Period Order Quantity
|
|
- Elizabeth Randall
- 6 years ago
- Views:
Transcription
1 IE Chapter 5 Dynamic Lot Sizing Techniques 1 Dynamic Lot Sizing Methods Simple Rules Period order quantity Fixed period demand Lot for lot (L4L) Heuristic Methods Silver-Meal method (SM) Least Unit Cost (LUC) Part Period Balancing (PPB) Dynamic Programming (Optimum) Wagner-Whitin 2 1
2 A Prototype Example Suppose for a certain product type you need to produce weekly demand below: A = $50 per order H = $0.5 per unit per week Assumption: Lead time is known with certainty (fixed lead time) 3 Period Order Quantity The average lot size desired is divided by the average period demand For weekly demand given above evaluate POQ for Q = 140 units, and 275 units. 4 2
3 POQ-Example Solution Total demand over 8 periods = 975 units Average weekly demand = 975 / 8 = 122 units per week 5 POQ-Example Solution Continued Fixed period for order Q is determined as follows: Where, Q = desired order (lot) size = average demand over the planning period T = number of periods (time interval between orders) 6 3
4 POQ-Example Solution Continued For Q = 140 T = fixed period between orders = 140 /122 = 1.14 = 1 week Week Beginning Inventory Demand Order End Inventory Total Cost = 8 ($50) ($0.5) = $ POQ-Example Solution Continued For Q = 275 T = fixed period between orders = 275 /122 = 2.25 = 2 weeks Week Beginning Inventory Demand Order End Inventory Total Cost = 4 ($50) ($0.5) = $
5 Fixed Period Demand Ordering m periods of demand, m = selected fixed period For weekly demand given above evaluate FPD for T = 2 weeks, and 4 weeks. 9 FPD-Example Solution For T = 2 weeks Q1 = 175 units, Q3 = 375 units, Q5 = 250 units, Q7 = 175 units For T = 4 weeks Q1 = 550 units, Q5 = 425 unit 10 5
6 FPD-Example Solution for T=2 t Beginning Inventory Demand Q t End Inventory Total cost = 4 ($50) ($0.5) = $ FPD-Example Solution for T=4 t Beginning Inventory Demand Q t End Inventory Total cost = 2 ($50) ($0.5) = $
7 Lot For Lot Rule L4L The order quantity is always the demand for one period For weekly demand given above evaluate L4L rule 13 L4L-Example Solution Lot size per order: Q 1 = 100 units, Q 2 = 75 units, Q 3 = 175 units, Q 4 = 200 units Q 5 = 150 units, Q 6 = 100 units, Q 7 = 75 units, Q 8 = 100 units 14 7
8 L4L-Example Solution Continued t Beginning Inventory Demand Q t End Inventory Total cost = 8 ($50) + 0 ($0.5) = $ Silver-Meal Method Heuristic approach to aim at a low-cost solution that is not necessarily optimal Aim to achieve the minimum average cost per period for the m-period span. The average cost per period includes ordering and inventory holding costs 16 8
9 Silver-Meal Method The average cost per period is as follows: Where; m = number of demand periods to be ordered in the present time. A = fixed ordering cost per order H = inventory holding cost per unit per period K(m) = average cost per period during m periods 17 Silver-Meal Method Compute K(m) for m = 1,2,,m Stop when, K(m+1) > K(m), i.e. the period in which the average cost per period start to increase. Order the quantity equals to m periods demand. Q i = D 1 + D D m Q i is the quantity ordered in period i, and it covers m periods into the future. The process repeats at period (m+i) and continues through the planning horizon. 18 9
10 SM-Example Determine the order quantities for the following lumpy demands using Silver Meal algorithm A = $50 per order H = $0.5 per unit per week 19 For Q 1 : m=1, K(1) = 50 m=2, K(2) = 1/2 ( (75)) = < K(1) m=3, K(3) = 1/3 ( (75) + (2)(0.5)(175)) = 87.6 > K(2) STOP m=2 is selected for Q 1 Q 1 = D 1 + D 2 Q 1 = = 175 units Next order should arrive in week 3, So continue for Q
11 For Q 3 : m=1, K(1) = 50 m=2, K(2) = 1/2 ( (200)) = 75 > K(1) STOP m=1 is selected for Q 3 Q 3 = D 3 Q 3 = 175 unit Next order should arrive in week 4, So continue for Q 4 21 For Q 4 : Q 4 = D 4 Q 4 = 200 units 22 11
12 SM-Example Solution Continued t Beginning Inventory Demand Q t End Inventory Total cost = 3 ($50) + 75 ($0.5) = $ Least Unit Cost Similar to SM algorithm except for the total cost calculation K( m) A hd 2hD... ( m 1) hd 2 3 m D D D... D m The stopping rule: K(m+1) > K(m) Order for m periods into the future : Q i = D 1 + D D m Continue from period (m+i) : Q (m+i) 24 12
13 LUC-Example Determine the order quantities for the following lumpy demands using Least Unit Cost method A = $50 per order H = $0.5 per unit per week 25 Part Period Balance Part Period (PP) is defined as the number of the inventory carrying periods. PP balancing is the quantity ordered which balance the A and H. PP m) D 2D... ( m 1) ( 2 3 PPF A H D m Economic part period factor The stopping rule: PP(m+1) > PPF Order for m periods into the future : Q i = D 1 + D D m Continue from period (m+1) : Q (m+1) 26 13
