MSA 640 Homework #2 Due September 17, points total / 20 points per question Show all work leading to your answers
|
|
- Marianna Wilkinson
- 5 years ago
- Views:
Transcription
1 Name MSA 640 Homework #2 Due September 17, 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 of each valve is $70, and the inventory carrying cost is 10% of the cost of each valve. The average ordering cost is $21 per order. Furthermore, it takes about two weeks (assume a 7-day week) for an order to arrive from the supplier, and during this time, the daily demand for valves is approximately 12. Use additional paper if necessary. N.B.: See the last page of the exam for a list of essential formulas. (a) (5 points) What is the EOQ? (144.91) (b) (3 points) What is the reorder point? (168) (c) (6 points) What is the average inventory? (72.46) What is the annual holding cost? (507.2) (d) (6 points) How many orders per year would be placed? (24.15) What is the annual ordering cost? (507.2) Page 1 of 5
2 Name 2. Consider the following linear programming problem: Maximize 10X + 12Y Subject to: 14X + 3Y 210 3X + 6Y 180 all variables 0 (a) Create a graphical LP solution on the attached graph paper, show the feasible region, and label the corner points. Show calculations for plotting the constraints and use simultaneous linear equations to determine corner point(s) when necessary. Use additional paper or the reverse of this sheet if necessary. Calculations for Plotting Constraints Calculations for Simultaneous Linear Equations Calculations for Corner Points (b) Compute values for all corner points and identify the maximum possible value for the objective function. (max value 398.4) Corner X Y Value A B C D Page 2 of 5
3 Problem
4 Name 3. Consider the following linear programming problem: Maximize 16X + 17Y Subject to: 8X + 4Y X + 6Y 780 9X + 12Y 1080 all variables 0 (a) Create a graphical LP solution on the attached graph paper, show the feasible region, and label the corner points. Show calculations for plotting the constraints and use simultaneous linear equations to determine corner point(s) when necessary. Use additional paper or the reverse of this sheet if necessary. Calculations for Plotting Constraints Calculations for Simultaneous Linear Equations Calculations for Corner Points (b) Compute values for all corner points and identify the maximum possible value for the objective function. (max value 1,566.3) Corner X Y Value A B C D E Page 3 of 5
5 Problem
6 Name 4. A development project has 13 major activities. The estimated times for the activities appear on the attached PERT Network. (a) Compute the ES, EF, LS, LF values and fill in the network chart. (b) What is the expected completion time for this project? (44) (c) Find the critical path for this project by computing slack times. (C E F H I K-M) (d) Assuming that the standard deviation is 3.2, what is the probability that the project will be finished in fewer than 46 weeks? Finish drawing and labeling the following normal curve to represent your solution. (0.73) Probability Calculations Page 4 of 5
7 PERT/CPM Project Network for Problem #4 Project Completion Time: Critical Path: Project Standard Deviation: 3.2 A 6 D 4 L 2 F 7 H 8 J 4 Start B 5 Finish G 4 I 5 K 3 C 8 E 9 M 4
8 Name 5. Automobiles arrive at the drive-through window at a fast food store at the rate of 7 every 10 minutes. The average service time is 10 every 12 minutes. The arrival rate is Poisson distributed and the service time is exponentially distributed. (a) (4 points) What are the values for lambda (λ) and mu (µ)? (42, 50 per hour) (b) (2 points) What is the average time a car is in the system? (0.13 hour or 7.5 minutes) (c) (2 points) What is the average number of cars in the system? (5.25) (d) (2 points) What is the average time that cars spend waiting in line to receive service? (e) (2 points) What is the average number of cars waiting in line to receive service? (f) (3 points) What is the probability that there are no cars at the food store? (0.16) (g) (2 points) What percentage of the time is the food store busy? (h) (3 points) What is the probability that there are more than 2 cars in the system? (0.59) Page 5 of 5
