty equipment, implementing one specialty hopper, implementing one specialty plow, and implementing one specialty hopper and plow. In addition, the efficiency increases that specialty equipment have on a fleet of vehicles is also determined using cost analysis, where the equipment purchase costs and the operation costs are considered. Since the purchase price for special equipment is higher, the cost-benefit curves are developed and the break-even time when the extra initial cost is paid off due to the lower operational costs is determined. 4.2 Research Objective With the rising costs of winter maintenance and the availability of specialty equipment, this research aims to quantify the benefits associated with adding a specialty hopper or specialty plow to a fleet of winter maintenance vehicles. The benefit to the fleet is a result of the reduced treatment time and total lane miles traveled by the fleet when including the specialty equipment. Such benefit will be quantified based on the lane mile changes from the route optimization, the probability of exceeding a given cycle time using reliability analysis with the use of data obtained from route optimization and ODOT operations, and the calculated cost benefit considering uncertainties. The failure probability and cost benefit analysis will aid agencies with determining whether or not they should implement specialty equipment. 42

55 4.3 Study Area The analysis in this study is conducted for three regions within the state of Ohio based on the amount of snowfall received and the number of snowfall events occurring annually. The average annual snowfall in the state of Ohio is shown in Figure 4.2, where the black thick boarders define Districts 1 to 12. Three regions are defined based on the total annual snowfall, Region I includes ODOT Districts 3, 4, and 12; Region II includes Districts 1, 2, 5, 6, 7, and 11; and Region III includes Districts 8, 9, and 10. Figure 3 shows the number of snowfall events each winter for these three regions. The classification of snowfall events is: light snowfall (less than two inches for the storm), moderate (between two and six inches for the storm), and heavy (greater than or equal to six inches for the storm. 43

56 Figure 4.2. Ohio Average Annual Snowfall The average and standard deviation for the number of snowfall events in each region were determined using 56 National Oceanic and Atmospheric Administration weather stations in Ohio. The weather data used are from 2009 to 2014 in most cases; however, some stations have data beginning in The number of events for each severity decrease as the total annual snowfall decreases from region to region as shown in Figure 4.3, providing further justification for categorizing the ODOT districts into three regions. 44

57 Region I Region II Region III μ = 40 μ = 34 σ = 4.9 μ = 26 σ = 4.2 μ = 6.3 σ = 1.8 (a) Light Snowfall μ = 4.1 σ = 1 μ = 3.2 σ = 0.69 μ = 1.5 σ = 0.54 (b) Moderate Snowfall μ = 0.95 μ = 0.3 (c) Heavy Snowfall Figure 4.3. Distribution of Events in Each Region for (a) Light, (b) Moderate, and (c) Heavy Snowfall 4.4 Methodology The methodology for this chapter is divided into three subsections to describe the changes in lane miles maintained, cycle time failure probability, and cost analysis. 45

58 4.4.1 Change in Lane Miles Maintained To evaluate the benefit of implementing the specialty equipment on the winter maintenance fleet, one can examine the changes in the snow plow routes (or lane miles maintained) before and after the implementation. In order to deal with the large optimization area and number of trucks included, the route optimization in this study is conducted using ArcGIS to expedite the process rather than traditional algorithms, which also allows the results to be implemented into ODOT s GIS department. ArcGIS uses the Dijkstra algorithm to determine the shortest path of the network and Tabu Search metaheuristic as the vehicle routing problem solving method and provides results comparable to or better than other optimization methods (Karadimas et al., 2008; Zsigraiova et al., 2013). Note that the optimization is conducted for each region and each truck in the state is used in the optimization analysis. The development of the route optimization begins with the preparation of layers for the map of the state of Ohio. Once a road layer for Ohio is input, a network analyst dataset is created to define the roadway edges to capture elevation differences. Network attributes in the road layer may include road hierarchy (freeway, arterial, collector, or local road), direction of travel (two-way vs. one-way roads), cost attributes (such as travel time), and distance. With the network attributes being defined, travel times may be calculated based on the length and the speed limit for each road segment. The cost attributes for each segment are minimized in order to find the most efficient route for each vehicle. The next step in the route optimization is to create the vehicle routing problem. The outposts and salt storage locations are input, as each truck will be assigned to start from and return to an outpost, and it is permitted to refill at any salt storage location in the 46

59 maintenance area. Several successive plowing locations are input on roadways to route the snow plow trucks along the roads. These locations allow salt application to each point, and the amount of salt is based on the application rate input (such as 200 or 300 pounds per lane mile). This provides the model with the capability to account for diminishing salt loads: the model will automatically route a truck to a salt depot before it exceeds its capacity to apply material, and a delay is applied at the depot to account for the time required to reload a truck with material. After the vehicle routing problem is created, it may be solved, at which time the program balances the routes based on travel times, distance traveled, and capacities of all the trucks The standard trucks are equipped with a front plow and single lane spreader and are implemented with a material capacity of 5 tons and a two hour maximum cycle time. The specialty hopper is implemented with a 6.5 ton material capacity and the maximum cycle time is 1.25 times greater than the standard truck when applying material only, which was found to be the equivalency of the standard trucks to specialty hopper (Schneider et al., 2013). The specialty hopper is implemented with a 10 ton capacity and a maximum cycle time 1.7 times greater than the standard truck, which was found to be the equivalency of standard trucks to specialty plow (Schneider et al., 2014). When the specialty equipment is implemented in the route optimization model, either one specialty hopper or specialty plow is added at a time. This is done for each garage to capture the effects the individual piece of specialty equipment has on the remainder of the fleet. A route optimization model is developed including each of ODOT s maintenance trucks. Models are developed with all standard trucks, one specialty hopper at each garage, and one specialty plow at each garage. The model results are examined for each region. For 47

60 each iteration of the route optimization model, the lane miles are recorded for every truck, resulting in a range of values for each truck type. The lane miles are different in each region due to the different configurations of equipment in the garages as well as the different characteristics of the maintenance areas including lane miles and roadway functional class. The lane miles maintained by each type of equipment in each region of Ohio are shown in Table 4.1. The amount of lane miles maintained by the standard equipment decreases after specialty equipment is implemented due to the increased treatment capabilities of the specialty equipment. Table 4.1. Lane Miles Maintained before and after Specialty Equipment are Implemented Before Implementation After Implementation Region I Region II Region III Equipment μ σ μ σ μ σ Standard Standard Specialty Hopper Specialty Plow Cycle Time Failure Probability Winter maintenance routes are often measured using the cycle time, or time to travel from the garage, maintain an area and return to the garage. By setting a maximum cycle time, agencies will control the amount of time it has been since a road segment has been treated. ODOT sets a maximum cycle time of 120 minutes, per discussions with ODOT management. This may not be attainable in every area based on the lane miles maintained and the distance from the garage to the maintenance routes. Specialty equipment allows for the treatment of multiple lanes in a single pass, which may reduce the probability of 48