14 PPB-Example Determine the order quantities for the following lumpy demands using Part Period Balancing method A = $50 per order H = $0.5 per unit per week 27 Wagner-Whitin Algorithm WW is an optimization procedure based on dynamic programming to find optimum order quantity policy Q i with a minimum cost solution. WW evaluates all possible ways of ordering to cover demand in each period of the planning horizon. Wagner-Whitin replaces EOQ for the case of lumpy demand
15 Wagner-Whitin Algorithm Cost of placing order: Where; K(t,m) = total cost of quantity ordered at period t for m periods A = ordering cost, H = inventory holding cost per unit per period D j = demand at period j t = 1,2,..,N and m = t,t+1,t+2,,n 29 Wagner-Whitin Algorithm For each period minimum cost is defined as: K*(m) = min t = 1,2,,m {K*(t-1) + K(t,m)} K*(0) = 0 K*(N) is defined as the least cost solution
16 WW-Example Solution A = $50 per order H = $0.5 per unit per week 31 WW-Example Solution For m=2 K*(2) = K*(0) = 0 For m=1 K*(1) = K*(0) + K(1,1) = 0 + A = 50 K*(0) + K(1,2) = 0 + (A+HD 2 ) = (75) = 87.5 min K*(1) + K(2,2) = 50 + A = = 100 K*(2) =
17 WW-Example Solution For m=3 K*(3) = min K*(3) = K*(0) + K(1,3) = 0+[50+0.5(75)+2(0.5)(175)]=262.5 K*(1) + K(2,3) = 50 +[50+0.5(175)]= K*(2) + K(3,3) = = K*(0) + K(1,m) K*(1) + K(2,m) should not be considered for m>3 33 WW-Example Solution For m=4 K*(2) + K(3,4) = [50+0.5(200)]= K*(4) = min K*(3) + K(4,4) = = K*(4) = K*(2) + K(3,m) should not be considered for m>
18 WW-Example Solution For m=4 K*(2) + K(3,4) = [50+0.5(200)]= K*(4) = min K*(3) + K(4,4) = = K*(4) = Q 4 = D 4 = 200 Continue with K*(3) 35 WW-Example Solution For m=3 K*(3) = min K*(3) = K*(0) + K(1,3) = 0+[50+0.5(75)+2(0.5)(175)]=262.5 K*(1) + K(2,3) = 50 +[50+0.5(175)]= K*(2) + K(3,3) = = Q 3 = D 3 = 175 Continue with K*(2) 36 18
19 WW-Example Solution For m=2 K*(2) = min K*(0) + K(1,2) = 0 + (A+HD 2 ) = (75) = 87.5 K*(1) + K(2,2) = 50 + A = = 100 K*(2) = 87.5 Q 1 = D 1 + D 2 = WW-Example Solution t Beginning Inventory Demand Q t End Inventory Total cost = 3 ($50) + 75 ($0.5) = $
A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters
A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters Wilco van den Heuvel a, Albert P.M. Wagelmans a a Econometric Institute and Erasmus Research Institute of Management,
More informationA Note on Ending Inventory Valuation in Multiperiod. Production Scheduling
A Note on Ending Inventory Valuation in Multiperiod Production Scheduling Wilco van den Heuvel Albert P.M. Wagelmans 1 Econometric Institute Report EI 2002-25 Econometric Institute, Erasmus University
More informationWorst case analysis for a general class of on-line lot-sizing heuristics
Worst case analysis for a general class of on-line lot-sizing heuristics Wilco van den Heuvel a, Albert P.M. Wagelmans a a Econometric Institute and Erasmus Research Institute of Management, Erasmus University
More informationMitigating end-effects in Production Scheduling
Mitigating end-effects in Production Scheduling Bachelor Thesis Econometrie en Operationele Research Ivan Olthuis 359299 Supervisor: Dr. Wilco van den Heuvel June 30, 2014 Abstract In this report, a solution
More informationISyE 6201: Manufacturing Systems Instructor: Spyros Reveliotis Spring 2006 Solutions to Homework 1
ISyE 601: Manufacturing Systems Instructor: Spyros Reveliotis Spring 006 Solutions to Homework 1 A. Chapter, Problem 4. (a) D = 60 units/wk 5 wk/yr = 310 units/yr h = ic = 0.5/yr $0.0 = $0.005/ yr A =
More informationProduction Planning and Control
Production Planning and Control MAERIAL REQUIREMEN PLANNING Haeryip Sihombing BMFP 453 4 Universiti eknikal Malaysia Melaka (UeM) HAERY SIHOMBING First widely available software implementation of a manufacturing
More informationReplenishment Planning for Stochastic Inventory System with Shortage Cost
Replenishment Planning for Stochastic Inventory System with Shortage Cost Roberto Rossi UCC, Ireland S. Armagan Tarim HU, Turkey Brahim Hnich IUE, Turkey Steven Prestwich UCC, Ireland Inventory Control
More informationA Fuzzy Inventory Model. Without Shortages Using. Triangular Fuzzy Number
Chapter 3 A Fuzzy Inventory Model Without Shortages Using Triangular Fuzzy Number 3.1 Introduction In this chapter, an inventory model without shortages has been considered in a fuzzy environment. Triangular