9 Homework 2 Essential Formulas Chapter 6 Inventory Control Models Annual Ordering Cost Annual Holding Cost Economic Order Quantity C h = I * C Reorder Point D Co Q Q C h 2 * 2 D C EOQ = Q = C EOQ = Q * = h 2 D C ROP = d L Average Inventory Q / 2 Optimal # of Orders/Year D / Q Example of Objective Function Example of Constraints Graphical Approach Corner Point Solution Chapter 7 Linear Programming 20X + 35Y I C 15X + 25Y X + 18Y 825 Determine where constraints cross axes Plot constraints Determine feasible region Determine corner points Use simultaneous equations if necessary Apply Objective Function to corner points Determine Optimal Solution o o Earliest finish time Earliest start time Latest start time Latest finish time Critical Path Probability of Project Completion Chapter 13 PERT Project Management EF = ES + time ES = largest EF of immediate predecessors LS = LF time LF = Smallest LS of following activities (1) Slack = LS ES or Slack = LF EF (2) Activities with Slack = 0 are critical activities and are on the critical path Use project completion time for the mean and the standard deviation. Z = X µ σ Chapter 14 Waiting Lines and Queuing Theory Models M/M/1 Average number in the system: Average length of the queue: Average time in the system: λ L = µ λ λ Lq = µ ( µ λ) 2 W = 1 µ λ λ Average time in the queue: Wq = µ ( µ λ) Percentage of time the system is idle: Utilization of the system: Probability number in the system > k: P 0 λ ρ = µ P n λ = 1 µ λ > k = µ k+1
10 Normal Distribution Table Z
CHAPTER 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 informationYORK UNIVERSITY FACULTY OF ARTS DEPARTMENT OF MATHEMATICS AND STATISTICS MATH , YEAR APPLIED OPTIMIZATION (TEST #4 ) (SOLUTIONS)
YORK UNIVERSITY FACULTY OF ARTS DEPARTMENT OF MATHEMATICS AND STATISTICS Instructor : Dr. Igor Poliakov MATH 4570 6.0, YEAR 2006-07 APPLIED OPTIMIZATION (TEST #4 ) (SOLUTIONS) March 29, 2007 Name (print)
More informationQueuing Theory. Using the Math. Management Science
Queuing Theory Using the Math 1 Markov Processes (Chains) A process consisting of a countable sequence of stages, that can be judged at each stage to fall into future states independent of how the process
More information11/8/2018. Overview. PERT / CPM Part 2
/8/08 PERT / CPM Part BSAD 0 Dave Novak Fall 08 Source: Anderson et al., 0 Quantitative Methods for Business th edition some slides are directly from J. Loucks 0 Cengage Learning Overview Last class introduce
More informationλ λ λ In-class problems
In-class problems 1. Customers arrive at a single-service facility at a Poisson rate of 40 per hour. When two or fewer customers are present, a single attendant operates the facility, and the service time
More informationQueuing Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall
Queuing Analysis Chapter 13 13-1 Chapter Topics Elements of Waiting Line Analysis The Single-Server Waiting Line System Undefined and Constant Service Times Finite Queue Length Finite Calling Problem The
More informationOperations Management
Universidade Nova de Lisboa Faculdade de Economia Oerations Management Winter Semester 009/010 First Round Exam January, 8, 009, 8.30am Duration: h30 RULES 1. Do not searate any sheet. Write your name
More informationOperations Management
Universidade Nova de Lisboa Faculdade de Economia Oerations Management Winter Semester 010/011 Second Round Exam January 6, 011, 5.30.m Duration: h30 RULES 1. Do not searate any sheet. Write your name
More informationA scheme developed by Du Pont to figure out
CPM Project Management scheme. A scheme developed by Du Pont to figure out Length of a normal project schedule given task durations and their precedence in a network type layout (or Gantt chart) Two examples
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 informationASSIGNMENT - 1 M.Sc. DEGREE EXAMINATION, MAY 2019 Second Year STATISTICS. Statistical Quality Control MAXIMUM : 30 MARKS ANSWER ALL QUESTIONS
ASSIGNMENT - 1 Statistical Quality Control (DMSTT21) Q1) a) Explain the role and importance of statistical quality control in industry. b) Explain control charts for variables. Write the LCL, UCL for X,
More informationGeneration of Discrete Random variables
Simulation Simulation is the imitation of the operation of a realworld process or system over time. The act of simulating something first requires that a model be developed; this model represents the key
More informationChapter 5: Special Types of Queuing Models
Chapter 5: Special Types of Queuing Models Some General Queueing Models Discouraged Arrivals Impatient Arrivals Bulk Service and Bulk Arrivals OR37-Dr.Khalid Al-Nowibet 1 5.1 General Queueing Models 1.
