An introduction to management science quantitive approaches to decision making 2nd by anderson

David R Anderson l Dennis J Sweeney Thomas A Williams l Mik Wisniewski AN INTRODUCTION TO MANAGEMENT SCIENCE QUANTITATIVE APPROACHES TO DECISION MAKING second edition Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it An Introduction to Management Science: Quantitative Approaches to Decision Making, 2nd Edition Anderson, Sweeney, Williams and Wisniewski Publisher: Andrew Ashwin Development Editor: Felix Rowe Senior Production Editor: Alison Burt Editorial Assistant: Jenny Grene Senior Manufacturing Buyer: Eyvett Davis Typesetter: Integra Software Services PVT LTD Cover design: Adam Renvoize Text design: Design Deluxe Ó 2014, Cengage Learning EMEA WCN: 02-300 ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, or applicable copyright law of another jurisdiction, without the prior written permission of the publisher While the publisher has taken all reasonable care in the preparation of this book, the publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions from the book or the consequences thereof Products and services that are referred to in this book may be either trademarks and/or registered trademarks of their respective owners The publishers and author/s make no claim to these trademarks The publisher does not endorse, and accepts no responsibility or liability for, incorrect or defamatory content contained in hyperlinked material All the URLs in this book are correct at the time of going to press; however the Publisher accepts no responsibility for the content and continued availability of third party websites For product information and technology assistance, contact emea.info@cengage.com For permission to use material from this text or product, and for permission queries, email emea.permissions@cengage.com British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-1-4080-8840-1 Cengage Learning EMEA Cheriton House, North Way, Andover, Hampshire, SP10 5BE United Kingdom Cengage Learning products are represented in Canada by Nelson Education Ltd For your lifelong learning solutions, visit www.cengage.co.uk Purchase your next print book, e-book or e-chapter at www.cengagebrain.com Printed by Croatia By Zrinsky d.d 10 – 16 15 14 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Brief contents About the Authors xi Preface xiii Acknowledgements xv Introduction An Introduction to Linear Programming 33 Linear Programming: Sensitivity Analysis and Interpretation of Solution 85 Linear Programming Applications 137 Linear Programming: The Simplex Method 211 Simplex-Based Sensitivity Analysis and Duality 254 Transportation, Assignment and Transshipment Problems 279 Network Models 344 Project Scheduling: PERT/CPM 370 10 Inventory Models 405 11 Queuing Models 451 12 Simulation 489 13 Decision Analysis 539 14 Multicriteria Decisions 593 Conclusion: Management Science in Practice 635 Appendices 639 Appendix A Areas for the Standard Normal Distribution 641 Appendix B Values of eÀl 642 Appendix C Bibliography and References 643 Appendix D Self-Test Solutions 645 Glossary 677 Index 683 ONLINE CONTENTS 15 Integer Linear Programming 16 Forecasting 17 Dynamic Programming 18 Markov Processes iii Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Contents About the Authors xi Preface xiii Acknowledgements xv Introduction 1.1 Introduction to Management Science Does it Work? 1.2 Where Did MS Come From? 1.3 Management Science Applications Assignment Data Mining Financial Decision Making Forecasting Logistics Marketing Networks Optimization Project Planning and Management Queuing Simulation Transportation 1.4 The MS Approach Problem Recognition Problem Structuring and Definition Modelling and Analysis 10 Solutions and Recommendations 11 Implementation 11 1.5 Models 12 1.6 Models of Cost, Revenue and Profit 15 Cost and Volume Models 15 Revenue and Volume Models 16 Profit and Volume Models 17 Breakeven Analysis 17 1.7 The Modelling Process 18 1.8 Management Science Models and Techniques 20 Linear Programming 20 Transportation and Assignment 20 Network Models 20 Project Management 20 Inventory Models 21 Queuing Models 21 Simulation 21 Decision Analysis 21 Multicriteria analysis 21 Integer Linear Programming 21 Forecasting 21 Dynamic Programming 22 Markov Process Models 22 Summary 22 Worked Example 22 Problems 24 Case Problem Uhuru Craft Cooperative, Tanzania 27 Appendix 1.1 Using Excel for Breakeven Analysis 27 Appendix 1.2 The Management Scientist Software 30 An Introduction to Linear Programming 33 2.1 A Maximization Problem 35 Problem Formulation 36 Mathematical Statement of the GulfGolf Problem 39 2.2 Graphical Solution Procedure 40 A Note on Graphing Lines 48 Summary of the Graphical Solution Procedure for Maximization Problems 50 Slack Variables 51 2.3 Extreme Points and the Optimal Solution 53 2.4 Computer Solution of the GulfGolf Problem 54 Interpretation of Computer Output 55 2.5 A Minimization Problem 57 Summary of the Graphical Solution Procedure for Minimization Problems 58 Surplus Variables 59 Computer Solution of the M&D Chemicals Problem 61 2.6 Special Cases 62 Alternative Optimal Solutions 62 Infeasibility 63 Unbounded Problems 64 2.7 General Linear Programming Notation 66 Summary 67 Worked Example 68 Problems 71 v Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it vi CONTENTS Case Problem Workload Balancing 76 Case Problem Production Strategy 77 Case Problem Blending 78 Appendix 2.1 Solving Linear Programmes With Excel 79 Appendix 2.2 Solving Linear Programmes With the Management Scientist 82 Linear Programming: Sensitivity Analysis and Interpretation of Solution 85 3.1 Introduction to Sensitivity Analysis 86 3.2 Graphical Sensitivity Analysis 88 Objective Function Coefficients 88 Right-Hand Sides 93 3.3 Sensitivity Analysis: Computer Solution 97 Interpretation of Computer Output 97 Simultaneous Changes 99 Interpretation of Computer Output – A Second Example 101 Cautionary Note on the Interpretation of Dual Prices 104 3.4 More than Two Decision Variables 105 The Modified GulfGolf Problem 106 The Kenya Cattle Company Problem 109 Formulation of the KCC Problem 111 Computer Solution and Interpretation for the KCC Problem 112 3.5 The Taiwan Electronic Communications (TEC) Problem 115 Problem Formulation 116 Computer Solution and Interpretation 117 Summary 121 Worked Example Problems 123 Case Problem Case Problem Case Problem 121 Product Mix 134 Investment Strategy 135 Truck Leasing Strategy 136 4.5 Financial Applications 168 Portfolio Selection 170 Financial Planning 174 Revenue Management 178 4.6 Data Envelopment Analysis 182 Summary 190 Problems 191 Case Problem Planning an Advertising Campaign 200 Case Problem Phoenix Computer 202 Case Problem Textile Mill Scheduling 202 Case Problem Workforce Scheduling 204 Case Problem Cinergy Coal Allocation 205 Appendix 4.1 Excel Solution of Hewlitt Corporation Financial Planning Problem 207 Linear Programming: The Simplex Method 211 5.1 An Algebraic Overview of the Simplex Method 212 Algebraic Properties of the Simplex Method 213 Determining a Basic Solution 213 Basic Feasible Solution 214 5.2 Tableau Form 216 5.3 Setting Up the Initial Simplex Tableau 217 5.4 Improving the Solution 218 5.5 Calculating the Next Tableau 222 Interpreting the Results of an Iteration 224 Moving Toward a Better Solution 225 Interpreting the Optimal Solution 228 Summary of the Simplex Method 228 Linear Programming