More informationA Non-Random Optimization Approach to a Disposal Mechanism Under Flexibility and Reliability Criteria
The Open Operational Research Journal, 2011, 5, 1-18 1 Open Access A Non-Random Optimization Approach to a Disposal echanism Under Flexibility and Reliability Criteria P.K. Tripathy 1 and. Pattnaik *,2
More informationSingle-part-type, multiple stage systems
MIT 2.853/2.854 Introduction to Manufacturing Systems Single-part-type, multiple stage systems Stanley B. Gershwin Laboratory for Manufacturing and Productivity Massachusetts Institute of Technology Single-stage,
More information1 Production Planning with Time-Varying Demand
IEOR 4000: Production Management Columbia University Professor Guillermo Gallego 28 September 1 Production Planning with Time-Varying Demand In this lecture we present a few key results in production planning
More informationOptimal Control of Stochastic Inventory System with Multiple Types of Reverse Flows. Xiuli Chao University of Michigan Ann Arbor, MI 48109
Optimal Control of Stochastic Inventory System with Multiple Types of Reverse Flows Xiuli Chao University of Michigan Ann Arbor, MI 4809 NCKU Seminar August 4, 009 Joint work with S. Zhou and Z. Tao /44
More informationInventory optimization of distribution networks with discrete-event processes by vendor-managed policies
Inventory optimization of distribution networks with discrete-event processes by vendor-managed policies Simona Sacone and Silvia Siri Department of Communications, Computer and Systems Science University
More informationABCβ A Heuristic for Dynamic Capacitated Lot Sizing with Random Demand under a Fillrate Constraint
ABCβ A Heuristic for Dynamic Capacitated Lot Sizing with Random Demand under a Fillrate Constraint Horst Tempelmeier, Sascha Herpers To cite this version: Horst Tempelmeier, Sascha Herpers. ABCβ A Heuristic
More information1 Production Planning with Time-Varying Demand
IEOR 4000: Production Management Columbia University Professor Guillermo Gallego 28 September 1 Production Planning with Time-Varying Demand In this lecture we present a few key results in production planning
More informationFaster Primal-Dual Algorithms for the Economic Lot-Sizing Problem
Acknowledgment: Thomas Magnanti, Retsef Levi Faster Primal-Dual Algorithms for the Economic Lot-Sizing Problem Dan Stratila RUTCOR and Rutgers Business School Rutgers University Mihai Pătraşcu AT&T Research
More informationCAPACITATED LOT-SIZING PROBLEM WITH SETUP TIMES, STOCK AND DEMAND SHORTAGES
CAPACITATED LOT-SIZING PROBLEM WITH SETUP TIMES, STOCK AND DEMAND SHORTAGES Nabil Absi,1 Safia Kedad-Sidhoum Laboratoire d Informatique d Avignon, 339 chemin des Meinajariès, 84911 Avignon Cedex 09, France
More informationMSA 640 Homework #2 Due September 17, points total / 20 points per question Show all work leading to your answers
Name MSA 640 Homework #2 Due September 17, 2010 100 points total / 20 points per question Show all work leading to your answers 1. The annual demand for a particular type of valve is 3,500 units. The cost
More informationInventory Management of Time Dependent. Deteriorating Items with Salvage Value
Applied Mathematical Sciences, Vol., 008, no. 16, 79-798 Inventory Management of ime Dependent Deteriorating Items with Salvage Value Poonam Mishra and Nita H. Shah* Department of Mathematics, Gujarat
More informationValid Inequalities for the Proportional Lotsizing and Scheduling Problem with Fictitious Microperiods. Waldemar Kaczmarczyk
Valid Inequalities for the Proportional Lotsizing and Scheduling Problem with Fictitious Microperiods Waldemar Kaczmarczyk Department of Operations Research AGH University of Science and Technology Kraków,
More informationKybernetika. Terms of use: Persistent URL: Institute of Information Theory and Automation AS CR, 2012
Kybernetika Kjetil K. Haugen; Guillaume Lanquepin-Chesnais; Asmund Olstad A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures Kybernetika, Vol. 48
More informationResearch Article A Deterministic Inventory Model of Deteriorating Items with Two Rates of Production, Shortages, and Variable Production Cycle
International Scholarly Research Network ISRN Applied Mathematics Volume 011, Article ID 657464, 16 pages doi:10.540/011/657464 Research Article A Deterministic Inventory Model of Deteriorating Items with
More informationCoordinated Replenishments at a Single Stocking Point
Chapter 11 Coordinated Replenishments at a Single Stocking Point 11.1 Advantages and Disadvantages of Coordination Advantages of Coordination 1. Savings on unit purchase costs.. Savings on unit transportation