More informationEssential Question: How are the mean and the standard deviation determined from a discrete probability distribution?
Probability and Statistics The Binomial Probability Distribution and Related Topics Chapter 5 Section 1 Introduction to Random Variables and Probability Distributions Essential Question: How are the mean
More informationSolutions to COMP9334 Week 8 Sample Problems
Solutions to COMP9334 Week 8 Sample Problems Problem 1: Customers arrive at a grocery store s checkout counter according to a Poisson process with rate 1 per minute. Each customer carries a number of items
More information57:022 Principles of Design II Final Exam Solutions - Spring 1997
57:022 Principles of Design II Final Exam Solutions - Spring 1997 Part: I II III IV V VI Total Possible Pts: 52 10 12 16 13 12 115 PART ONE Indicate "+" if True and "o" if False: + a. If a component's
More informationIEOR 4106: Spring Solutions to Homework Assignment 7: Due on Tuesday, March 22.
IEOR 46: Spring Solutions to Homework Assignment 7: Due on Tuesday, March. More of Chapter 5: Read the rest of Section 5.3, skipping Examples 5.7 (Coupon Collecting), 5. (Insurance claims)and Subsection
More informationQueueing Systems: Lecture 3. Amedeo R. Odoni October 18, Announcements
Queueing Systems: Lecture 3 Amedeo R. Odoni October 18, 006 Announcements PS #3 due tomorrow by 3 PM Office hours Odoni: Wed, 10/18, :30-4:30; next week: Tue, 10/4 Quiz #1: October 5, open book, in class;
More informationNANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION MH4702/MAS446/MTH437 Probabilistic Methods in OR
NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION 2013-201 MH702/MAS6/MTH37 Probabilistic Methods in OR December 2013 TIME ALLOWED: 2 HOURS INSTRUCTIONS TO CANDIDATES 1. This examination paper contains
More informationST. JOSEPH S COLLEGE OF ARTS & SCIENCE (AUTONOMOUS) CUDDALORE-1
ST. JOSEPH S COLLEGE OF ARTS & SCIENCE (AUTONOMOUS) CUDDALORE-1 SUB:OPERATION RESEARCH CLASS: III B.SC SUB CODE:EMT617S SUB INCHARGE:S.JOHNSON SAVARIMUTHU 2 MARKS QUESTIONS 1. Write the general model of
More informationGraph the linear inequality. 1) x + 2y 6
Assignment 7.1-7.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequality. 1) x + 2y 6 1) 1 2) x + y < -3 2) 2 Graph the
More informationPREPARED BY: INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 PREPARED BY: A. SOMAIAH, ASST. PROFESSOR T. VANAJA, ASST. PROFESSOR DEPT. OF MECHANICAL ENGINEERING 1 Syllabus UNIT-I Development
More informationQuiz Queue II. III. ( ) ( ) =1.3333
Quiz Queue UMJ, a mail-order company, receives calls to place orders at an average of 7.5 minutes intervals. UMJ hires one operator and can handle each call in about every 5 minutes on average. The inter-arrival
More information5/15/18. Operations Research: An Introduction Hamdy A. Taha. Copyright 2011, 2007 by Pearson Education, Inc. All rights reserved.
The objective of queuing analysis is to offer a reasonably satisfactory service to waiting customers. Unlike the other tools of OR, queuing theory is not an optimization technique. Rather, it determines
More informationGoing from graphic solutions to algebraic
Going from graphic solutions to algebraic 2 variables: Graph constraints Identify corner points of feasible area Find which corner point has best objective value More variables: Think about constraints
More information10.2 For the system in 10.1, find the following statistics for population 1 and 2. For populations 2, find: Lq, Ls, L, Wq, Ws, W, Wq 0 and SL.