61 exceeding 120 minutes per cycle. The probability of a truck exceeding the cycle time, P f,j, can be defined as follows: P f,j = P(g j [C D j ] 0) (4.1) where, j refers to the type of equipment and j = 1, 2, and 3 are for the standard truck, specialty hopper and specialty plow, respectively, g( ) is the limit state function, C is the target cycle time that is 120 minutes, and D j is the demand corresponding to the lane miles maintained and the speed of the truck. The limit state function is defined as follows in this study: g C D j j (1) where g j ( ) 0 refers to the failure domain. The demand is estimated as follows: D j = L j V j (3) where, L j is the number of lane miles maintained that can be found in Table 4.1, V j is the average speed (per minute) while maintaining, which is determined using data collected in the field and its value is shown in Table 4.2. Both parameters L j and V j are treated as random variable with normal distributions to consider the uncertainties in the distance maintained and travel speed. There are multiple trucks based out of each garage. Accordingly, the performance of each garage may be evaluated using two methods based on failure probability. One method is to consider the garage fails to meet the cycle time requirement if any truck in the garage exceeds the 120 minute cycle time. Thus, the failure probability of the garage is formulated as follows: 49

62 3 P f,s1 = 1 (1 P f,j ) N j j=1 (4.4) where, N j is the amount of equipment of j th type. The other failure method is to consider the garage fails to meet the cycle time requirement if the summation of the time used by all the trucks in the garage exceeds the total cycle time. The total cycle time is found by multiplying 120 minutes and the total number of trucks in the garage. Thus, the second way to evaluate the failure probability of the garage is formulated as follows: 3 3 P f,s2 = P (C N j N j D j 0) (4.5) j=1 j=1 where, all parameters are defined as above Cost Analysis The total cost of a garage includes the equipment purchase costs and the operating expenses. Thus, the cost benefit of using specialty equipment can be determined using the following equation: C B,j = (C T+H,1 C T+H,j ) + (C op,1 C op,j ) ( 1 e zn ) (4.6) z where, C B,j is the benefit cost for using j th type equipment (j = 2 or 3), C T+H,1 is the purchase price of the standard equipment, C T+H,j is the purchase price of the specialty equipment of j th type, C op,1 and C op,j are the operational cost of the standard equipment and the specialty equipment, respectively, n is the number of years used in the evaluation period, and z is the discount rate. Based on the equation above, C B starts with a negative 50

63 value but increases with time, since the operation cost of specialty equipment is lower compared with the standard truck, although the initial cost of specialty equipment is higher. Using the cost benefit formulation, one can also determine the break-even point at which the reduced operating costs will pay for the increased purchase costs. The operating costs consist of three main components including labor, fuel and materials as shown below: C op,j = (C L,j + C F,j + C MS,j ) (4.7) where, C L,j is the costs associated with the labor required for j th type of equipment, C F,j is the fuel costs for j th type of equipment, and C Ms,j is the costs associated with the salt applied during maintenance operations for j th type of equipment. The labor costs associated with each equipment type is calculated as shown below: 3 C L,j = C d (H j,n E n ) n=1 (4.8) where, C d is the hourly wages paid to operators, H j,n is the operation time for the j th equipment type at the n th snowfall level, E n is the number of events at the nth snowfall level, and n = 1, 2, and 3 for light, moderate, and heavy snowfall, respectively. Due to the increased capacities of the specialty equipment found from the field data collection and route optimization, the operation time is decreased by 15% and 48% for the specialty hopper and plow, respectively. The fuel costs are determined using the following equation: 51

64 C F,j = C f U j V j (H j,n E n ) 3 n=1 (4.9) where, C f is the cost of fuel, and U j is the fuel used by the j th equipment type per mileage. The amount of salt used for the garage is calculated from the equation below: 3 C MS,j = C s V j ε j (H j,n M S,j,n E n ) n=1 (4.10) where, C s is the cost of salt per ton, M S,n is the salt applied per lane mile during the n th snowfall level by standard truck, and ε j is the reduction factor to account for reduced amount of salt applied when the j th type equipment is used. It is found that no reduction is found for specialty plow, while specialty hopper reduces the amount of salt applied by 25% ±15%, which was found from the field data collection. The expected cost benefit can be determined based on Equation 4.6 using Monte Carlo simulation techniques. The parameters used in the failure probability and cost benefit analyses are shown in Table

65 Salt Fuel Purchase cost Operation time Table 4.2: Average and Standard Deviation of Parameters used in Cost Analysis Parameter Symbol Units Mean Standard Deviation light event standard truck H 1,1 5 2 light event specialty hopper H 2, light event specialty plow H 3, moderate event standard truck H 1,2 8 3 moderate event specialty plow H 2,2 hours/event moderate event specialty hopper H 3, heavy event standard truck H 1, heavy event specialty hopper H 2, heavy event specialty plow H 3, Labor rate C d $/hour standard truck C T,1 160,000 4,000 standard hopper C H,1 23,000 2,000 specialty hopper truck C T,2 125,000 4,000 specialty hopper C $ H,2 110,000 5,000 specialty plow truck C T,3 200,080 18,067 specialty plow C H,3 101,000 4,000 standard truck U specialty hopper U 2 gallons specialty plow U Fuel cost C f $/gallon 4 1 light event M Sj, tons/lanemile moderate event M Sj, heavy event M Sj, Specialty Hopper Salt Reduction ε 2 percent Salt Price C s $/ton Note: All data used in the analysis are collected by the researchers. * The value varies for each garage, so the average and standard deviation for the study area are presented. 4.5 Analysis and Discussion When determining the benefits of adding additional equipment, the probability of exceeding the cycle time and the cost benefit are determined with a garage having all standard trucks; a garage having an equivalent number of standard trucks replaced by one specialty hopper and one specialty plow; a garage having one standard truck replaced by one specialty hopper and; a garage having one standard truck replaced by one specialty 53

66 plow. When specialty equipment is implemented, an equivalent number of standard trucks are removed so the total number of trucks is always the same in the garage Failure Probability The main benefit of the specialty equipment is the ability to maintain more lane-miles of road in the same amount of time. By decreasing the probability of exceeding the 120 minute cycle times, ODOT is providing a greater level of service to the motoring public. Reductions in the cycle time will allow for more frequent treatments during winter events, resulting in better driving conditions and potentially fewer crashes (Fu et al., 2006). When implementing specialty equipment in the fleet within a garage, the probability of exceeding the cycle time decreases as a result of the increased capabilities of the specialty equipment. Figure 4.4 shows the failure probability of a garage if the failure is defined as any of the trucks exceeds the cycle time in each region based on Equation (4.4) Probability of failure, P f,s Probability of failure, P f,s Number of trucks (a) Region I Number of trucks (b) Region II 54

67 10 0 Probability of failure, P f,s Number of trucks (c) Region III Figure 4.4. Failure Probability of a Garage if any of the Trucks Exceeds the Cycle Time in (a) Region I, (b) Region II, and (c) Region III As shown in Figure 4.4, the failure probabilities of a garage with the specialty equipment are lower than a garage with only the standard equipment. If any of trucks exceeds a cycle time of 120 minutes the entire garage will fail, when the number of trucks increases, the failure probability of the garage increases. The lowest failure probability is found when implementing a specialty hopper and plow within the maintenance fleet, while utilizing all standard trucks results in the highest failure probability. When there are eight or more trucks in the garage, the failure probability becomes nearly equal when implementing the specialty equipment, indicating that garages this size may need to implement multiple pieces of specialty equipment to realize a decrease in the failure probability. In addition, the probability of exceeding the total cycle time is determined for each region of Ohio using Equation (4.5). This probability of failure shows how likely a garage would be to exceed a total cycle time equal to two hours multiplied by the number of trucks in 55