Applications 137 5.6 Tableau Form: The General Case 230 Greater-Than-or-Equal-to Constraints (‡) 230 Equality Constraints 234 Eliminating Negative Right-Hand Side Values 235 Summary of the Steps to Create Tableau Form 236 4.1 The Process of Problem Formulation 138 5.7 Solving a Minimization Problem 237 4.2 Production Management Applications 140 Make-or-Buy Decisions 140 Production Scheduling 143 Workforce Assignment 150 4.3 Blending, Diet and Feed-Mix Problems 156 5.8 Special Cases 239 Infeasibility 239 Unbounded Problems 240 Alternative Optimal Solutions 242 Degeneracy 243 4.4 Marketing and Media Applications 163 Media Selection 163 Marketing Research 166 Summary 244 Worked Example 245 Problems 248 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it CONTENTS Simplex-Based Sensitivity Analysis and Duality 254 Case Problem Distribution System Design 336 Appendix 7.1 Excel Solution of Transportation, Assignment and Transshipment Problems 338 6.1 Sensitivity Analysis with the Simplex Tableau 255 Objective Function Coefficients 255 Right-Hand Side Values 258 Simultaneous Changes 265 Network Models 6.2 Duality 266 Interpretation of the Dual Variables 268 Using the Dual to Identify the Primal Solution 270 Finding the Dual of Any Primal Problem 270 344 8.1 Shortest-Route Problem 345 A Shortest-Route Algorithm 346 8.2 Minimal Spanning Tree Problem 354 A Minimal Spanning Tree Algorithm 355 8.3 Maximal Flow Problem 357 Summary 272 Worked Example 273 Problems 274 Summary 362 Worked Example 362 Problems 363 Case Problem Ambulance Routing 368 Transportation, Assignment and Transshipment Problems 279 Project Scheduling: PERT/CPM 370 7.1 Transportation Problem: A Network Model and a Linear Programming Formulation 280 Problem Variations 283 A General Linear Programming Model of the Transportation Problem 285 9.1 Project Scheduling With Known Activity Times 372 The Concept of a Critical Path 373 Determining the Critical Path 374 Contributions of PERT/CPM 378 Summary of the PERT/CPM Critical Path Procedure 379 Gantt Charts 380 7.2 Transportation Simplex Method: A SpecialPurpose Solution Procedure 286 Phase I: Finding an Initial Feasible Solution 288 Phase II: Iterating to the Optimal Solution 291 Summary of the Transportation Simplex Method 300 Problem Variations 302 7.3 Assignment Problem: The Network Model and a Linear Programming Formulation 303 Problem Variations 305 A General Linear Programming Model of the Assignment Problem 306 Multiple Assignments 307 7.4 Assignment Problem: A Special-Purpose Solution Procedure 307 Finding the Minimum Number of Lines 311 Problem Variations 311 7.5 Transshipment Problem: The Network Model and a Linear Programming Formulation 314 Problem Variations 319 A General Linear Programming Model of the Transshipment Problem 320 7.6 A Production and Inventory Application 320 Summary 324 Worked Example 325 Problems 327 vii 9.2 Project Scheduling With Uncertain Activity Times 381 The Daugherty Porta-Vac Project 382 Uncertain Activity Times 382 The Critical Path 385 Variability in Project Completion Time 386 9.3 Considering Time–Cost Trade-Offs 388 Crashing Activity Times 389 Summary 392 Worked Example 392 Problems 394 Case Problem R.C Coleman 401 Appendix 9.1 Activity on Arrow Networks 402 10 Inventory Models 405 10.1 Principles of Inventory Management 406 The Role of Inventory 406 Inventory Costs 407 10.2 Economic Order Quantity (EOQ) Model 408 The How-Much-to-Order Decision 411 The When-to-Order Decision 413 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it viii CONTENTS Sensitivity Analysis for the EOQ Model 414 Excel Solution of the EOQ Model 415 Summary of the EOQ Model Assumptions 415 10.3 Economic Production Lot Size Model 416 Total Cost Model 418 Economic Production Lot Size 420 10.4 Inventory Model with Planned Shortages 421 10.5 Quantity Discounts for the EOQ Model 425 10.6 Single-Period Inventory Model with Probabilistic Demand 427 Juliano Shoe Company 428 Arabian Car Rental 431 10.7 Order-Quantity, Reorder Point Model with Probabilistic Demand 433 The How-Much-to-Order Decision 434 The When-to-Order Decision 435 10.8 Periodic Review Model with Probabilistic Demand 437 More Complex Periodic Review Models 440 Summary 441 Worked Example 442 Problems 443 Case Problem Wagner Fabricating Company 447 Case Problem River City Fire Department 448 Appendix 10.1 Development of the Optimal Order Quantity (Q) Formula for the EOQ Model 449 Appendix 10.2 Development of the Optimal Lot Size (Q*) Formula for the Production Lot Size Model 450 11 Queuing Models 451 11.1 Structure of a Queuing System 452 Single-Channel Queue 454 Distribution of Arrivals 454 Distribution of Service Times 455 Steady-State Operation 456 11.4 Some General Relationships for Queuing Models 466 11.5 Economic Analysis of Queues 468 11.6 Other Queuing Models 470 11.7 Single-Channel Queuing Model with Poisson Arrivals and Arbitrary Service Times 471 Operating Characteristics for the M/G/1 Model 471 Constant Service Times 472 11.8 Multiple-Channel Model with Poisson Arrivals, Arbitrary Service Times and No Queue 473 Operating Characteristics for the M/G/k Model with Blocked Customers Cleared 473 11.9 Queuing Models with Finite Calling Populations 476 Operating Characteristics for the M/M/1 Model with a Finite Calling Population 476 Summary 479 Worked Example 479 Problems 481 Case Problem Regional Airlines 486 Case Problem Office Equipment, Inc 487 12 Simulation 489 12.1 Risk Analysis 492 PortaCom Project 492 What-If Analysis 492 Simulation 493 Simulation of the PortaCom Problem 501 12.2 Inventory Simulation 504 Simulation of the Butler Inventory Problem 507 11.2 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times 456 Operating Characteristics 457 Operating Characteristics for the Dome Problem 458 Managers’ Use of Queuing Models 458 Improving the Queuing Operation 459 Excel Solution of the Queuing Model 461 12.3 Queuing Simulation 509 Hong Kong Savings Bank ATM Queuing System 510 Customer Arrival Times 510 Customer Service Times 511 Simulation Model 511 Simulation of the ATM Problem 515 Simulation with Two ATMs 516 Simulation Results with Two ATMs 518 11.3 Multiple-Channel Queuing Model with Poisson Arrivals and Exponential Service Times 462 Operating Characteristics 462 Operating Characteristics for the Dome Problem 464 12.4 Other Simulation Issues 520 Computer Implementation 520 Verification and Validation 521 Advantages and Disadvantages of Using Simulation 522 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 674 APPENDIX D SELF-TEST SOLUTIONS c Step 1: Step 3: Style Accord Saturn Cavalier Accord Saturn Cavalier Row Average 0.235 0.706 0.059 0.226 0.677 0.097 0.333 0.583 0.083 0.265 0.656 0.080 3 3 7 0:5034 1=3 ỵ 0:3484 ỵ 0:1484 5 1=2 1=5 Weighted Sum: 3 3 0:503 1:044 0:296 1:845 7 7 0:168 ỵ 0:348 ỵ 0:740 ¼ 1:258 0:252 0:070 0:148 0:470 Consistency Ratio Step 1: 3 1=3 7 7 0:2654 ỵ 0:6564 þ 0:0804 7 1=4 1=7 3 3 0:265 0:219 0:320 0:802 7 7 0:795 ỵ 0:656 ỵ 0:560 ẳ 2:007 5 5 0:066 0:094 0:080 0:239 Step 2: 1:845=0:503 ¼ 3:668 1:258=0:348 ¼ 3:615 0:470=0:148 ¼ 3:123 Step 3: lmax ¼ (3.668 + 3.615 + 3.123)/3 ¼ 3.469 Step 4: CI ¼ (3.469 À 3)/2 ¼ 0.235 Step 5: CR ¼ 0.235/0.58 ¼ 0.415 Since CR ¼ 0.415 is greater than 0.10, the individual’s judgements are not consistent Step 2: 0:802=0:265 ¼ 3:028 2:007=0:656 ¼ 3:062 14 a Laptops in order: 4, 1, 2, b Since CR ¼ 0.083 is less than 0.10, the judgements are consistent 15 a Criteria: Yield and Risk Step 