Bibliography Asmussen, S. (2003). Applied probability and queues (2nd ed). New York: Springer. Baccelli, F., & Bremaud, P. (2003). Elements of queueing theory: Palm martingale calculus and stochastic recurrences
More informationSpring 2018 IE 102. Operations Research and Mathematical Programming Part 2
Spring 2018 IE 102 Operations Research and Mathematical Programming Part 2 Graphical Solution of 2-variable LP Problems Consider an example max x 1 + 3 x 2 s.t. x 1 + x 2 6 (1) - x 1 + 2x 2 8 (2) x 1,
More informationISyE 2030 Practice Test 2
1 NAME ISyE 2030 Practice Test 2 Summer 2005 This test is open notes, open books. You have exactly 75 minutes. 1. Short-Answer Questions (a) TRUE or FALSE? If arrivals occur according to a Poisson process
More informationEE 368. Weeks 3 (Notes)
EE 368 Weeks 3 (Notes) 1 State of a Queuing System State: Set of parameters that describe the condition of the system at a point in time. Why do we need it? Average size of Queue Average waiting time How
More informationQueuing Theory. 3. Birth-Death Process. Law of Motion Flow balance equations Steady-state probabilities: , if
1 Queuing Theory 3. Birth-Death Process Law of Motion Flow balance equations Steady-state probabilities: c j = λ 0λ 1...λ j 1 µ 1 µ 2...µ j π 0 = 1 1+ j=1 c j, if j=1 c j is finite. π j = c j π 0 Example
More informationLinear Programming Test Review. Day 6
Linear Programming Test Review Day 6 Warm-Up: Test Review Practice A machine can produce either nuts or bolts, but not both at the same time. The machine can be used at most 8 hours a day. Furthermore,
More informationExam of Discrete Event Systems
Exam of Discrete Event Systems - 04.02.2016 Exercise 1 A molecule can switch among three equilibrium states, denoted by A, B and C. Feasible state transitions are from A to B, from C to A, and from B to
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 informationPBW 654 Applied Statistics - I Urban Operations Research
PBW 654 Applied Statistics - I Urban Operations Research Lecture 2.I Queuing Systems An Introduction Operations Research Models Deterministic Models Linear Programming Integer Programming Network Optimization
More informationQueueTraffic and queuing theory
QueueTraffic and queuing theory + Queues in everyday life You have certainly been in a queue somewhere. Where? How were they different? At ticket vending machines, cash desks, at the doctors, at printers,
More information56:171 Operations Research Fall 1998
56:171 Operations Research Fall 1998 Quiz Solutions D.L.Bricker Dept of Mechanical & Industrial Engineering University of Iowa 56:171 Operations Research Quiz
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 information. Introduction to CPM / PERT Techniques. Applications of CPM / PERT. Basic Steps in PERT / CPM. Frame work of PERT/CPM. Network Diagram Representation. Rules for Drawing Network Diagrams. Common Errors
More informationI, A BRIEF REVIEW ON INFINITE QUEUE MODEL M.
A BRIEF REVIEW ON INFINITE QUEUE MODEL M. Vasuki*, A. Dinesh Kumar** & G. Vijayaprabha** * Assistant Professor, Department of Mathematics, Srinivasan College of Arts and Science, Perambalur, Tamilnadu
More informationCS 1538: Introduction to Simulation Homework 1
CS 1538: Introduction to Simulation Homework 1 1. A fair six-sided die is rolled three times. Let X be a random variable that represents the number of unique outcomes in the three tosses. For example,
More informationQueuing Theory. The present section focuses on the standard vocabulary of Waiting Line Models.