68 the garage, which can be used to measure the efficiency of a garage as a whole. Such failure probability for each region is shown in Figure 4.5. Probability of failure, P f,s Probability of failure, P f,s Number of trucks Number of trucks (a) Region I (b) Region II Probability of failure, P f,s Number of trucks (c) Region III Figure 4.5. Failure Probability of a Garage if the Total Time used by all the Trucks Exceeds the Total Cycle Time in (a) Region I, (b) Region II, and (c) Region III The total failure probability is constant when only considering standard trucks because the capacity of all standard equipment is the same. However, when implementing specialty equipment, the failure probability increases as the baseline number of standard 56

69 Cost benefit Cost benefit trucks increases. The benefits of the specialty equipment become less apparent as more standard trucks are included. When evaluating a garage as a whole, the failure probabilities are less than 0.15, indicating that the total cycle time is not likely to exceed two hours per truck. Overall, based on Figures 4.4 and 4.5, larger fleets need to add multiple specialty equipment to improve the performance of the garage Annual Benefit to Garage Adding the specialty equipment to a garage presents benefits by reducing the operational cost, and such benefits should become more obvious with the increase of time. The main aspect concerning agencies is whether or not the cost benefits outweigh the increased initial costs of the specialty equipment within the expected life span of the equipment. The cost benefit of implementing one specialty hopper or plow to one standard plow truck are evaluated based on Equation (4.6), and the results are shown in Figure 4.6. x x Year (a) Region I Year 57

70 Cost benefit Cost benefit Cost benefit Cost benefit x x Year (b) Region II x Year 4 x Year Year (c) Region III Figure 4.6. Cumulative Benefit Costs of Implementing One Specialty Hopper (left) and One Specialty Plow (right) in (a) Region I, (b) Region II, and (c) Region III -1 In Figure 4.6 the solid lines refers to the expected cost benefit and the dashed lines indicated the ± 1standard deviation band. Figure 4.6 shows the cumulative benefit of implementing specialty equipment. The curves start with negative values since the purchase price of the specialty equipment is significantly more than the standard equipment. The curves increase over time as a result of the operational costs being lower for the specialty equipment than the standard equipment. Considering the upper bound 58

71 (mean + 1 standard deviation), for Regions I and II, the specialty hopper will be paid off by the second winter season it is being utilized, while for Region III, it will be the third winter season, as shown in plots on the left in Figure 4.6. For specialty plow as shown in the plots on the right in Figure 4.6, the expected pay off time is about year 6, year 18, and year 25 for Regions I, II, and III, respectively; and the lower bound pay off time is about year 12, larger than 25, and larger than 25, for Regions I, II, and III, respectively. As the life time for specialty plow is 24 years while the lifespan of the truck associated with the specialty plow is 12 years, this result indicates that the specialty plow may not be beneficial in areas receiving less snowfall (Regions II and III). One thing to note with each of these curves is that they are comparing one piece of specialty equipment (either hopper of plow) to one piece of standard equipment. When implementing specialty equipment, it may be possible to remove multiple pieces of standard equipment, which will increase the benefits of the specialty equipment. 4.6 Conclusions This research conducted route optimization analysis which included all standard trucks, one specialty hopper and one specialty plow in each garage. This analysis was conducted to determine the number of lane miles maintained by each type of truck. These results were combined with field data to estimate the failure probability of the trucks exceeding a cycle time of 120 minutes. The failure probability was evaluated in two ways: the garage is considered to fail if any truck exceeds the cycle time and the garage is considered to fail if the summation of the time used by all the trucks in the garage exceeds the total cycle time (120 minutes multiplied by the number of trucks). Cost benefit analysis was conducted to determine the payback period for the specialty equipment. 59

72 The failure probabilities were evaluated as a system of trucks such that if one truck exceeds a cycle time of 120 minutes the entire garage is considered to fail. As a result, the failure probability increases as the number of trucks in a garage increases. However, the specialty equipment has a lower failure probability than the standard plow truck resulting in greater service provided to the motoring public. The total failure probability is constant when only considering standard trucks because the capacity of all standard equipment is the same. However, when implementing specialty equipment, the failure probability increases as the baseline number of standard trucks increases. When there are eight or more trucks in the garage, the probability of exceeding the 120 minute cycle time for the specialty equipment becomes nearly equal to that of the standard equipment, indicating that garages of this size may need to implement multiple pieces of specialty equipment to improve the performance of the garage. The cumulative benefit costs are calculated comparing one specialty hopper to one standard plow truck and one specialty plow to one standard plow truck. The initial purchase price of the equipment is considered to occur in the first year then the remaining costs result from the lower operational costs for the specialty equipment. For Regions I and II, the specialty hopper will be paid off by the second winter season it is being utilized, while for Region III, it will be the third winter season. For the specialty plow, the expected pay off time is year 6, year 18, and year 25 for Regions I, II, and III, respectively. This indicates that the specialty plow is more effective in areas receiving more snowfall. One thing to note is that the comparison of the benefits is made for one piece of specialty equipment to one piece of standard equipment. When implementing 60

73 specialty equipment, more than one piece of standard equipment may be able to be replaced which would increase the benefits of the specialty equipment. 61

74 CHAPTER V ASSESSING THE VULNERABILITY OF WINTER MAINTENANCE MATERIAL STORAGE FACILITIES 5.1 Introduction One of the most difficult challenges facing transportation agencies in cold climates is the removal of snow and ice from roads during winter storms. Winter road maintenance is imperative for the safe and efficient transportation of people and goods. Winter maintenance agencies recognize this need and are devoting a large amount of their maintenance budgets to winter maintenance, with state and local agencies in America spending $2.3 billion annually on snow and ice control operations (FHWA, 2013). Typically, a combination of plowing and material application is used to maintain roadways. With limited budgets and the increasing price of salt, agencies have looked to optimize their operations in all facets and have taken steps to more efficiently schedule maintenance for their equipment and facilities. As a result, facility management has become a key point of interest in recent years. 62

75 Much of the relevant research in facilities management has focused on optimizing maintenance schedules for equipment and facilities (Chun, 1992; Chan and Shaw, 1993; Morcous and Lounis, 2005). With advances in computing, many algorithms and programs have been developed with the intent of determining which maintenance activities are necessary to optimize the life cycle costs (Chou, 2009; Tarighat and Miyamoto, 2009). Additional research has focused on the optimization of facilities themselves, including the location and capacity. Many studies have modeled manufacturing capacity using multiple agent problems (Harris et al, 1982; Porteus and Whang, 1991). More recent work has focused on determining the minimum number of facilities to open given demand, facility capacity, and cost to open a facility (Aardal et al., 2015). Other researchers have developed a methodology for analyzing the throughput capacity of a facility based on environmental conditions such as ambient temperature, icing, dust, and wind (Barabadi et al., 2011). Few researchers, however, have studied the material supply used for winter maintenance. The type of material used depends on the availability to the local agencies, but generally includes salt, abrasives, and deicing liquids. Regardless of the type of material used, agencies must have facilities to store the materials and make decisions about how much material to store/purchase considering the changing weather patterns. However, such decisions are usually made based on engineering judgment and experience, which is subjective. With the rising costs of winter maintenance equipment, material and operations, there is a need to develop a quantitative tool to aid such decision making. Accordingly, this research seeks to address this need by developing a methodology to 63