More informationPolynomial time algorithms for the Minimax Regret Uncapacitated Lot Sizing Model
Polynomial time algorithms for the Minimax Regret Uncapacitated Lot Sizing Model Dong Li a,, Dolores Romero Morales a a Säid Business School, University of Oxford, Park End Street, Oxford, OX1 1HP, United
More informationA Primal-Dual Algorithm for Computing a Cost Allocation in the. Core of Economic Lot-Sizing Games
1 2 A Primal-Dual Algorithm for Computing a Cost Allocation in the Core of Economic Lot-Sizing Games 3 Mohan Gopaladesikan Nelson A. Uhan Jikai Zou 4 October 2011 5 6 7 8 9 10 11 12 Abstract We consider
More informationClassification of Dantzig-Wolfe Reformulations for MIP s
Classification of Dantzig-Wolfe Reformulations for MIP s Raf Jans Rotterdam School of Management HEC Montreal Workshop on Column Generation Aussois, June 2008 Outline and Motivation Dantzig-Wolfe reformulation
More informationSection 1.3: A Simple Inventory System
Section 1.3: A Simple Inventory System Discrete-Event Simulation: A First Course c 2006 Pearson Ed., Inc. 0-13-142917-5 Discrete-Event Simulation: A First Course Section 1.3: A Simple Inventory System
More informationDiscrete Event and Process Oriented Simulation (2)
B. Maddah ENMG 622 Simulation 11/04/08 Discrete Event and Process Oriented Simulation (2) Discrete event hand simulation of an (s, S) periodic review inventory system Consider a retailer who sells a commodity
More informationNew Bounds for the Joint Replenishment Problem: Tighter, but not always better
New Bounds for the Joint Replenishment Problem: ighter, but not always better Eric Porras, Rommert Dekker Econometric Institute, inbergen Institute, Erasmus University Rotterdam, P.O. Box 738, 3000 DR
More informationThe Subcoalition Perfect Core of Cooperative Games
The Subcoalition Perfect Core of Cooperative Games J. Drechsel and A. Kimms 1 August 2008 Address of correspondence: Julia Drechsel and Prof. Dr. Alf Kimms Lehrstuhl für Logistik und Verkehrsbetriebslehre
More informationEconomic lot-sizing games
Economic lot-sizing games Wilco van den Heuvel a, Peter Borm b, Herbert Hamers b a Econometric Institute and Erasmus Research Institute of Management, Erasmus University Rotterdam, P.O. Box 1738, 3000
More informationAn EPQ Model of Deteriorating Items using Three Parameter Weibull Distribution with Constant Production Rate and Time Varying Holding Cost"
An EPQ Model of Deteriorating Items using Three Parameter Weibull Distribution with Constant Production Rate and Time Varying Holding Cost" KIRTAN PARMAR, U. B. GOTHI Abstract - In this paper, we have
More informationPart A. Ch (a) Thus, order quantity is 39-12=27. (b) Now b=5. Thus, order quantity is 29-12=17
Homework2Solution Part A. Ch 2 12 (a) b = 65 40 = 25 from normal distribution table Thus, order quantity is 39-12=27 (b) Now b=5 from normal distribution table Thus, order quantity is 29-12=17 It is interesting
More informationAn Inventory Model for Gompertz Distribution Deterioration Rate with Ramp Type Demand Rate and Shortages
International Journal of Statistics and Systems ISSN 0973-675 Volume, Number (07), pp. 363-373 Research India Publications http://www.ripublication.com An Inventory Model for Gompertz Distribution Deterioration
More informationDecision Sciences, Vol. 5, No. 1 (January 1974)
Decision Sciences, Vol. 5, No. 1 (January 1974) A PRESENT VALUE FORMULATION OF THE CLASSICAL EOQ PROBLEM* Robert R. Trippi, California State University-San Diego Donald E. Lewin, Joslyn Manufacturing and
More informationIntroduction into Vehicle Routing Problems and other basic mixed-integer problems
Introduction into Vehicle Routing Problems and other basic mixed-integer problems Martin Branda Charles University in Prague Faculty of Mathematics and Physics Department of Probability and Mathematical
More informationARTICLE IN PRESS. Int. J. Production Economics ] (]]]]) ]]] ]]]
B2v:c GML4:: PROECO : Prod:Type:COM pp:2ðcol:fig::nilþ ED:JayashreeSanyasi PAGN: bmprakashscan: nil Int. J. Production Economics ] (]]]]) ]]] ]]] 2 2 2 4 4 4 Policies for inventory/distribution systems:
More informationAn Optimal Rotational Cyclic Policy for a Supply Chain System with Imperfect Matching Inventory and JIT Delivery
Proceedings of the 010 International onference on Industrial Engineering and Operations Management Dhaa, Bangladesh, January 9 10, 010 An Optimal Rotational yclic Policy for a Supply hain System with Imperfect