Queuing Theory Introduction Waiting lines are the most frequently encountered problems in everyday life. For example, queue at a cafeteria, library, bank, etc. Common to all of these cases are the arrivals
More informationReview Questions, Final Exam
Review Questions, Final Exam A few general questions 1. What does the Representation Theorem say (in linear programming)? 2. What is the Fundamental Theorem of Linear Programming? 3. What is the main idea
More informationExercises Solutions. Automation IEA, LTH. Chapter 2 Manufacturing and process systems. Chapter 5 Discrete manufacturing problems
Exercises Solutions Note, that we have not formulated the answers for all the review questions. You will find the answers for many questions by reading and reflecting about the text in the book. Chapter
More informationPerformance Evaluation of Queuing Systems
Performance Evaluation of Queuing Systems Introduction to Queuing Systems System Performance Measures & Little s Law Equilibrium Solution of Birth-Death Processes Analysis of Single-Station Queuing Systems
More information56:171 Operations Research Final Exam December 12, 1994
56:171 Operations Research Final Exam December 12, 1994 Write your name on the first page, and initial the other pages. The response "NOTA " = "None of the above" Answer both parts A & B, and five sections
More informationLinear Programming Test Review. Day 6
Linear Programming Test Review Day 6 Arrival Instructions Take out: Your homework, calculator, and the unit outline Pick up: 1. Warm-Up Test Review Day 2. Test Review HW Sheet A sponge Yes, it is different
More informationClassification of Queuing Models
Classification of Queuing Models Generally Queuing models may be completely specified in the following symbol form:(a/b/c):(d/e)where a = Probability law for the arrival(or inter arrival)time, b = Probability
More informationNetwork analysis. A project is a temporary endeavor undertaken to create a "unique" product or service
Network analysis Introduction Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects. One definition of a project
More informationFURTHER MATHEMATICS Units 3 & 4 - Written Examination 2
THIS BOX IS FOR ILLUSTRATIVE PURPOSES ONLY 2016 Examination Package - Trial Examination 4 of 5 Figures STUDENT NUMBER Letter Words FURTHER MATHEMATICS Units 3 & 4 - Written Examination 2 (TSSM s 2014 trial
More informationEECS 126 Probability and Random Processes University of California, Berkeley: Fall 2014 Kannan Ramchandran November 13, 2014.
EECS 126 Probability and Random Processes University of California, Berkeley: Fall 2014 Kannan Ramchandran November 13, 2014 Midterm Exam 2 Last name First name SID Rules. DO NOT open the exam until instructed
More informationII BSc(Information Technology)-[ ] Semester-III Allied:Computer Based Optimization Techniques-312C Multiple Choice Questions.
Dr.G.R.Damodaran College of Science (Autonomous, affiliated to the Bharathiar University, recognized by the UGC)Re-accredited at the 'A' Grade Level by the NAAC and ISO 9001:2008 Certified CRISL rated
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 informationRecord your answers and work on the separate answer sheet provided.
MATH 106 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually.
More informationMA 162: Finite Mathematics - Section 3.3/4.1
MA 162: Finite Mathematics - Section 3.3/4.1 Fall 2014 Ray Kremer University of Kentucky October 6, 2014 Announcements: Homework 3.3 due Tuesday at 6pm. Homework 4.1 due Friday at 6pm. Exam scores were
More informationComputer Networks More general queuing systems
Computer Networks More general queuing systems Saad Mneimneh Computer Science Hunter College of CUNY New York M/G/ Introduction We now consider a queuing system where the customer service times have a
More informationSince D has an exponential distribution, E[D] = 0.09 years. Since {A(t) : t 0} is a Poisson process with rate λ = 10, 000, A(0.
IEOR 46: Introduction to Operations Research: Stochastic Models Chapters 5-6 in Ross, Thursday, April, 4:5-5:35pm SOLUTIONS to Second Midterm Exam, Spring 9, Open Book: but only the Ross textbook, the
More informationMS-E2140. Lecture 1. (course book chapters )
Linear Programming MS-E2140 Motivations and background Lecture 1 (course book chapters 1.1-1.4) Linear programming problems and examples Problem manipulations and standard form problems Graphical representation
More informationOperations Research II, IEOR161 University of California, Berkeley Spring 2007 Final Exam. Name: Student ID:
Operations Research II, IEOR161 University of California, Berkeley Spring 2007 Final Exam 1 2 3 4 5 6 7 8 9 10 7 questions. 1. [5+5] Let X and Y be independent exponential random variables where X has
More informationPage 0 of 5 Final Examination Name. Closed book. 120 minutes. Cover page plus five pages of exam.