76 evaluate the vulnerability of winter maintenance material storage facilities using reliability analysis. Engineering risk analysis accounts for the likelihood that a given system meets or exceeds the failure criteria (Cadini et al., 2014). Risk analysis techniques have been used extensively in other areas including natural disasters, business interruptions, security risks, financial risks, and transportation travel time (Tamasi and Demichela, 2011; Tu et al., 2012). Currently, there is a dearth of literature concerning the risk assessment for the depletion of materials at winter maintenance material storage facilities. The methodology will expand on the existing facility management literature and combine engineering risk analysis to evaluate the vulnerability of winter maintenance material storage facilities. In this study, the principles of engineering risk analysis are applied to enhance the management of material storage facilities and to determine the vulnerability of material storage facilities. In particular, the developed methodology is applied to winter operations for the Ohio Department of Transportation (ODOT). By determining the vulnerability of storage facilities, a plan may be developed to optimize the distribution of material, resulting in a higher level of service and potentially reducing ODOT s maintenance budget. 5.2 Methodology The methodology for this chapter is divided into five subsections describing the data required to estimate the failure probabilities as well as the reliability analysis methods and cost analysis applied to the analysis. 64

77 5.2.1 Performance of Storage Facilities The performance of storage facilities is evaluated using the probability of exceeding the material storage capacity, which will have many benefits for agencies including aiding with short- and long-term facility planning. With the rising cost of winter maintenance materials, knowing which areas need more salt and which may be overstocked will help agencies tailor their budgets and improve the level of service provided to the public. The failure event in this study is defined as the point where the material demand exceeds the material supply in the storage facility during winter operations. The analysis can be conducted at the individual facility, county, or district level. Since ODOT orders salt at the county level, the analysis in this paper is conducted at the county level. In addition, conducting the analysis at the county level provides the flexibility to distribute the material amongst the salt storage facilities within the same county as needed. Using the conventional notation in structural reliability theory (Ditlevsen and Madsen 1996), the probability of failure in county i, P f,i, is expressed as: P P g S D 0 (5.2) f, i i i i where, g i ( ) is the limit state function, S i is the material supply that equals to the total storage capacity for the i th county in this study, and D i is the material usage/demand that equals to the amount of material being utilized during maintenance operations. The limit state function is defined as follows in this study: g i S D (5.3) i i where g i ( ) 0 refers to the failure domain. 65

78 5.2.2 Facility Material Capacity As shown in Equation (5.1), to determine the vulnerability of material storage facilities, the end user needs to determine the material supply, which is the capacity of the material storage facilities in each county. Ohio is comprised of 88 counties and ODOT has a total of 221 salt storage facilities. ODOT maintains a database with the capacity of their storage facilities that is used for material purchasing. Additionally, the number of trucks and lane miles that need to be maintained by each facility are determined. Thus, ODOT s storage capacity for each county can be calculated by summing up the storage capacity of all the ODOT facilities in that county. Similarly, the number of trucks utilizing material and the lane miles for each county can be calculated as well. For all the counties in Ohio, the salt storage capacity ranges from 2,350 tons to 50,400 tons, the number of trucks ranges from 10 to 59, and the number of lane miles ranges from 90 to 853. The average capacity per facility is 3,108 tons, and the average capacity per county is 7,946 tons. Table 5.1 provides an overview of selected counties with a various number of facilities, which includes the total storage capacity, number of trucks available, and the total lane miles in the county. The data for all counties in Ohio may be found in Appendix A. Table 5.1. Examples of Salt Storage Facility Data Collected County name Number of Storage Number of Lane miles facilities capacity (tons) trucks (miles) Cuyahoga 6 25, Franklin 7 23, Henry 1 3, Medina 2 9,

79 5.2.3 Material Usage One option for determining the amount of material being drawn from the facilities is to collect material usage data. ODOT estimates the amount of salt used based on the number of buckets loaded into the snow plow truck, and an ODOT plow truck operator typically will record the amount of material applied by completing forms during maintenance operations. However, operators are focused on maintaining roadways during winter events, and they may only periodically record their activities, resulting in a lower level of clarity in the material usage records. In addition, using completed forms to determine the total material usage can be a cumbersome task if the county covers a large geographical region. Recently, many agencies have begun to implement vehicle tracking and material application sensors on their plow trucks to automatically track the amount of material applied. As such, the total material (including salt, brine and grit) used each day for each truck should be recorded. It is reasonable to assume that the material application amounts are similar in regions receiving a similar amount of annual snowfall. Thus, this study assumes that the amount of material applied per lane mile per truck only depends on the levels of snowfall that can be determined by the classification of winter storm. Particularly, this research used a classification of light snowfall (less than two inches for the storm), moderate (between two and six inches for the storm), and heavy (greater than or equal to six inches for a winter storm). Therefore, the material usage/demand in ith county, D i, may be determined by: 67

80 3 D N L E M M i i i n 1 i, n S, n B, n (5.3) where N i, and L i are the number of maintenance trucks and the number of lane miles, respectively, maintained in the i th county as shown in Table 1; E i, n is the number of events at the n th snowfall level in a given year in the i th county; M S,n and M B,n are the amount of salt and brine applied per lane mile per truck, respectively, at the n th snowfall level in a given year; κ is a constant (that equals to 0.008/2000) to account for the amount of salt in the brine and convert that value to tons; and n = 1, 2, and 3, which refer to light, moderate and heavy snowfall levels, respectively. To assess E i, n, this study uses the weather data collected from a total of 56 weather stations operated by the National Oceanic and Atmospheric Administration (NOAA) throughout the state of Ohio, and the nearest station is assigned to each ODOT storage facility. To accomplish this, the coordinates of the storage facilities and weather stations are recorded, and ArcGIS is used to calculate the nearest station to each facility. If more than one facility is located in a given county, then the average weather data for all facilities in that county is used. For most stations, weather data were collected from 2009 to 2014; some stations only had data available beginning in The statewide average number of winter events per year is found to be 33, 4.3 and 0.9 for light, moderate and heavy snowfall, respectively. A sample of the weather data for two cities (Cincinnati and Cleveland), one receiving a large number of snow events and one receiving a small number, is shown in Figure

81 μ = 32.3 σ = 5.79 μ = 22.0 σ = 6.20 (a) Light Snowfall μ = 11.7 σ = 3.61 μ = 4.17 σ = 1.83 (b) Moderate Snowfall μ = 0.83 σ = 1.17 μ = 0.33 σ = 0.82 (c) Heavy Snowfall Figure 5.1. Number of Light, Moderate and Heavy Snowfall Events in Cleveland (left) and Cincinnati (right). Note that the weather data (the number of events in each storm category) are collected over time, and it is very common for such data to exhibit serial correlation. This is because the data for the current time is normally correlated with the weather from the previous year. By checking the correlation between the number of events of one year and 69