More informationA Proof of the EOQ Formula Using Quasi-Variational. Inequalities. March 19, Abstract
A Proof of the EOQ Formula Using Quasi-Variational Inequalities Dir Beyer y and Suresh P. Sethi z March, 8 Abstract In this paper, we use quasi-variational inequalities to provide a rigorous proof of the
More informationAn extended MIP formulation and dynamic cut generation approach for the stochastic lot sizing problem
Submitted to INFORMS Journal on Computing manuscript (Please, provide the mansucript number!) Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes
More informationAn optimal batch size for a production system under linearly increasing time-varying demand process
Computers & Industrial Engineering 4 (00) 35±4 www.elsevier.com/locate/dsw An optimal batch size for a production system under linearly increasing time-varying demand process Mohd Omar a, *, David K. Smith
More informationOptimal ordering policies for periodic-review systems with replenishment cycles
European Journal of Operational Research 17 (26) 44 56 Production, Manufacturing and Logistics Optimal ordering policies for periodic-review systems with replenishment cycles Chi Chiang * Department of
More informationName: MA 160 Dr. Katiraie (100 points) Test #3 Spring 2013
Name: MA 160 Dr. Katiraie (100 points) Test #3 Spring 2013 Show all of your work on the test paper. All of the problems must be solved symbolically using Calculus. You may use your calculator to confirm
More informationAn O(n 2 ) Algorithm for Lot Sizing with Inventory Bounds and Fixed Costs
An O(n 2 ) Algorithm for Lot Sizing with Inventory Bounds and Fixed Costs Alper Atamtürk and Simge Küçükyavuz September 4, 2007 Abstract We present an O(n 2 ) dynamic programming algorithm for lot sizing
More informationThe economic lot-sizing problem with an emission constraint
The economic lot-sizing problem with an emission constraint Mathijn J. Retel Helmrich,1, Raf Jans 2, Wilco van den Heuvel 1, and Albert P. M. Wagelmans 1 1 Erasmus School of Economics, Erasmus University
More informationMaximum-Profit Inventory Model with Stock-Dependent Demand, Time-Dependent Holding Cost, and All-Units Quantity Discounts
Mathematical Modelling and Analysis Publisher: Taylor&Francis and VGTU Volume 20 Number 6, November 2015, 715 736 http://www.tandfonline.com/tmma http://dx.doi.org/10.3846/13926292.2015.1108936 ISSN: 1392-6292
More informationFormulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds
International Journal of Production Research ISSN: 0020-7543 (Print) 1366-588X (Online) Journal homepage: http://www.tandfonline.com/loi/tprs20 Formulations and heuristics for the multi-item uncapacitated
More informationA Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains
A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains Florian Sahling, Institute of Production Management, Leibniz Universität Hannover, Germany, E-mail:
More informationA unified modeling approach for the static-dynamic uncertainty strategy in stochastic lot-sizing
A unified modeling approach for the static-dynamic uncertainty strategy in stochastic lot-sizing arxiv:1307.5942v5 [math.oc] 5 Feb 2014 Roberto Rossi,,1 Onur A. Kilic, 2 S. Armagan Tarim, 2 1 Business
More informationMechanical Engineering 101
Mechanical Engineering 101 University of alifornia, Berkeley Lecture #16 1 Today s lecture MRP scheduling LFL EOQ/EMQ POQ apacity planning 2 Formulae I it max{ 0, I i t 1 SR GR, it it } NR it max 0, GR
More informationPractical Tips for Modelling Lot-Sizing and Scheduling Problems. Waldemar Kaczmarczyk
Decision Making in Manufacturing and Services Vol. 3 2009 No. 1 2 pp. 37 48 Practical Tips for Modelling Lot-Sizing and Scheduling Problems Waldemar Kaczmarczyk Abstract. This paper presents some important
More informationCHAPTER 12. (The interpretation of the symbols used in the equations is given in page 3)
CHAPTER 12 The equations needed: (The interpretation of the symbols used in the equations is given in page 3) 1. ATI = t D 35 4. ws = I average weekly CU 2. I turn = CU I average 5. ds = I average daily
More informationAPPLICABILITY OF DETERMINISTIC INVENTORY MODELS TO SOLVE STOCHASTIC INVENTORY SYSTEMS A THESIS. Presented to. The Faculty of the Division of Graduate
APPLICABILITY OF DETERMINISTIC INVENTORY MODELS TO SOLVE STOCHASTIC INVENTORY SYSTEMS A THESIS Presented to The Faculty of the Division of Graduate Studies and Research By Orlando Enrique Medina Benatuil
More informationGoal Programming. Note: See problem for the problem statement. We assume that part-time (fractional) workers are allowed.