1: Column totals are 1.5 and Step 2: 0:239=0:080 ¼ 3:007 Step 3: lmax ¼ (3.028 + 3.062 + 3.007)/3 ¼ 3.032 Step 4: CI ¼ (3.032 À 3)/2 ¼ 0.016 Step 5: CR ¼ 0.016/0.58 ¼ 0.028 Since CR ¼ 0.028 is less than 0.10, the degree of consistency exhibited in the pairwise comparison matrix for style is acceptable 12 a Flavour A B C A B C 1/3 1/2 1/5 Criterion Yield Risk Priority Yield Risk 0.667 0.333 0.667 0.333 0.667 0.333 With only two criteria, CR ¼ and no computation of CR is made The same calculations for the Yield and the Risk pairwise comparison matrices provide the following: b Step 1: Column totals are 11/6, 21/5, and Step 2: Flavour A B C A B C 6/11 2/11 3/11 15/21 5/21 1/21 2/8 5/8 1/8 Stocks Yield Priority Risk Priority CCC SRI 0.750 0.250 0.333 0.667 Step 3: Flavour A B C Row Average A B C 0.545 0.182 0.273 0.714 0.238 0.048 0.250 0.625 0.125 0.503 0.348 0.148 b Overall Priorities: CCC 0:6670:750ị ỵ 0:3330:333ị ẳ 0:611 SRI 0:6670:250ị ỵ 0:3330:667ị ẳ 0:389 CCC is preferred Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com APPENDIX D SELF-TEST SOLUTIONS 16 a Candidate 675 b Overall Priorities: Leadership Priority Personal Priority Administrative Priority 0.800 0.200 0.250 0.750 0.667 0.333 Jacobs 0:128ð0:800Þ ỵ 0:5120:250ị ỵ 0:3600:667ị ẳ 0:470 Martin 0:1280:200ị ỵ 0:5120:250ị ỵ 0:3600:333ị ẳ 0:530 Martin is preferred Jacobs Martin Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com Glossary 100 per cent rule A rule indicating when simultaneous changes in two or more objective function coefficients will not cause a change in the optimal solution It can also be applied to indicate when two or more right-hand-side changes will not cause a change in any of the dual prices Activities Specific jobs or tasks that are parts of a project AHP See Analytic Hierarchy Process Alternative optimal solution The case in which more than one solution provides the optimal value for the objective function All-integer linear programme An integer linear programme in which all variables are required to be integer Analytic hierarchy process (AHP) An approach to multicriteria decision making based on pairwise comparisons for elements in a hierarchy Arcs The lines connecting the nodes in a network Arrival rate In a queuing system the number of arrivals within a given time period Artificial variable In linear programming, a variable that is added to a constraint taking the form ! or = to enable a basic feasible solution to be created for starting the simplex method Assignment model A type of mathematical programming model where agents are assigned to tasks Assignment problem A class of optimization problems where agents are to be assigned to tasks to optimize a given objective function Backorder In stock control models, the receipt of an order for a product when no units are in inventory These backorders become shortages, which are eventually satisfied when a new supply of the product becomes available Backward pass Part of the PERT/CPM project planning procedure that involves moving backward through the network to determine the latest start and latest finish times for each activity Basic feasible solution In mathematical programming, a basic solution that is also feasible; that is, it satisfies the nonnegativity constraints A basic feasible solution corresponds to an extreme point Basic solution Given a linear programme in standard form, with n variables and m constraints, a basic solution is obtained by setting n-m of the variables equal to zero and solving the constraint equations for the values of the other m variables If a unique solution exists, it is a basic solution Basic variable One of the m variables not required to equal zero in a basic solution In mathematical programming, the set of variables that are not restricted to equal zero in the current basic solution The variables that make up the basis are termed basic variables, and the remaining variables are called nonbasic variables Bayes’ theorem A theorem that enables the use of sample information to revise prior probabilities Beta probability distribution A probability distribution used to describe project activity times Binary integer programme An all-integer or mixedinteger linear programme in which the integer variables are only permitted to assume the values or Also called 0-1 integer programme Binding constraint In mathematical programming a binding constraint is one that passes through the optimal solution and therefore binds, or restricts, the solution from improving further Branch Lines showing the alternatives from decision nodes and the outcomes from chance nodes Branch and bound In integer programming a solution method for finding the optimal solution by keeping the best solution found so far If a partial solution cannot improve on the best, it is abandoned Breakeven point The volume at which total revenue equals total cost Calling population The population of customers or units that may seek service in a queueing situation Canonical form for a maximization problem A maximization problem with all less-than- or-equal-to constraints and nonnegativity requirements for the decision variables Canonical form for a minimization problem A minimization problem with all greater-than- or-equalto constraints and nonnegativity requirements for the decision variables Capacitated transportation problem A variation of the basic transportation problem in which some or all of the arcs are subject to capacity constraints Chance event An uncertain future event affecting the consequence, or payoff, associated with a decision Chance nodes Nodes indicating points where an uncertain event will occur Coefficient of determination A statistical measure of the strength of the relationship between variables in a regression equation Conditional probabilities The probability of one event given the known outcome of a (possibly) related event Consequence The result obtained when a decision alternative is chosen and a chance event occurs A measure of the consequence is often called a payoff 677 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 678 GLOSSARY Conservative approach An approach to choosing a decision alternative without using probabilities For a maximization problem, it leads to choosing the decision alternative that maximizes the minimum payoff; for a minimization problem, it leads to choosing the decision alternative that minimizes the maximum payoff Constraint A restriction or limitation imposed on a problem In a mathematical programming model a mathematical relationship that imposes a restriction on possible solutions to the problem Correlation A statistical measure of the strength of a relationship between two variables in regression analysis CPM Critical Path Method Crashing The shortening of project activity times by adding resources and hence usually increasing cost Critical activities The activities on the critical path of a project network Critical path The longest path in a project network Critical path method (CPM) A network-based project scheduling procedure Data envelopment analysis (DEA) A linear programming application used to measure the relative efficiency of operating units with the same goals and objectives Decision nodes Nodes indicating points where a decision is made Decision strategy A strategy involving a sequence of decisions and chance outcomes to provide the optimal solution to a decision problem Decision tree A graphical representation of the decision problem that shows