82 the various values for different years (this is also called autocorrelation), it is found the serial correlation effect can be ignored. In other words, the collected weather data can be considered as stationary and its statistical properties can be used for future weather prediction. If autocorrelation is present, time series analysis should be used to predict the number of events in a future year for planning purposes. To assess M S,n and M B,n, the application data for salt and brine are collected from 21 ODOT plow trucks in Ashtabula, Medina, Stark, and Summit counties in northeastern Ohio. These counties were chosen due to the readily available and accurate material application data obtained through the use of truck sensors as part of other research activities in these counties (Schneider et al., 2013; Schneider et al., 2014). The data are grouped based on the three snowfall levels defined above. Note that the material usage data used to assess M S,n and M B,n are normalized to the lane miles being maintained to account for maintenance areas of different sizes. Figure 5.2 shows the histograms of the material application data for M S,n and M B,n at each storm level for all 21 trucks. Next, the data were fitted using a normal distribution. The fitted distribution density curves and the corresponding mean and standard deviation are shown in Figure 5.2. M S,n M B,n 70

83 (a) Light Snowfall (b) Moderate Snowfall (c) Heavy Snowfall Figure 5.2. Salt Application (left) and Brine Application (right) during (a) Light, (b) Moderate, and (c) Heavy Snowfall Events Reliability Analysis, Sensitivity Measures, and Importance Measures The program Finite Element Reliability Using Matlab (FERUM) (Haukaas, 2001) was used to evaluate the failure probability defined in Equation (1) through reliability analysis. Let x = (x r, x d ) refer to the input variables for the reliability analysis in which x r are random variables and x d are deterministic variables. The random variables considered are the amount of salt per lane mile per truck, M S,n, the amount of brine per lane mile per truck, M B,n, and the number of events at each storm severity, E i,n ; the statistical properties 71

84 are shown in Figures 5.1 and 5.2. The deterministic variables considered are capacity of the storage facility, S i, the number of trucks, N t,i, and the lane miles, L i, as shown in Table 5.1. In addition to the reliability analysis, a sensitivity analysis is conducted to assess which parameters are the most critical. The parameters include x d and the distribution parameters that defines the distributions of x r (e.g., means, standard deviations). Identifying which parameters have the greatest impact on the probability of exceeding the storage capacity will allow agencies to develop plans to limit the exposure to depleting supplies for resource allocation and will provide insight into the performance of winter maintenance material storage facilities. The sensitivity of the failure probability is measured with respect to each parameter appearing in the limit-state function as follows: Θ 1 p (5.4) Θ where Θ = (x d, Θ f ), Θ p 1 Θ p 1 is the gradient representing the sensitive measure, that is the change in failure probability due to unit change in each parameter, p 1 is the first-order reliability approximation of the failure probability, φ(β) is the standard normal probability density function, and Θ β is the gradient of the reliability index β (which is equal to Φ 1 [1 P f ], where Φ 1 denotes the inverse of the standard normal cumulative probability). One could also determine which random variable has a greater impact on the variability of the limit state function defined in Equation (5.2), which can be done by calculating an 72

85 importance measure for each random variable used in the reliability analysis. Following Der Kiureghian and Ke (1995), a measure of importance γ is defined as: γ T α J * * B T u, xr (5.5) α T J * * u, xr B where the subscript T denotes transpose, α = G(u)/ G(u), G(u) = g(x r (u)), where G(u) is the gradient vector evaluated at the design point x r * (the most likely failure point) in the standard normal space u; J u*,xr* is the Jacobian matrix of the probability transformation from the original space x r to the standard normal space u with respect to the design point and is equal to the inverse of J xr*,u* ; B is a diagonal matrix consisting of the standard deviations of equivalent normal variables x rʹ that can be calculated with respect to the design point (i.e., x rʹ = x * r + J xr*,u* (u u * )); and the elements of B are the square roots of the corresponding diagonal elements of the covariance matrix Σʹ = J xr*,u* J T xr*,u* of x rʹ Annual Risk Costs Currently, ODOT purchases a quantity of salt so that each county has the amount equal to the storage capacity of that county every year. Accordingly, we can assess the expected annual cost associated with the risk of having too much or too little salt. The costs result from the purchase of additional salt when supplies are exceeded and storage costs for the leftover salt that is not depleted. This annual risk cost, C i, can be calculated using the following equation: C i C D S H D S C S D H S D (5.6) s i i i i l s i i i i 73

86 where C s is the purchase price of salt, ξ ( 1) is the price increase factor to account for price increase for the salt purchased after the winter season starts, α l is the percentage of salt lost during storage, and H(x) is a unit step function (i.e., H(x) = 1 if x 0 and H(x) = 1 if x < 0). Through the discussion with ODOT, α l can be considered to have a mean value of 1% and standard deviation of 0.1%. Considering all the possible uncertainties, the expectation of the annual risk costs, E[C i ] can be calculated by: E C i C s Di S i d x r l C s S i Di d x (5.7) r g i 0 g i 0 where, g i is defined in Equation (5.2) and g i 0 defines the failure domain, and x r are the random variables. Particularly, the first and second integrals represent the risk cost due to having too little and too much salt, respectively. As the probability of failure P f,i, describes the probability of being in the failure domain (as shown in Equation (5.1)) and α l < 1, it is obvious that the increase of P f,i will increase the expectation of risk costs. 5.3 Results and Discussion Based on the theories described in the previous section, the probability of exceeding the salt supply is analyzed for each county in the state of Ohio, and the results are presented in Figure 5.3. The minimum, maximum, and average probabilities of exceedance were found to be less than 0.01%, 61%, and 23.1%, respectively. The results are divided into three categories that depict the likelihood of exceeding the salt supply: light grey, grey, and black shading correspond to counties with a 0 to 20.0%, a 20.1 to 40.0%, and greater than 40% chance of exceeding their supply, respectively. 74

87 Figure 5.3. Probability of Exceeding Salt Supply for Each County in Ohio Of the total 88 counties in Ohio, 47 have a low probability, 18 have a moderate probability, and 23 have a high probability of exceeding their salt supply. The 23 counties with a high probability of exceeding their salt supply have an average of 531 lane miles and an average storage capacity of 5,803 tons, compared to the statewide average of 439 lane miles and 7,946 tons. The increased lane miles and decreased storage capacity in these counties may result in higher probabilities of exceeding the storage capacity. However, the results are varied throughout the state, with no geographical trends 75

88 emerging. Accordingly, further analysis is needed to determine the underlying causes of exceeding the salt supply. Additionally, the sensitivity and importance measures are determined. Table 5.2 shows the sensitivity and importance measure of each variable for three counties: Stark, Washington and Paulding counties. These three counties provide a sample for counties with low, moderate and high probabilities of failure, respectively. Table 5.2. Sensitivity and Importance Measures for Several Counties in Ohio County Parameter Stark Washington Paulding Failure Probability 0.09% 26% 61% Sensitivity measures Supply (ton) Lane miles Mean of number of light events Mean of number of moderate events Mean of number of heavy events Mean of salt usage for light event (lb/lane mile) Mean of salt usage for moderate event (lb/lane mile) Mean of salt usage for heavy event (lb/lane mile) Mean of brine usage for light event (gal/lane mile) Mean of brine usage for moderate event (gal/lane mile) Mean of brine usage for heavy event (gal/lane mile) Importance measures Number of light events Number of moderate events Number of heavy events Salt usage for light event Salt usage for moderate event