Goal Programming Note: See problem 13.13 for the problem statement. We assume that part-time (fractional) workers are allowed. Example 1: Preemptive Goal Programming The problem is currently stated as
More informationAN EOQ MODEL FOR TWO-WAREHOUSE WITH DETERIORATING ITEMS, PERIODIC TIME DEPENDENT DEMAND AND SHORTAGES
IJMS, Vol., No. 3-4, (July-December 0), pp. 379-39 Serials Publications ISSN: 097-754X AN EOQ MODEL FOR TWO-WAREHOUSE WITH DETERIORATING ITEMS, PERIODIC TIME DEPENDENT DEMAND AND SHORTAGES Karabi Dutta
More informationStochastic Optimization
Chapter 27 Page 1 Stochastic Optimization Operations research has been particularly successful in two areas of decision analysis: (i) optimization of problems involving many variables when the outcome
More informationPoint Process Control
Point Process Control The following note is based on Chapters I, II and VII in Brémaud s book Point Processes and Queues (1981). 1 Basic Definitions Consider some probability space (Ω, F, P). A real-valued
More informationOperations Research Letters. Joint pricing and inventory management with deterministic demand and costly price adjustment
Operations Research Letters 40 (2012) 385 389 Contents lists available at SciVerse ScienceDirect Operations Research Letters journal homepage: www.elsevier.com/locate/orl Joint pricing and inventory management
More informationAN APPROPRIATE LOT SIZING TECHNIQUE FOR INVENTORY POLICY PROBLEM WITH DECREASING DEMAND
AN APPROPRIATE LOT SIZING TECHNIQUE FOR INVENTORY POLICY PROBLEM WITH DECREASING DEMAND A THESIS Submitted in Partial Fulfillment of the Requirement for the Bachelor Degree of Engineering in Industrial
More informationOn the Convexity of Discrete (r, Q) and (s, T ) Inventory Systems
On the Convexity of Discrete r, Q and s, T Inventory Systems Jing-Sheng Song Mingzheng Wang Hanqin Zhang The Fuqua School of Business, Duke University, Durham, NC 27708, USA Dalian University of Technology,
More informationQ3) a) Explain the construction of np chart. b) Write a note on natural tolerance limits and specification limits.
(DMSTT 21) Total No. of Questions : 10] [Total No. of Pages : 02 M.Sc. DEGREE EXAMINATION, MAY 2017 Second Year STATISTICS Statistical Quality Control Time : 3 Hours Maximum Marks: 70 Answer any Five questions.
More informationAn Order Quantity Decision System for the Case of Approximately Level Demand
Capter 5 An Order Quantity Decision System for te Case of Approximately Level Demand Demand Properties Inventory problems exist only because tere are demands; oterwise, we ave no inventory problems. Inventory
More informationCalculation exercise 1 MRP, JIT, TOC and SOP. Dr Jussi Heikkilä
Calculation exercise 1 MRP, JIT, TOC and SOP Dr Jussi Heikkilä Problem 1: MRP in XYZ Company fixed lot size Item A Period 1 2 3 4 5 6 7 8 9 10 Gross requirements 71 46 49 55 52 47 51 48 56 51 Scheduled
More informationA Mathematical (Mixed-Integer) Programming Formulation for. Microbrewery. Spyros A. Reveliotis. Spring 2001
A Mathematical (Mixed-Integer) Programming Formulation for the Production Scheduling Problem in the McGuinness & Co. Microbrewery Spyros A. Reveliotis Spring 2001 This document provides an analytical formulation
More informationEffect of repair cost on the rework decision-making in an economic production quantity model
Effect of repair cost on the rework decision-making in an economic production quantity model Singa Wang Chiu Department of Business Administration Chaoyang University of Technology 68, Gifeng E. Rd. Wufeng,
More information2007/48. Single Item Lot-Sizing with Non-Decreasing Capacities
CORE DISCUSSION PAPER 2007/48 Single Item Lot-Sizing with Non-Decreasing Capacities Yves Pochet 1 and Laurence A. Wolsey 2 June 2007 Abstract We consider the single item lot-sizing problem with capacities
More informationFuzzy Inventory Model for Imperfect Quality Items with Shortages
Annals of Pure and Applied Mathematics Vol. 4, No., 03, 7-37 ISSN: 79-087X (P), 79-0888(online) Published on 0 October 03 www.researchmathsci.org Annals of Fuzzy Inventory Model for Imperfect Quality Items
More informationMulti level inventory management decisions with transportation cost consideration in fuzzy environment. W. Ritha, S.