the sequential nature of the decision-making process Decision variable A controllable value for a linear programming model Degeneracy In mathematical programming, when one or more of the basic variables has a value of zero Deterministic A decision situation where there is no uncertainty Deterministic inventory model A model where demand is considered known and not subject to uncertainty Deviation variables Variables that are added to the goal equation to allow the solution to deviate from the goal’s target value Discrete-event simulation model A simulation model that describes how a system evolves over time by using events that occur at discrete points in time Dual price The change in the value of the objective function per unit increase in the right-hand side of a constraint Dual problem A linear programming problem related to the primal problem Solution of the dual also provides the solution to the primal Dual value At the optimal solution point, the change in the value of the objective function for a unit change in the right hand side of the constraint Dual variable The variable in a dual linear programming problem Its optimal value provides the dual price for the associated primal resource Dummy activity A branch that is required to construct the CPM network but that takes zero time to complete Dummy destination A destination added to a transportation problem to make the total supply equal to the total demand The demand assigned to the dummy destination is the difference between the total supply and the total demand Dummy origin An origin added to a transportation problem in order to make the total supply equal to the total demand The supply assigned to the dummy origin is the difference between the total demand and the total supply Dynamic simulation model A simulation model used in situations where the state of the system affects how the system changes or evolves over time Earliest finish time The earliest time a project activity may be completed Earliest start time The earliest time a project activity may begin Economic order quantity (EOQ) The order quantity that minimizes the annual holding cost plus the annual ordering cost Expected time The average time a project activity is expected to take Expected utility approach An approach that considers the expected utility for each decision alternative and then selects the decision alternative yielding the highest expected utility Expected value (EV) For a chance node, it is the weighted average of the payoffs The weights are the state-ofnature probabilities Expected value approach An approach to choosing a decision alternative based on the expected value of each decision alternative The recommended decision alternative is the one that provides the best expected value Expected value of perfect information (EVPI) The expected value of information that would tell the decision maker exactly which state of nature is going to occur (i.e., perfect information) Exponential probability distribution A probability distribution used to describe the service time for some waiting line models Extreme point Graphically speaking, extreme points are the feasible solution points occurring at the vertices or ‘corners’ of the feasible region With two-variable problems, extreme points are determined by the intersection of the constraint lines Feasible region The set of all feasible solutions Feasible solution A solution that satisfies all the constraints First-come, first-served (FCFS) The queue discipline that serves waiting units on a first come, first-served basis Float The length of time an activity can be delayed without affecting the project completion time Flow capacity The maximum flow for an arc of the network The flow capacity in one direction may not equal the flow capacity in the reverse direction Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com GLOSSARY Forward pass Part of the PERT/CPM procedure that involves moving forward through the project network to determine the earliest start and earliest finish times for each activity Gantt chart A graph showing time information for each activity in a project Goal programming A linear programming approach to multicriteria decision problems whereby the objective function is designed to minimize the deviations from goals Goodwill cost A cost associated with a backorder, a lost sale or any form of stock-out or unsatisfied demand This cost may be used to reflect the loss of future profits because a customer experienced an unsatisfied demand Hard MS Quantitative analysis and modelling approaches used in management science Heuristic A common-sense procedure for quickly finding a solution to a problem Heuristics are used to find initial feasible solutions for the transportation simplex method and in other applications Holding cost The cost associated with maintaining an inventory investment, including the cost of the capital investment in the inventory, insurance, taxes, warehouse overhead and so on This cost may be stated as a percentage of the inventory investment or as a cost per unit Hungarian method A special-purpose solution procedure for solving an assignment problem Iconic model A physical replica or prototype, often scaled down, of a real object that may be impractical or expensive to build full scale (such as a vehicle or aeroplane) Infeasibility The situation in which no solution to the problem satisfies all the constraints Interpretation The stage at which findings from the problem solution are translated into usable information Inventory The stock of an item kept on hand to meet customer demand Inventory position The amount of inventory on hand plus the amount of inventory on order Iteration The process of moving from one basic feasible solution to another Joint probability The probability of several events occurring simultaneously Latest finish time The latest time an activity may be completed without increasing the project completion time Latest start time The latest time an activity may begin without increasing the project completion time Lead time The time between the placing of an order and its receipt in the inventory system 679 Linear functions Mathematical expressions in which the variables appear in separate terms and are raised to the first power Linear programme Another term for linear programming models Linear programming model A mathematical model with a linear objective function, a set of linear constraints and nonnegative variables Linear regression A method for determining the linear equation that represents the relationship between two or more variables Lot size The order quantity in the production inventory model MAD Mean absolute deviation Mathematical model A representation of a problem where the objective and all constraint conditions are described by mathematical expressions Maximal flow The maximum amount of flow that can enter and exit a network system during a given period of time Minimal spanning tree The spanning tree with the minimum length Minimax regret approach An approach to choosing a decision alternative without using probabilities For each alternative, the maximum regret is calculated, which leads to choosing the decision alternative that minimizes the maximum regret Minimum cost method A heuristic used to find an initial feasible solution to a transportation problem; it is easy to use and usually provides a good (but not optimal) solution Model An abstract representation of a real object or situation