89 Salt usage for heavy event Brine usage for light event Brine usage for moderate event Brine usage for heavy event The sensitivities and importance measures for all counties may be found in Appendix B. The sensitivities can be used to determine the change in the failure probability due to a one unit change in a given parameter. For example, if Washington County were to increase the number of lane miles maintained by ten, the probability of exceeding their salt supply would increase from 26% to 27.9%. The sensitivity for the mean values of salt usage has high sensitivity for all three counties, especially for light and moderate events, indicating that the snow events impact the probability failure significantly. Note that the sensitivity for the salt usage is measured in pounds per lane mile instead of tons per lane miles so that agencies may easily see the effects of changing their application rates. For example, if Washington County were to decrease the salt application rates by one pound per lane miles during light snowfall events, the probability of exceeding the salt dome capacity would decrease by 1.29%. The importance measures are unitless and may be used to compare the importance of the parameters with various units to the variance of the limit state function. The values of important measures range from zero to one, with values closer to one having a higher influence on the probability of failure. As shown in Table 2, the parameter with the highest importance is the amount of salt applied during light events with values of , and for Stark, Washington and Paulding counties, respectively. The next highest importance values are the number of light or moderate events and the amount of salt applied during moderate events. In addition, the brine application during 77

90 all event types has a low importance to the probability of exceeding the salt supply with values below for the sample counties presented. Accordingly, as one could change the number of snow event, agencies should be cognizant of the amount of salt they apply and may want to increase the amount of brine applied, especially during light and moderate snow events. Theoretically (as shown in Equation (5.7)), if the probability of exceeding the storage capacity is low, the amount of salt purchased mid-season will be minimal, while the risk associated with the storage costs will be higher. The opposite is true when the probability of exceeding the salt capacity is high. To provide a more general sense about those risks, the cost analysis is conducted over three regions of Ohio instead of for each of the 88 counties. Counties are assigned to one of three regions are based on the amount of snowfall and number of events received throughout the state. On average, Region I receives 30 to greater than 100 inches of snowfall with 40 light, 6.3 moderate, and 1.5 heavy events annually. Region II receives on average 20 to 40 inches of snowfall with 34 light, 4.1 moderate, and 3.2 heavy events annually. Region III averages less than 20 to 30 inches of snowfall with 26 light, 0.95 moderate, and 0.3 heavy events annually. The number of trucks and the lane miles for each region are calculated based on the average of the corresponding quantities of all the counties in that region. The mean of the number of trucks are: 19 in Region I, 18 in Region II, and 16 in Region III. The mean of the lane miles are: 510 in Region I, 415 in Region II, and 438 in Region III. As shown in Equation (5.7), the risk annual cost depends on the salt supply. Figure 5.4 shows the relationship between the normalized expected risk annual cost and the material supplies that are purchased before the winter season. Note that it is assumed 78

91 that the salt prices after the beginning of a winter season is twice the salt price before the season starts (i.e., ξ = 2.0). As expected, the expected risk annual costs decrease when the supply is increased even though the risk cost associated with the storage increases, as the storage costs are much less expensive than the purchase costs. In addition, the normalized expected risk costs are associated with the failure probability, as shown in Equation (5.7), and such relation for each region is shown in Figure 5.4 by changing material supplies only. Thus, knowing the risk cost that an agency is willing to accept, the corresponding probability of exceeding material supply can be determined. Even though increasing the material supply can reduce the risk costs, a transportation agency will need to pay the cost for purchasing the increased supply of materials. On the other hand, if the supply is not sufficient to last the entire season, the risk for purchasing additional material at an escalated salt price during mid-season can be costly. To find a balance between the costs for storing material purchased prior to the beginning of the season and the costs of purchasing additional material in mid-season, an expected total cost that includes the risk cost and the cost for purchasing the given material supply is calculated. Figure 5.5 shows the normalized expected total cost for each region by changing the amount of material supply. Note that in Figures 5.4 and 5.5, the costs are normalized so that they can be generalized for use by other agencies, and the actual cost can be easily calculated by multiplying the amount material required by the price of salt in a given area. 79

92 Figure 5.4. Normalized Expected Risk Costs over the Price of Salt versus Material Supply in the Three Regions of Ohio Figure 5.5. Normalized Expected Total Costs over the Price of Salt versus Material Supply in the Three Regions of Ohio 80

93 As shown in Figure 5.5, for each region, there is one optimum amount of material supply that should be purchased before the season: 7,000 tons for Region I, 4,000 tons for Region II, and 3,000 tons for Region III. Note that those optimum numbers will vary with the number of trucks and the number of lane miles that need to be maintained. As expected, this optimum number for Region I is the highest, as Region I is the only area in Ohio that receives lake effect snowfalls. 5.4 Conclusions This research examined the salt supply vulnerability to depletion for ODOT county maintenance facilities in Ohio. Data were collected regarding the amount of salt storage, number of trucks, and lane miles maintained by each county. These data were combined with the number of snowfall events in each county (found by using data from NOAA weather stations) to determine the failure probability in each county. Sensitivity and importance measures were determined for the parameters used in the model to determine the impacts each parameter can have on the failure probability and which parameters have the most influence on the failure probability. Annual risk costs were estimated using the purchase and storage costs of salt, keeping in mind that purchasing additional cost during mid-season may be more expensive than purchasing the salt prior to the start of the winter season. The total cost was then determined to estimate the optimal salt supply for different regions of Ohio based on the amount of snowfall and the number of snowfall events in a winter season. The failure probability analysis determined that the probability of exceeding the salt capacity ranged from less than 0.01 to 61%, with an average of 23.1%. Sensitivity analysis was conducted to determine the influence of individual model parameters on the 81

94 probability of exceeding the salt storage capacity. For example, in Paulding County, the number of lane miles maintained has a sensitivity of 0.1. A sensitivity rate at this level indicates that if a road is widened and ten lanes miles were to be added to Paulding County s maintenance area, the probability of exceeding the salt supply would increase from 61% to 62%. Additionally, the importance vectors were determined for each random parameter to compare the influence of each parameter to the others. The parameter with the highest importance is the amount of salt applied during light events, with values of , and for Stark, Washington and Paulding counties, respectively. The brine application rates during all event types have a low importance to the probability of exceeding the salt supply, with values below for the sample counties presented. Accordingly, agencies should be cognizant of the amount of salt they apply and may want to increase the amount of brine applied, especially during light snow events. This research applied costs to the risk assessment of exceeding the salt storage supply. It was found that the risk cost decreases as the salt supply increases as a result of the probability of exceeding the supply decreases. However, the total cost will increase as the material supply increases since the purchase of additional material after the start of the winter season is expensive. To serve as a guide to agencies in other areas, the state of Ohio is divided into three regions based on the annual snowfall and number of snow events in a winter season, with risk and total cost curves normalized for the price of salt being developed for each region. These curves may be used as a guide for agencies to estimate their costs by multiplying the value obtained from the curve by the cost per ton of salt in their areas. 82