Final Examination Closed book. 120 minutes. Cover page plus five pages of exam. To receive full credit, show enough work to indicate your logic. Do not spend time calculating. You will receive full credit
More informationHomework 4 Math 11, UCSD, Winter 2018 Due on Tuesday, 13th February
PID: Last Name, First Name: Section: Approximate time spent to complete this assignment: hour(s) Homework 4 Math 11, UCSD, Winter 2018 Due on Tuesday, 13th February Readings: Chapters 16.6-16.7 and the
More informationName of the Student: Problems on Discrete & Continuous R.Vs
SUBJECT NAME : Probability & Queueing Theory SUBJECT CODE : MA 2262 MATERIAL NAME : Problem Material MATERIAL CODE : JM08AM1008 (Scan the above Q.R code for the direct download of this material) Name of
More informationIE 400 Principles of Engineering Management. Graphical Solution of 2-variable LP Problems
IE 400 Principles of Engineering Management Graphical Solution of 2-variable LP Problems Graphical Solution of 2-variable LP Problems Ex 1.a) max x 1 + 3 x 2 s.t. x 1 + x 2 6 - x 1 + 2x 2 8 x 1, x 2 0,
More informationDiscrete Event Systems Exam
Computer Engineering and Networks Laboratory TEC, NSG, DISCO HS 2016 Prof. L. Thiele, Prof. L. Vanbever, Prof. R. Wattenhofer Discrete Event Systems Exam Friday, 3 rd February 2017, 14:00 16:00. Do not
More informationA Study on Performance Analysis of Queuing System with Multiple Heterogeneous Servers
UNIVERSITY OF OKLAHOMA GENERAL EXAM REPORT A Study on Performance Analysis of Queuing System with Multiple Heterogeneous Servers Prepared by HUSNU SANER NARMAN husnu@ou.edu based on the papers 1) F. S.
More informationOperation management
Operation management Vigneron Loic December 3, 2008 1 Operations and productivity 1.1 Productivity Productivity = Units produced Imput used Units produced Labor productivity = Labor hours used One resource
More informationReview of Queuing Models
Review of Queuing Models Recitation, Apr. 1st Guillaume Roels 15.763J Manufacturing System and Supply Chain Design http://michael.toren.net/slides/ipqueue/slide001.html 2005 Guillaume Roels Outline Overview,
More informationMULTIPLE CHOICE QUESTIONS DECISION SCIENCE
MULTIPLE CHOICE QUESTIONS DECISION SCIENCE 1. Decision Science approach is a. Multi-disciplinary b. Scientific c. Intuitive 2. For analyzing a problem, decision-makers should study a. Its qualitative aspects
More informationTotal No. of Questions : 10] [Total No. of Pages : 02. M.Sc. DEGREE EXAMINATION, DEC Second Year STATISTICS. Statistical Quality Control
(DMSTT21) Total No. of Questions : 10] [Total No. of Pages : 02 M.Sc. DEGREE EXAMINATION, DEC. 2016 Second Year STATISTICS Statistical Quality Control Time : 3 Hours Maximum Marks : 70 Answer any five
More informationIE 5112 Final Exam 2010
IE 5112 Final Exam 2010 1. There are six cities in Kilroy County. The county must decide where to build fire stations. The county wants to build as few fire stations as possible while ensuring that there
More informationMath Week in Review #3 - Exam 1 Review
Math 166 Exam 1 Review Fall 2006 c Heather Ramsey Page 1 Math 166 - Week in Review #3 - Exam 1 Review NOTE: For reviews of the other sections on Exam 1, refer to the first page of WIR #1 and #2. Section
More informationCS418 Operating Systems