Modelling The process of translating the verbal statement of a problem into a mathematical statement MODI method A procedure in which a modified distribution method determines the incoming arc in the transportation simplex method Monte Carlo process The random selection of values from a distribution Most probable time The most probable activity time under normal conditions MSE Mean squared error Multicriteria decision making A situation in which there are several distinct decision criteria that must be considered in the decision making process Multiple-channel waiting line A queuing system with two or more parallel service facilities Multiple regression A regression equation between three or more variables Network A graphical representation of a problem consisting of numbered circles (nodes) interconnected by a series of lines (arcs); arrowheads on the arcs show the direction of flow Network flow model A model that shows the flows through a system Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 680 GLOSSARY Nodes The intersection or junction points of a network Nonbasic variable One of n-m variables set equal to zero in a basic solution Non-binding constraint In mathematical programming a non-binding constraint is one that does pass through the optimal solution and therefore does not bind, or restrict, the solution from improving further Nonnegativity constraints A set of constraints that requires all variables to be nonnegative Objective function A mathematical statement of the required objective for a decision problem Operating characteristics The performance measures for a queuing system including the probability that no units are in the system, the average number of units in the waiting line, the average waiting time and so on Opportunity cost At the optimal solution point, the change in the value of the objective function for a unit change in the right hand side of the constraint Opportunity loss, or regret The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature Optimal solution The best solution to a given problem Optimistic approach An approach to choosing a decision alternative without using probabilities For a maximization problem, it leads to choosing the decision alternative corresponding to the largest payoff; for a minimization problem, it leads to choosing the decision alternative corresponding to the smallest payoff Optimistic time The minimum activity time if everything progresses ideally Ordering cost The fixed cost (salaries, paper, transportation, etc.) associated with placing an order for an item Parameters Numerical values that appear in the mathematical relationships of a model PERT Programme Evaluation and Review Technique Payoff A measure of the consequence of a decision such as profit, cost or time Each combination of a decision alternative and a state of nature has an associated payoff (consequence) Payoff table A tabular representation of the payoffs for a decision problem Pessimistic time The maximum activity time if significant delays are encountered Phase I When artificial variables are present in the initial simplex tableau, phase I refers to the iterations of the simplex method that are required to eliminate the artificial variables At the end of phase I, the basic feasible solution in the simplex tableau is also feasible for the real problem Pivot column The column in the simplex tableau corresponding to the nonbasic variable that is about to be introduced into solution Pivot element The element of the simplex tableau that is in both the pivot row and the pivot column Pivot row The row in the simplex tableau corresponding to the basic variable that will leave the solution Poisson probability distribution A probability distribution used to describe the arrival pattern for some waiting line models Posterior (revised) probabilities The probabilities of the states of nature after revising the prior probabilities based on sample information Preemptive priorities Priorities assigned to goals that ensure that the satisfaction of a higher level goal cannot be traded for the satisfaction of a lower level goal Primal problem The original formulation of a linear programming problem Prior probabilities The probabilities of the states of nature prior to obtaining sample information Probabilistic inventory model A model where demand is not known exactly; probabilities must be associated with the possible values for demand Problem formulation The process of translating the verbal statement of a problem into a mathematical statement called the mathematical model Problem solution The stage at which an answer to the specific decision problem is found Programme evaluation and review technique (PERT) A network-based project scheduling procedure Project network A graphical representation of a project that depicts the activities and shows the predecessor relationships among the activities Qualitative forecasting Non-quantitative subjective forecasting methods Quantity discounts Discounts or lower unit costs offered by the manufacturer when a customer purchases larger quantities of the product Queue discipline The order in which customers waiting in a queue are served Range of feasibility The range of values over which the dual price is applicable Range of optimality The range of values over which an objective function coefficient may vary without causing any change in the values of the decision variables in the optimal solution Reduced cost The amount by which an objective function coefficient would have to improve (increase for a maximization problem, decrease for a minimization problem) before it would be possible for the corresponding variable to assume a positive value in the optimal solution Redundant constraint A constraint that does not affect the feasible region If a constraint is redundant, it can be removed from the problem without affecting the feasible region Relevant cost A cost that depends on the decision made The amount will vary depending on the values of the decision variables Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com GLOSSARY Reorder point The inventory position at which a new order should be placed Risk analysis The process of predicting the outcome of a decision in the face of uncertainty Safety stock Inventory maintained in order to reduce the number of stock-outs resulting from higher-thanexpected demand Scoring model An approach to multicriteria decision making that requires the user to assign weights to each criterion that describes the criterion’s relative importance and to assign a rating that shows how well each decision alternative satisfies each criterion The output is a score for each decision alternative Sensitivity analysis The study of how changes in the coefficients of problems affect the optimal solution Service rate The average number of customers or units that can be served by one service facility in a given period of time Setup cost The fixed cost (labour, materials, lost production) associated with preparing for a new production run Shadow price At the optimal solution point, the change in the value of the objective function for a unit change in the right hand side of the constraint Shortage or stock-out Demand that cannot be supplied from inventory Shortest route Shortest path between two nodes in a network Simplex method A common algebraic procedure for solving linear programming problems Simplex tableau A table used to keep track of the calculations required