95 CHAPTER VI PLOW TRUCK SENSOR FAILURE AND CALIBRATION 6.1 Introduction Winter maintenance costs are rising, with state and local agencies spending more than $2.3 billion on snow and ice control annually (FHWA, 2013). As a result, state transportation agencies are implementing systems to better monitor equipment and material usage. An agency as defined in this research is any group conducting winter maintenance activities, which in the US typically includes state, county, and local governments. Agencies have been implementing global positioning systems (GPS) and automatic vehicle location (AVL) into their maintenance fleets in order to determine the current location of deployed equipment. Vehicle sensors may be added to the trucks to monitor environmental conditions, material usage, plow status and engine diagnostics (Strong et al., 2007). Winter maintenance personnel are able to better track the amount of material used when implementing material application sensors. Material application sensors allow for application rates to be used for training purposes if operators in similar areas are found to use significantly different application rates. Additionally, material 83

96 application sensors allow agencies to better track material stockpiles and potentially reduce costs by reducing material application rates. By utilizing GPS/AVL systems, agencies have the ability to drastically increase the amount and accuracy of data collected when compared to information on reports or forms completed by truck operators. GPS/AVL data may be used to track material and equipment as well as develop performance measures to determine the effectiveness of winter maintenance operations. Adams et al. (2003) defined several winter maintenance performance measures utilizing GPS/AVL data that include measures pertaining to road section pavement temperature, material application rates, material inventory, equipment costs, and equipment operations. Other researchers have combined several types of data including weather, vehicle speed, and truck telemetry data to develop winter maintenance performance measures (Kwon et al., 2012; Kipp and Sanborn, 2013). Implementing GPS/AVL systems and combining GPS/AVL data with other remote sensing data such as weather and traffic data gives transportation agencies the ability to better monitor equipment and materials as well as to develop performance measures for tracking the benefits of winter maintenance operations. However, these sensors are placed in a very harsh environment and exposed to cold temperatures, moisture, and corrosive materials such as salt. As a result of the harsh operating conditions, sensors placed on trucks may fail and need to be replaced, or they may require calibration to ensure that they will record data accurately. To date, little work has been conducted to examine the impacts of the failure of GPS/AVL sensors on winter maintenance equipment; this study aims to fill the gap. 84

97 Typically, winter maintenance personnel have been focused on keeping their plow trucks in good operating condition. Mechanics tend to focus on major mechanical issues such as the engine and transmission repair/maintenance while ignoring any issues with the sensors. However, a paradigm shift may be necessary as vehicle sensors becomes more prevalent and agencies begin to rely more heavily on the sensor data when making decisions about winter maintenance. The role of vehicle sensors has been increasing in recent years and, as a result, the maintenance of these sensors must be addressed more thoroughly. 6.2 Data The data used in this analysis were collected over three winter seasons from 20 standard snow plow trucks maintained by the Ohio Department of Transportation (ODOT) that are equipped with GPS/AVL systems. These systems recorded the position (latitude and longitude), speed, and heading of the vehicle; the salt application rate, the plow status (on or off); and the position of the plow (up or down). Additionally, eight of these trucks are also equipped with scale weight sensors in the bed of the truck. These bed scales sensors are capable of recording the weight of material in the salt hopper, and the data are recorded continuously while the trucks are operating. The bed scale data for each truck were compared to weight data obtained from a drive-up truck scale and from scales operated by the Ohio State Highway Patrol to ensure that the weight data obtained by the sensors are accurate and reliable. This study does not consider every sensor on the truck ; only the sensors relating to material usage and vehicle location are considered, so that costs may be applied to sensor failures and calibration requirements. 85

98 The GPS/AVL sensors used in this research may be classified into three general categories: proximity sensors, position sensors, and output sensors. Proximity sensors, which record an output as either one or zero to indicate if the sensor detects an object or does not, are used to detect the plow status to determine if a plow is installed or not installed. Position sensors record an output as either one or zero based on the angle of the sensor; these types of sensors are used for detecting the plow position, as the sensor is able to determine if the plow is up or down based on the angle of the sensor. Output sensors, which report the actual values from a given system of the truck,are used for obtaining the weights from the bed scales and the rates of material application. This research focuses mainly on the output sensors from the truck. Output sensors are extremely important to a GPS/AVL system, since they are typically used to monitor material usage. The application rates recorded from the hydraulic controllers of plow trucks are known to be unreliable. As a result, bed scale sensors may be implemented to track the weight of material contained in the bed of a plow truck. When these sensors are implemented as a part of a GPS/AVL system, the material application rate may be determined using the distance the vehicle travels and the difference in weight in the bed at the start and end point of the maintenance route. This approach eliminates any issues with the hydraulic controllers reporting incorrect application rate data. Due to the importance of bed scale sensors in obtaining accurate material usage data, an in-depth evaluation of the failures and calibration requirements for these sensors is conducted. Different regions in Ohio receive various amounts of snowfall during a typical winter season. The state can be divided into three regions based on the amount of snowfall. 86

99 Region I, which is located in northeast Ohio, receives the highest amounts of snowfall. Region II, which includes northwest and central Ohio, receives moderate amounts of snowfall. Region III is located in southern Ohio and receives the lowest amounts of snowfall. The average number of winter storm events for each region in Ohio was determined using data from 56 weather stations maintained by the National Oceanic and Atmospheric Administration (NOAA). For most weather stations, weather data were available from 2009 to 2014; however, some weather stations only began recording weather data beginning in The data from the NOAA weather stations was grouped by region, and Table 6.1 shows the average amount of snowfall and number of snow events encountered annually for each region. Table 6.1. Average Snowfall and Number of Events in Regions of Ohio Average Snowfall (inches) Average Number of Snowfall Events Region Minimum Maximum Light Moderate Heavy I 30 > II III < Note: Snowfall data were obtained from weather stations maintained by the National Oceanic and Atmospheric Association (NOAA). The different regions in Ohio were identified in this study to allow transportation agencies in other areas to use the results of this study as a guide. Once an agency has identified similarities between the weather patterns in their areas and the weather patterns of a particular region in Ohio (based on the number of events and total annual snowfall), the results for that region in Ohio can be used to estimate the expected costs in their areas. 87

100 6.3 Methodology This study includes a sensor reliability analysis and an analysis of costs associated with sensors failing or requiring recalibration. The following subsections describe the methods utilized to analyze the sensor failures and the associated costs Sensor Reliability and Calibration When sensors are to be implemented for the collection of winter maintenance data, the sensors must be working properly and transmitting data from the trucks. Knowing how frequently sensors do not work properly is useful for determining the reliability of the sensor system. Equation 6.1 is developed to determine the percentage of time that a given sensor is not working: R k = 1 ( T a T t ) 100% (6.1) where R k is the percentage of time the k th sensor is not functioning, T a is the time that the sensor is reporting data, and T t is the total operational time of the truck. By determining the percentage of time that each sensor is working, agencies will be able to determine which sensors tend to fail the most. Bed scale sensors require frequent calibration due to the harsh environment in which the sensors are placed. The cold temperatures and exposure to moisture and salt causes the reported weight values to drift from the ground truth values. To determine the percentage of drift in the weight values, Equation 6.2 may be used: Q p = ( W p W d W p ) 100% (6.2) 88