Annals of Fuzzy Mathematics and Informatics Volume 2, No. 2, October 2011, pp. 171-181 ISSN 2093 9310 http://www.afmi.or.kr @FMI c Kyung Moon Sa Co. http://www.kyungmoon.com Multi level inventory management
More informationmin X φ X U (f φ )+ X
. 1 Review of wired optimization {φ:l P (φ)} f φ R l where R l is the capacity of link l. L (f,µ) = φ q (µ) =inf f φ =inf f φ = φ min φ U (f φ )+ µ l U (f φ )+ µ l φ U (f φ )+ φ l inf f φ U (f φ )+f φ
More informationSHORT TERM LOAD FORECASTING
Indian Institute of Technology Kanpur (IITK) and Indian Energy Exchange (IEX) are delighted to announce Training Program on "Power Procurement Strategy and Power Exchanges" 28-30 July, 2014 SHORT TERM
More informationDynamic Pricing for Non-Perishable Products with Demand Learning
Dynamic Pricing for Non-Perishable Products with Demand Learning Victor F. Araman Stern School of Business New York University René A. Caldentey DIMACS Workshop on Yield Management and Dynamic Pricing
More informationBuyer - Vendor incentive inventory model with fixed lifetime product with fixed and linear back orders
National Journal on Advances in Computing & Management Vol. 5 No. 1 April 014 1 Buyer - Vendor incentive inventory model with fixed lifetime product with fixed and linear back orders M.Ravithammal 1 R.
More informationK L_. ef A-9 LE.13ASMUS UNIVERSITY ROTTERDAM - P.O. BOX DR ROTTERDAM - THE NETHERLANDS. WilffOR*Wilw
1071 1 1 JLJ_J K L_ 1 WilffOR*Wilw A BAYESIAN LEARNING PROCEDURE FOR THE (s,q) INVENTORY POLICY C.G.E. BOENDER AND A.H.G. RINNOOY KAN REPORT 8966/A ef.---6-2. 0441A-9 LE.13ASMUS UNIVERSITY ROTTERDAM -
More information7.1 INTRODUCTION. In this era of extreme competition, each subsystem in different
7.1 INTRODUCTION In this era of extreme competition, each subsystem in different echelons of integrated model thrives to improve their operations, reduce costs and increase profitability. Currently, the
More informationA Multi-Item Inventory Control Model for Perishable Items with Two Shelves
The Eighth International Symposium on Operations Research and Its Applications (ISORA 9) Zhangjiajie, China, September 2 22, 29 Copyright 29 ORSC & APORC, pp. 36 314 A Multi-Item Inventory Control Model
More informationA Class of Random Algorithms for Inventory Cycle Offsetting
A Class of Random Algorithms for Inventory Cycle Offsetting Ernest Croot Department of Mathematics Georgia Institute of Technology Atlanta, GA 30332, U.S.A. ecroot@math.gatech.edu Kai Huang School of Management
More informationProduction Inventory Model with Different Deterioration Rates Under Linear Demand
IOSR Journal of Engineering (IOSRJEN) ISSN (e): 50-0, ISSN (p): 78-879 Vol. 06, Issue 0 (February. 06), V PP 7-75 www.iosrjen.org Production Inventory Model with Different Deterioration Rates Under Linear
More informationM.Sc. (Final) DEGREE EXAMINATION, MAY Final Year. Statistics. Paper I STATISTICAL QUALITY CONTROL. Answer any FIVE questions.
(DMSTT ) M.Sc. (Final) DEGREE EXAMINATION, MAY 0. Final Year Statistics Paper I STATISTICAL QUALITY CONTROL Time : Three hours Maximum : 00 marks Answer any FIVE questions. All questions carry equal marks..