by the simplex method Simulation A method for learning about a real system by experimenting with a model that represents the system Single-channel queuing system A queuing system with only one service facility Slack variable A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality The value of this variable can usually be interpreted as the amount of unused resource Soft MS Qualitative analysis and modelling approaches used in management science Spanning tree A set of N - arcs that connects every node in the network with all other nodes where N is the number of nodes Standard form A linear programme in which all the constraints are written as equalities The optimal solution of the standard form of a linear programme is the same as the optimal solution of the original formulation of the linear programme States of nature The possible outcomes for chance events that affect the payoff associated with a decision alternative 681 Static simulation model A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time Each trial of the simulation is independent Steady-state operation The normal operation of a queuing system after it has gone through a start-up or transient period The operating characteristics of queues are calculated for steady-state conditions Stepping-stone method Using a sequence or path of occupied cells to identify flow adjustments necessary when flow is assigned to an unused arc in the transportation simplex method This identifies the outgoing arc Stochastic (probabilistic) A model in which at least one uncontrollable input is uncertain and subject to variation; stochastic models are also referred to as probabilistic models Stockout cost The cost involved when customer demand cannot be met because of insufficient inventory Sunk cost A cost that is not affected by the decision made It will be incurred no matter what values the decision variables assume Surplus variable A variable subtracted from the left-hand side of a greater-than-or equal-to constraint to convert the constraint into an equality The value of this variable can usually be interpreted as the amount over and above some required minimum level Tableau form The form in which a linear programme must be written before setting up the initial simplex tableau When a linear programme is written in tableau form, its A matrix contains m unit columns corresponding to the basic variables, and the values of these basic variables are given by the values in the b column A further requirement is that the entries in the b column be greater than or equal to zero Transient period The start-up period for a queuing system, occurring before the queue reaches a normal or steady-state operation Transportation problem A network flow problem that often involves minimizing the cost of shipping goods from a set of origins to a set of destinations; it can be formulated and solved as a linear programme by including a variable for each arc and a constraint for each node or solved using a specialized algorithm Transportation tableau A table representing a transportation problem in which each cell corresponds to a variable, or arc Transshipment problem An extension of the transportation problem to distribution problems involving transfer points and possible shipments between any pair of nodes Unbounded If the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints, the problem is said to be unbounded Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 682 GLOSSARY Unit column or unit vector A vector or column of a matrix that has a zero in every position except one In the nonzero position there is a There is a unit column in the simplex tableau for each basic variable Utility A measure of the total worth of an outcome reflecting a decision maker’s attitude toward considerations such as profit and loss and intangibles such as risk Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com Index Abu Dhabi Savings Bank 133 activities 371 crashing 389–91 critical 374, 378 project scheduling with known activity time 372–81 project scheduling with uncertain activity times 381–8 activity on arrow (AOA) 402–4 activity on node (AON) 402–4 additivity 40 advertising campaign 200–1 Agan Interior Design problem 482–4 Air New Zealand airline reservations problem 529–30 Ajax Fuels problem 192 alternative optimal solutions 62–3, 242–3 ambulance routing 368–9 American Airlines 3, 178 analysis 10 breakeven 17 decision 21 multicriteria 21 analytic hierarchy process (AHP) 21, 594, 614–15 consistency 620–2 developing hierarchy 615 establishing priorities 615–23 overall priority ranking 623–4 pairwise comparison matrix 617–18 pairwise comparisons 616–17 synthesization 619–20 Arabian Car Rental (Saudi Arabia) 431–2 Arnoff Enterprises problem 329–30 arrival rate 453 assignment 20 unacceptable 314 assignment problem Excel solution 339–41 general linear programming model 306–7 network model 303–5 special purpose solution procedure 307–14 variations 305–6 Atlantic Seafood Company problem 194–5 ATMs 452, 510–19 Baba Toy Company problem 528 backorder 421–2 backward pass 376 Bahrain Manufacturing Company problem 331–2 basic feasible solution 214–16 basic solution 213–14 basic variables 214 Bayer Pharmaceuticals 543 Bayes’ theorem 566 beta probability distribution 384 Better Fitness Inc (Germany) 77–8 binding constraints 48 Blair & Rosen plc (UK) 68–70 blending 78, 156–62 Bollinger Electronics Company 145-51, 152 branch probabilities 566–8 branches 543 breakeven analysis 17–18, 27–30 breakeven point 17, 28–30 British Airways 613–24 British Telecommunications plc 3, Butler Electrical Supply Company 504–7 Excel simulation 535–6 simulation of inventory problem 507–8 Cairo City Cab Company problem 365, 485 call centre simulation model 491 calling population 453, 476–9 canonical form for a minimization problem 266 Capetown Beverage Company (South Africa) 408–16 car selection problem 613–24 Catholic Relief Services 18 chance events 541 change-in-production-level costs 145–6 Channel 10 problem 134 Cinergy Corporation 205–7 Citibank 452 City of Copenhagen problem 365 coal allocation 205–7 communication network design 358 computer-generated random numbers 496 conditional probability 566–7 consequences 541 conservative approach 544 consistency 620–2 constant service times 472 constraints 14, 34, 56, 61, 103 equality 234–5 goal equations 595–7 greater-than-or-equal to 230–4 Continental Airlines 157 Contois Carpets 321–4, 336 Cossack Grill (St Petersburg) 200–1 crashing 389–91 critical activity 374, 378 critical path 385–6 concept 373–4 determining 374–8 summary 379–80 critical path method (CPM) 371–2 Dante Development Corporation problem 581 data envelopment analysis (DEA) 182–9 data mining 5–6 data requirements 635 decision analysis 21, 540–1 branch probabilities 566–8 with probabilities 546–50 problem formulation 541–3 risk analysis 551–2 with sample information 556–66 sensitivity analysis 552–5 with TreePlan 587–92 utility and 568–74 without probabilities 543–6 decision strategy 558–62 decision tree 540–1, 542–3, 556–8, 565 decision variables 37 more than two 105–15 Deere & Company 442 degeneracy 239, 243–4, 296 Delta Air Lines 212 Delta Oil Company (Nigeria) 157, 160–2 dentist’s office problem 483–4 Deskpro model 212 deterministic 427–8 deviation variables 596 diet problem 156–62 Digital Controls Inc problem 130–1 Digital Imaging (DI) 76–7 discrete-event simulation model 509 distribution of arrivals 454–5 distribution of service times 