101 where Q p is the percent drift in calibration for the p th truck, W p is the bed scale weight measurement, and W d is the drive-up scale weight measurement. The bed scale sensors are installed so that they constantly report data when the trucks are in operation. Testing was conducted multiple times throughout the year to compare the data reported by the bed scale sensors with the weights reported from a platform drive-up scale. The weights from the bed scale sensors and from platform scale are summed for each truck during the testing events and are compared to one another. In addition to knowing the percentage of time that a given sensor is working, it is necessary to know the percentage of time that it is not giving a credible value. Equation 6.3 is developed to determine the percentage of time a sensor is reporting an incorrect value: Z k = 1 ( F o F t ) 100% (6.3) where Z k is the percent time the kth sensor is reporting an incorrect value, F o is the number of sensor readings that are incorrect, and F t is the total number of sensor readings. Determining which sensor readings are correct and incorrect is a cumbersome process, but one that is necessary for utilizing Equation XX. A sensor reading that is an outlier may be considered to be an incorrect reading. To determine which sensor readings are outliers, the Grubbs test for outliers is utilized (Grubbs, 1950). The Grubbs test statistic, which is a two-sided test (one that considers a high or low value to be an outlier), is shown in Equation 6.4: G = max Y x Y x=1,,n s (6.4) 89

102 where G is the Grubbs test statistic, N is the observation number, Y x is the value being examined, Y is the sample mean, and s is the standard deviation. This methodology is applied to the sensor reading dataset such that it conducts the Grubbs test one measurement at a time to determine if each value is an outlier as compared to the remaining values. To determine if a value being analyzed is an outlier, Equation 6.5 is applied: 2 t α (2N),N 2 G > N 1 N 2 N 2 + t α (2N),N 2 (6.5) 2 where t α (2N),N 2 denotes the critical value of a t-distribution with N 2 degrees of freedom and a significance level of α/(2n). When applying the Grubbs test in an iterative fashion, the outlier detection method is known as the generalized extreme Studentized deviate test Sensor Costs The sensor failures and calibration requirements may have costs associated with lost or incorrect data representing fuel and material usage that is unaccounted for. These costs may be estimated by using the equations developed in this section and by employing Monte Carlo simulations. The costs are analyzed for the sensors relating to the material usage and the location of the trucks. The costs associated with the material sensors may be formulated as shown in Equation 6.6: C MS = φ LM C S G (E n M S,n ) 3 n=1 (6.6) 90

103 where, C Ms represents the costs associated with the salt application, ϕ is the failure percentage equal to R k, Q p, or Z k ; LM is the number of lane miles maintained by a truck; C S is the cost per ton of salt; G is the number of cycles a truck makes during winter events; E n is the number of events at the n th snowfall level; and M S,n is the amount of salt applied during the n th snowfall level, where n = 1, 2, or 3 for light, moderate, and heavy snowfall events, respectively. Knowing the location of the truck as well as the distance traveled is crucial in determining the amount of fuel used and fuel costs. Accordingly, Equation 6.7 is developed to determine the costs associated with not knowing the location of the trucks: C F = R k C f U V (H n E n ) 3 n=1 (6.7) where C F is the costs associated with the fuel, C f is the cost per gallon of fuel, U is the fuel efficiency, V is the speed of trucks, and H n is the hours worked by operators during the n th snowfall level. 6.4 Results and Discussion There are two sets of results from this research: 1) the sensor reliability and calibration analysis results and 2) the costs associated with the sensor failures and calibration requirements. The results and costs are discussed in the following subsections Sensor Analysis Sensors are the basis for the GPS/AVL system used in snow plow trucks. Knowing the accuracy and reliability of the sensors allows agencies to be aware of the potential limitations of the system and the resulting data. Processing of the sensor data was a 91

104 Bed Scale Weight (pounds) cumbersome task, but one that is necessary for performing the data analysis and for generating useful results for material reporting and tracking purposes. At times, the sensors may report a constant or a value that changes only slightly, which may indicate that the sensor has failed or that the weight in the bed is not changing. Figure 6.1 shows data collected by a bed scale sensor with a constant value for a 30-minute period on the morning of January 29, :00 AM 7:10 AM 7:20 AM 7:30 AM Time Figure 6.1. Constant Bed Scale Weight Reported on January 29, 2015 Situations such as this highlight the need to combine the data from multiple sensors in order to obtain a clear picture of maintenance activities. Using the location data collected from the GVS/AVL system, it is known that on January 29, 2015, at 7:00 am, this truck was at location A on the map in Figure 6.1 and was en route to an ODOT garage at point B. Based on previous activity, the truck operator was likely returning to the garage to refill the truck with additional material. When a sensor failure occurs, the sensor will either report no data or, for certain types of sensors, report an error value. One particular 92

105 Bed Scale Weight (pounds) bed scale sensor reported a value of over 1 billion pounds when the sensor failed, as shown in Figure E E E E E E+00 1:00 PM 1:10 PM 1:20 PM 1:30 PM Time Figure 6.2. Bed Scale Sensor that Failed and Reported an Erroneous Value on December 18, 2014 The trend of the data is similar to data reported for the sensor in Figure 6.2, but the weight being reported by this sensor is over 2.5 billion pounds. Based on the unlikely value reported by the sensor and the GPS/AVL data showing that the truck was on a route between 1:00 pm and 1:30 pm, it is surmised that the bed scale sensor experienced a failure during this time frame. Sensors will often report noisy values with outliers, and the data requires cleaning before it can be used in the analysis. Figure 6.3 presents a sample of raw and cleaned bed scale data. The outliers were removed using an iterative process of Grubbs testing where individual weight values are tested against the remaining values, and those values that are 93

106 Bed Scale Weight (pounds) Bed Scale Weight (pounds) significantly far away from the mean are considered to be outliers, as described in Grubbs (1950) :00 AM 5:20 AM 5:40 AM 6:00 AM 6:20 AM 6:40 AM 7:00 AM Time 5000 (a) Raw Bed scale Data 0 5:00 AM 5:20 AM 5:40 AM 6:00 AM 6:20 AM 6:40 AM 7:00 AM Time (b) Cleaned Bed scale Data Figure 6.3. Bed Scale Data from January 30, 2015 (a) Raw and (b) Cleaned When filtering the raw bed scale data, the outliers are first removed from the dataset. Even with the outliers removed, the data may require further smoothing before the material application rates can be calculated. In this study, a Savitzky Golay filter is used 94

107 Bed Scale Weight (pounds) to smooth noise out of the sensor data while preserving the trend of the data. A Savitzky Golay filter uses a smoothing method based on local least-squares polynomial approximation, which smooths noisy data while maintaining the shape and height of the peaks (Savitzky and Golay, 1964). When comparing the two curves, the values are found to be similar, indicating that the smoothed values are still useful for determining the application rates. In some cases, noisy data arises from roadway characteristics of the maintenance route. When the plow trucks drive over bridge joints, the suspension rises and falls, causing the bed scale sensors to report noisy weight values that can be correlated to the spikes in the raw bed scale weight data. Figure 6.4 is developed to show this more clearly by focusing on a specific peak in the bed scale data and finding the corresponding location of the plow truck at that time :21:36 AM 3:22:02 AM 3:22:28 AM 3:22:54 AM Time Figure 6.4. Bed Scale Weight Noise when Driving over Bridge Joint in Summit County, Ohio, on February 3,