More informationM.Sc FINAL YEAR (CDE) ASSIGNMENT SUBJECT : STATISTICS Paper-I : STATISTICAL INFERENCE
M.Sc FINAL YEAR (CDE) ASSIGNMENT SUBJECT : STATISTICS Paper-I : STATISTICAL INFERENCE I. Give the correct choice of the Answer like a or b etc in the brackets provided against the question. Each question
More informationEconomics 2: Growth (Growth in the Solow Model)
Economics 2: Growth (Growth in the Solow Model) Lecture 3, Week 7 Solow Model - I Definition (Solow Model I) The most basic Solow model with no population growth or technological progress. Solow Model
More informationExtreme Point Solutions for Infinite Network Flow Problems
Extreme Point Solutions for Infinite Network Flow Problems H. Edwin Romeijn Dushyant Sharma Robert L. Smith January 3, 004 Abstract We study capacitated network flow problems with supplies and demands
More informationOptimal stock allocation in single echelon inventory systems subject to a service constraint
Abstract number: 011-0137 Optimal stock allocation in single echelon inventory systems subject to a service constraint Annalisa Cesaro Dario Pacciarelli Dipartimento di Informatica e Automazione, Università
More informationLesson 27 Linear Programming; The Simplex Method
Lesson Linear Programming; The Simplex Method Math 0 April 9, 006 Setup A standard linear programming problem is to maximize the quantity c x + c x +... c n x n = c T x subject to constraints a x + a x
More information3E4: Modelling Choice. Introduction to nonlinear programming. Announcements
3E4: Modelling Choice Lecture 7 Introduction to nonlinear programming 1 Announcements Solutions to Lecture 4-6 Homework will be available from http://www.eng.cam.ac.uk/~dr241/3e4 Looking ahead to Lecture
More informationOnline bin packing with delay and holding costs
Online bin packing with delay and holding costs Lauri Ahlroth, André Schumacher, Pekka Orponen Aalto University School of Science, Department of Information and Computer Science and Helsinki Institute
More informationh Edition Money in Search Equilibrium
In the Name of God Sharif University of Technology Graduate School of Management and Economics Money in Search Equilibrium Diamond (1984) Navid Raeesi Spring 2014 Page 1 Introduction: Markets with Search
More informationSimulation of less master production schedule nervousness model
Simulation of less master production schedule nervousness model Carlos Herrera, André Thomas To cite this version: Carlos Herrera, André Thomas. Simulation of less master production schedule nervousness
More informationA LAGRANGEAN DECOMPOSITION ALGORITHM FOR MULTI-ITEM LOT-SIZING PROBLEMS WITH JOINT PURCHASING AND TRANSPORTATION DISCOUNTS 1. Alain Martel.
A LAGRANGEAN DECOMPOSITION ALGORITHM FOR MULTI-ITEM LOT-SIZING PROBLEMS WITH JOINT PURCHASING AND TRANSPORTATION DISCOUNTS 1 Alain Martel Nafee Rizk Amar Ramudhin Network Enterprise Technology Research
More informationOnline Appendices: Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information
Online Appendices: Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information Christian Howard christian.howard@vti.se VTI - The Swedish National Road and Transport
More informationF E M M Faculty of Economics and Management Magdeburg
OTTO-VON-GUERICKE-UNIVERSITY MAGDEBURG FACULTY OF ECONOMICS AND MANAGEMENT On the alignment of lot sizing decisions in a remanufacturing system in the presence of random yield Tobias Schulz Ivan Ferretti
More informationInventory Model (Karlin and Taylor, Sec. 2.3)
stochnotes091108 Page 1 Markov Chain Models and Basic Computations Thursday, September 11, 2008 11:50 AM Homework 1 is posted, due Monday, September 22. Two more examples. Inventory Model (Karlin and Taylor,
More informationResearch Article Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount
Mathematical Problems in Engineering Volume 2012, Article ID 582323, 21 pages doi:10.1155/2012/582323 Research Article Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems
More information1 Positive Ordering Costs
IEOR 4000: Production Management Professor Guillermo Gallego November 15, 2004 1 Positive Ordering Costs 1.1 (Q, r) Policies Up to now we have considered stochastic inventory models where decisions are
More informationEOQ Model for Weibull Deteriorating Items with Linear Demand under Permissable Delay in Payments
International Journal of Computational Science and Mathematics. ISSN 0974-389 Volume 4, Number 3 (0), pp. 75-85 International Research Publication House http://www.irphouse.com EOQ Model for Weibull Deteriorating
More informationEconomics 2010c: Lectures 9-10 Bellman Equation in Continuous Time
Economics 2010c: Lectures 9-10 Bellman Equation in Continuous Time David Laibson 9/30/2014 Outline Lectures 9-10: 9.1 Continuous-time Bellman Equation 9.2 Application: Merton s Problem 9.3 Application:
More informationRobust Storage Assignment in Unit-Load Warehouses
Robust Storage Assignment in Unit-Load Warehouses Marcus Ang Yun Fong Lim Melvyn Sim Lee Kong Chian School of Business, Singapore Management University, 5 Stamford Road, Singapore 178899, Singapore NUS
More informationStochastic Shortest Path Problems
Chapter 8 Stochastic Shortest Path Problems 1 In this chapter, we study a stochastic version of the shortest path problem of chapter 2, where only probabilities of transitions along different arcs can
More informationDiscrete lot sizing and scheduling on parallel machines: description of a column generation approach
126 IO 2013 XVI Congresso da Associação Portuguesa de Investigação Operacional Discrete lot sizing and scheduling on parallel machines: description of a column generation approach António J.S.T. Duarte,
More informationSolving a Multi-Level Capacitated Lot Sizing. Problem with Multi-Period Setup Carry-Over via a. Fix-and-Optimize Heuristic
Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic Florian Sahling a, Lisbeth Buschkühl b, Horst Tempelmeier b and Stefan Helber a
More informationFormulation for less master production schedule instability under rolling horizon
Formulation for less master production schedule instability under rolling horizon Carlos Herrera, André Thomas To cite this version: Carlos Herrera, André Thomas. Formulation for less master production
More information