455–6 divisibility 40 DJS Investment Services problem 628 Dollar Discounts 437–41 Dome hospital cafeteria 453–5, 482, 529 distribution of service times 455–6 economic analysis of queues 468–9 improving queuing operation 459–60 managers’ use of queuing models 458–9 multiple-channel queue 462–6 operating characteristics 458, 464–6 single-channel queue 454 steady-state operation 456–7 drug development 543 dual of a maximization problem in canonical form 266–7 dual price 95, 104–5, 259–61 dual problem 266, 270 dual value 95 dual variables 266 interpretation of 268–70 duality 266–8 finding any primal problem 270–2 identifying primal solution 270 interpretation of dual variables 268–70 Duke University Medical Center 569 dummy activities 404 dummy destination 302 dummy origin 284, 302 683 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 684 INDEX Duncan Industries Limited (India) 119 Dunes Golf Course (Scotland) 530–1 Dutch companies 436 dynamic programming 22 dynamic simulation models 509 earliest finish time 374 earliest start time 374 Eastman Kodak 87, 540 economic analysis of queues 468–9 economic order quantity (EOC) 408–11 Excel solution 415 how-much-to-order decision 411–13 sensitivity analysis 414–15 summary of assumptions 415–16 when-to-order decision 413–14 economic production lot size model 416–20 EDS (Piano, Texas) 358 Effortless Events 531–2 elementary row operations 222 equality constraints 234–5 Erlang, A.K 452 Excel 27–30 assignment problem 339–41 EOQ model 415 Hewlitt Corporation financial planning problem 207–10 linear programme solutions 79–82 market survey problem 169 multicriteria decision problems 634 PortaCom project 501–2, 533–4 queuing model 461 transportation problem 338–9 transshipment problem 341–3 TreePlan add-in 587–92 expected utility approach 573–4 expected value approach 546 expected value (EV) 547 of perfect information 548–50 of sample information 564 expected value of perfect information (EVPI) 549–50 exponential probability distribution 456 extreme points 54 EZ Trailers 633 EZ Windows problem 198 feasible region 44 feasible solutions 44 Federal Express 15 feed-mix problem 156–62 Films Tonight problem 482 Filton Corporation problem 197–8 finance 168 portfolio selection 170–3 revenue management 178–82 financial decision making financial planning 174–7 flow capacity 357 flows 491 Ford Motor Company 2, 613–24 Ford-Otasan 406 forecasting 6, 21–2 forward pass 376 Foster Electronics 280–6, 287–302 Fowle Marketing Research 303–12 Frandec Company problem 195–6 Frankfurt highway problem 367 Fresh Juice Company (South Africa) 245–8 FRILAC Company (Spain) 361 Gantt chart 380–1 Gap clothing 406–7 GE Capital 174, 175 Glasgow road system 357–60 goal programming 21, 594 complex problem-solving 602–7 computer solution 605–7 equations 603–4 formulation and graphical solution 40–52 model 601 priority levels 595 603 goodwill cost 422 Government Development Agency (Brunei) 346–53 graphical lines 48–50 graphical sensitivity analysis 88–95 graphical solution 40–52 goal programming 594–601 greater-than-or-equal-to constraints 230–4 Groebler Publishing Company problem 444 Gubser Welding Inc problem 484 GulfGolf (United Arab Emirates) 125, 126, 275–6 alternative optimal solutions 62–6 computer solution 54–6, 97–105 Excel solution to linear programming problem 79–84 extreme points/optimal solution 53–4, 86–7 graphical solution procedure 40–52 maximization problem 35–9 modified problem 106–9 objective function coefficients 88–93 right-hand sides 93–5 sensitivity analysis 86–8 Simplex method 250 Gunnarsson Air-Conditioning Company problem 445–6 Hanshin Expressway (China) 71 hard MS 10 Harling Equipment problem 632–3 Hartlage Seafood Supply 472 Hartman Company problem 191–2 health service (Scotland) 625–7 Heery International 308 Herman Company distribution system problem 333 heuristic 288 Hewlitt Corporation 174–7 Excel solution to financial planning problem 207–10 High Tech Industries 212–28, 239, 255–64, 266–72, 274–5 High-Price Oil Company problem 368 Higley Electronic Components 424 holding cost 145 holding costs 407 holiday decision making problem 630–2 Hong Kong Savings Bank (HKSB) ATM queuing system 510 customer arrival times 510–11 customer service times 511 Excel simulation 536–8 simulation model 511–19 hospital data 185–9, 194, 204–5, 381 how-much-to-order decision 411–13, 434–5 H.S Daugherty (Ireland) Porta-Vac project 381–8 Hungarian method 307–11 maximization objective function 312–13 number of people not equal to number of tasks 311–12 unacceptable assignments 314 iconic models 12 implementation 11 Industrial Chemicals problem 629–30 infeasibility 63–4, 239–40 Innis Investments problem 276–7 inputs 185 integer linear programming 21 Integrated Project Management (IPM) 371 interpretation 36 inventory cost 145, 407–8 position 413 problem 321–4 systems 490 inventory management principles 406–8 role of inventory 406–7 inventory models 21 economic order quantity (EOQ) 408–16 economic production lot size 416–20 order quantity, reorder point with probabilistic demand 433–7 periodic review with probabilistic demand 437–41 with planned shortages 421–4 principles of inventory management 406–8 quantity discounts for EOQ model 425–7 single-period with probabilistic demand 427–32 inventory simulation 504–7 Butler system 507–8 Investment Advisors Inc problem 125–7 investment strategy 135 Isa Distributors Inc problem 446–7 iteration 224–5 Jacobsen Corporation problem 527 Jan de Wit Company (Brazil) 56 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com INDEX Janders Company engineering products 141–4 Jansson Cabinets problem 198 J.D Williams Inc 135 joint probabilities 567 Juliano Shoe Company 428–31 Kellogg Company 35 Kendall, D.G 470 Kendall notation 470, 471 Kenya Cattle Company 109–15 Khan Corporation problem 579 Khobar Corporation problem 578 Kimberley-Clark Europe 391 Klein Chemicals Inc problem 331 Kolkmeyer Manufacturing Company 477–9 Kotze Publishing Company problem 582 Kunz and Sons problem 193 Ladies’ Professional Golf Association problem 629–30 Landon Corporation problem 398–9 latest finish time 374 latest start time 374, 376 lawsuit defence strategy 587 lead time 413 Leisure Air (Scotland) 178–82, 200 linear functions 39 linear programming 20, 34–5 assignment problem 306–7 blending, diet, feed-mix problems 156–62 computer solution of GulfGolf problem 54–6 data envelopment analysis 182–9 extreme points 53–4 financial applications 168–82 general model of transportation problem 285–6 general notation 64–76 graphical solution procedure 40–53 marketing/media applications 163–8 maximization problem 35–40 minimization problem 57–61 more than two decision variables 105–15 optimal solution 53–4 problem formulation 138–9 production management applications 140–56 sensitivity analysis 86–105 Simplex method 212–48 solving with Excel 79–82 solving with management Scientist software 82–4 special cases 62–6 Taiwan Electronic Communications problem 115–20 transshipment problem 320 Little, John D.C 466 Little’s flow equations 466–7 Liva’s Lumber problem 251 Lloyds TSB Lochside Development Corporation (Scotland) 163–5 logistics M&D Chemicals (Germany) 57-60, 66–7, 101–3, 237–9 M/G/1 model 471–2 M/G/k model 473–5 M/M/1 model 476–9 McCormick Manufacturing Company 151, 153–6 machine repair problem 477 Madeira Manufacturing Company problem 525–7 maintaining m + n - occupied cells 296–300 make-or-buy decisions 140–3 Malaysian Government 