CS418 Operating Systems Lecture 14 Queuing Analysis Textbook: Operating Systems by William Stallings 1 1. Why Queuing Analysis? If the system environment changes (like the number of users is doubled),
More informationSession-Based Queueing Systems
Session-Based Queueing Systems Modelling, Simulation, and Approximation Jeroen Horters Supervisor VU: Sandjai Bhulai Executive Summary Companies often offer services that require multiple steps on the
More informationProgrammers A B C D Solution:
P a g e Q: A firm has normally distributed forecast of usage with MAD=0 units. It desires a service level, which limits the stock, out to one order cycle per year. Determine Standard Deviation (SD), if
More informationQUEUING MODELS AND MARKOV PROCESSES
QUEUING MODELS AND MARKOV ROCESSES Queues form when customer demand for a service cannot be met immediately. They occur because of fluctuations in demand levels so that models of queuing are intrinsically
More information57:022 Principles of Design II Midterm Exam #2 Solutions
57:022 Principles of Design II Midterm Exam #2 Solutions Part: I II III IV V Total Possible Pts: 20 15 12 16 12 75 PART ONE Indicate "+" if True and "O" if False: _+_a. If a component's lifetime has exponential
More informationPROGRAMMING CPM. Network Analysis. Goal:
PROGRAMMING CPM 5/21/13 Network Analysis Goal: Calculate completion time Calculate start and finish date for each activity Identify critical activities Identify requirements and flows of resources (materials,
More informationM.Sc. (Final) DEGREE EXAMINATION, MAY Final Year STATISTICS. Time : 03 Hours Maximum Marks : 100
(DMSTT21) M.Sc. (Final) DEGREE EXAMINATION, MAY - 2013 Final Year STATISTICS Paper - I : Statistical Quality Control Time : 03 Hours Maximum Marks : 100 Answer any Five questions All questions carry equal
More informationMS-E2140. Lecture 1. (course book chapters )
Linear Programming MS-E2140 Motivations and background Lecture 1 (course book chapters 1.1-1.4) Linear programming problems and examples Problem manipulations and standard form Graphical representation
More informationAnswers to selected exercises
Answers to selected exercises A First Course in Stochastic Models, Henk C. Tijms 1.1 ( ) 1.2 (a) Let waiting time if passengers already arrived,. Then,, (b) { (c) Long-run fraction for is (d) Let waiting
More informationName of the Student: Problems on Discrete & Continuous R.Vs
SUBJECT NAME : Probability & Queueing Theory SUBJECT CODE : MA 6453 MATERIAL NAME : Additional Problems MATERIAL CODE : JM08AM1004 REGULATION : R2013 UPDATED ON : March 2015 (Scan the above Q.R code for
More informationReview Questions, Final Exam
Review Questions, Final Exam A few general questions. What does the Representation Theorem say (in linear programming)? In words, the representation theorem says that any feasible point can be written
More informationThe Behavior of a Multichannel Queueing System under Three Queue Disciplines
The Behavior of a Multichannel Queueing System under Three Queue Disciplines John K Karlof John Jenkins November 11, 2002 Abstract In this paper we investigate a multichannel channel queueing system where
More informationProblem #1. The following matrices are augmented matrices of linear systems. How many solutions has each system? Motivate your answer.
Exam #4 covers the material about systems of linear equations and matrices (CH. 4.1-4.4, PART II); systems of linear inequalities in two variables (geometric approach) and linear programming (CH.5.1-5.2,
More informationCourse Outline Introduction to Transportation Highway Users and their Performance Geometric Design Pavement Design
Course Outline Introduction to Transportation Highway Users and their Performance Geometric Design Pavement Design Speed Studies - Project Traffic Queuing Intersections Level of Service in Highways and
More informationVELOCITY. If you have a graph of position and you take the derivative, what would the derivative represent? Position. Time
VELOCITY If you have a graph of position and you take the derivative, what would the derivative represent? Position Time Average rate of Change What is the average rate of change of temperature over the
More informationM.SC. MATHEMATICS - II YEAR
MANONMANIAM SUNDARANAR UNIVERSITY DIRECTORATE OF DISTANCE & CONTINUING EDUCATION TIRUNELVELI 627012, TAMIL NADU M.SC. MATHEMATICS - II YEAR DKM24 - OPERATIONS RESEARCH (From the academic year 2016-17)
More information57:022 Principles of Design II HW 96 Instructor: Dennis L Bricker
57:022 Principles of Design II Homework Assignments, Spring 1996 Prof. Dennis L Bricker, Dept. of Industrial Engineering University of Iowa HW #1 Be sure to state what probability distribution you assume
More informationAn M/M/1/N Queuing system with Encouraged Arrivals
Global Journal of Pure and Applied Mathematics. ISS 0973-1768 Volume 13, umber 7 (2017), pp. 3443-3453 Research India Publications http://www.ripublication.com An M/M/1/ Queuing system with Encouraged
More information56:171 Operations Research Final Examination December 15, 1998
56:171 Operations Research Final Examination December 15, 1998 Write your name on the first page, and initial the other pages. Answer both Parts A and B, and 4 (out of 5) problems from Part C. Possible
More informationBachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.)
AOR-01 ASSIGNMENT BOOKLET Bachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.) It is compulsory to submit the assignment before filling in the exam form.
More informationMATH 445/545 Homework 1: Due February 11th, 2016
MATH 445/545 Homework 1: Due February 11th, 2016 Answer the following questions Please type your solutions and include the questions and all graphics if needed with the solution 1 A business executive
More informationAP Calculus AB Course Syllabus
AP Calculus AB Course Syllabus Grant Community High School Mr. Rous Textbook Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. Calculus Graphical, Numerical, Algebraic, Fourth Addition,
More informationBasic Queueing Theory
After The Race The Boston Marathon is a local institution with over a century of history and tradition. The race is run on Patriot s Day, starting on the Hopkinton green and ending at the Prudential Center
More informationISyE 2030 Practice Test 1
1 NAME ISyE 2030 Practice Test 1 Summer 2005 This test is open notes, open books. You have exactly 90 minutes. 1. Some Short-Answer Flow Questions (a) TRUE or FALSE? One of the primary reasons why theoretical
More informationChapter 8 Queuing Theory Roanna Gee. W = average number of time a customer spends in the system.
8. Preliminaries L, L Q, W, W Q L = average number of customers in the system. L Q = average number of customers waiting in queue. W = average number of time a customer spends in the system. W Q = average
More informationChapter 3 Introduction to Linear Programming PART 1. Assoc. Prof. Dr. Arslan M. Örnek
Chapter 3 Introduction to Linear Programming PART 1 Assoc. Prof. Dr. Arslan M. Örnek http://homes.ieu.edu.tr/~aornek/ise203%20optimization%20i.htm 1 3.1 What Is a Linear Programming Problem? Linear Programming
More information9.5 THE SIMPLEX METHOD: MIXED CONSTRAINTS
SECTION 9.5 THE SIMPLEX METHOD: MIXED CONSTRAINTS 557 9.5 THE SIMPLEX METHOD: MIXED CONSTRAINTS In Sections 9. and 9., you looked at linear programming problems that occurred in standard form. The constraints
More informationDeterministic Operations Research, ME 366Q and ORI 391 Chapter 2: Homework #2 Solutions
Deterministic Operations Research, ME 366Q and ORI 391 Chapter 2: Homework #2 Solutions 11. Consider the following linear program. Maximize z = 6x 1 + 3x 2 subject to x 1 + 2x 2 2x 1 + x 2 20 x 1 x 2 x
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 informatione) Find the average revenue when 100 units are made and sold.
Math 142 Week in Review Set of Problems Week 7 1) Find the derivative, y ', if a) y=x 5 x 3/2 e 4 b) y= 1 5 x 4 c) y=7x 2 0.5 5 x 2 d) y=x 2 1.5 x 10 x e) y= x7 5x 5 2 x 4 2) The price-demand function
More information