522–4 Management Decision Systems problem 394–5 management science 2–4 applications 5–8 approach 8–11 business benefits 636–7 changing business environment 636 client vs decision maker 636 complexity 635 data requirements 635 effective model building 635 managing change 636 models 12–14, 15–20 need for optimal solution 635–6 origins 4–5 techniques 20–2 Management Scientist software 30–2 minimal spanning tree problem 357 management scientists Marathon Oil Company (US) 140 Market Survey International 166–8 marketing 6, 163–5 planning model 140 research 165–8 resource allocation model 170 Markov process models 22 mathematical model 12–14, 39 mathematical programming models 40 maximal flow 357–60 maximization objective function 285 maximization problem 35-40, 302 dual of a maximization problem in canonical form 266–8 media selection 163–4 medical screening 569 Merrill Lynch 13 Metrovision Cable Company problem 367 Microdata Software 474–5 Micromedia (South Africa) problem 26 Miguel’s Mexican food products 74–5, 127–8 minimal spanning tree 354 minimal spanning tree algorithm 355–7 minimax regret approach 545–6 685 minimization problem 57–61 canonical form 266 solving 237–9 minimum cost method 288–91 minimum number of lines 311 models 10, 12 cost and volume 15–16 inventory 21 Markov process 22 network 20 process 18–20 profit and volume 17 queuing 21 revenue and volume 16 MODI method (modified distribution) 292, 297–9 Motorola multicriteria analysis 21 multicriteria decision making 594 analytic hierarchy process 414–15 at NASA 625 establishing priorities using AHP 615–23 goal programming: formulation/ graphical solution 594–601 goal programming: solving more complex problems 602–7 scoring models 609–14 using AHP to develop overall priority ranking 623–4 multiple-channel queuing with Poisson arrivals, arbitrary service times and no queue 473–5 with Poisson arrivals and exponential service times 462–6 N&D Chemicals (Germany) 57–61 Naples Fishing Supply problem 333–4 NASA 625 Naser Publishing Company problem 26 National Car Rental 178 National Health Service (NHS, UK) 314–20 National School Assistance and Scholarship Board (Chile) 96 negative dual price 95 negative right-hand side values 235 network 6-7, 280 network models 20, 345 assignment problem 303–6 maximal flow problem 357–61 minimal spanning tree problem 354–6 shortest-route problem 345–52 transshipment problem 314–19 New Haven Fire Department (Connecticut) 481 new product development 490 Nicolo Investment Advisors (Edinburgh) 594–601 nodes 280–1 Nokia Networks 371 non-basic variables 214 non-binding constraints 48 non-negativity constraints 38 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 686 INDEX North Somerset Police Department problem 193 North Yorkshire University problem 366 Nutricia Dairy and Drinks Group (Hungary) 114 100 per cent rule 99–101 Oak Hills Swimming Club problem 398 objective function 14 formulating 604–5 maximization 285 preemptive priorities 597 objective function coefficients 88–92, 255–8 Oceanview Development Corporation (Portugal) 585–6 Office Automation problem 400–1 Office Equipment Inc 487–8 Oglethorpe Power Corporation 577 Ohio Edison Company 550 O’Neill Shoe Manufacturing Company (Ireland) 26 operating characteristics 452–3, 457–8 M/G/1 model 471–2 M/G/k model with blocked customers cleared 473–5 M/M/1 model with a finite calling population 476–9 Operational Research 2, 3, 4–5 opportunity cost 95 opportunity loss 313, 546 opportunity regret 545 optimal lot size 450 optimal order quantity 449 optimal solution 53-4, 228 alternative 242–3 transportation simplex method 291–300 optimality criterion 227 optimistic approach 543–4 optimization orange harvest scheduling (Brazil) 152 ordering cost 407–8, 409 Our-Bags-Don’t-Break problem 252 outputs 185 P2 problem 599–601 pairwise comparison 616–17 pairwise comparison matrix 617–18 parameters 492 particulate emission control 550 payoff 542 developing utilities for 571–3 tables 542 perfect information 548–9 periodic review model complex versions 440–1 with probabilistic demand 437–41 PERT/CPM 371–2 project scheduling with known activity times 372–81 project scheduling with uncertain activity times 381–8 petroleum distribution (Gulf of Mexico) 509 Peugeot Pfizer 504 Pharmacia & Upjohn 504 Phoenix Computer 202 Photo Chemicals problem 277–8 pivot column 223 pivot element 223 pivot row 223 Planning and Development Council (Oman) calculating branch probabilities 566–8 decision analysis with sample information 556–66 decision making with probabilities 546–50 decision making without probabilities 543–6 decision tree/payoff table 580–1 problem formulation 541–3 risk analysis/sensitivity analysis 551–5 Poisson probability distribution 454–5 PortaCom 492, 525 what-if analysis 492–3 PortaCom simulation model 493–501 direct labour cost 493 with Excel 533–4 first-year demand 494–5 parts cost 494 random numbers/generating probabilistic values 496–500 results 501–3 running 500 portfolio selection 170–3 post offices (Scotland) 479–80 post-optimality analysis 86, 120 posterior probabilities 556 Potsdam City Council (Germany) 575–7 preemptive priorities 595 objective function 597 Premier Consulting problem 330–1 primal problem 266, 269 finding the dual of any primal problem 270–2 primal solution 270 primary goal (priority level 1) 595, 603 prior probability 556 priority ranking 623–4 probabilities branch 566–8 conditional 566–7 decision making with 546–50 decision making without 543–6 joint 567 posterior 556 prior 556 problem recognition solution 36 structuring/definition 9–10 problem formulation 36-9 541 decision trees 542–3 payoff tables 542 process 138–9 Procter & Gamble (P&G) 321 product mix 134–5 product sourcing 321 production cost 145 production management 140–56 make-or-buy decisions 140–3 scheduling 143–50 workforce assignment 150–6 production scheduling 321–4 production strategy 77–8 productivity 481 program evaluation and review technique (PERT) 371–2 project completion time 386–7 project management 20 project network 372 project planning project scheduling known activity times 372–81 uncertain activity times 381–8 property purchase strategy 585–6 proportionality 40 pupil transportation (North Carolina) 190 Quality Air Conditioning problem 128–9 quantitative analysis 13 quantity discounts 425–7 queue discipline 453 queuing 7, 452 queuing models 21 economic analysis 468–9 Excel solution 461 finite calling populations 476–9 general relationships 466–7 Kendall notation 470 multiple-channel with Poisson arrivals, arbitrary service times and no queue 473–5 multiple-channel with Poisson arrivals and exponential service times 462–6 single-channel with Poisson arrivals and arbitrary service times 471–2 single-channel with Poisson arrivals and exponential service times 456–61 system structure 452–6 queuing operation 459–60 queuing simulation 491, 509–10 Hong Kong Savings Bank ATM 510–19 Quick and Easy fast-food problem 199–200 random numbers 496–500 range of feasibility 261–5 range of optimality 88, 255 R.C Coleman 401–2 Reckitt and Coleman 170 recommendations 11 reduced costs 97, 103 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com INDEX redundant constraint 52 Regional Airlines 486 regression analysis 22 relevant cost 104 rental car problem 333 reorder point 413 reservation systems 490 revenue management 178–82 right-hand side of a constraint 93–5 right-hand side values 258–65 risk analysis 492 decision making 551 PortaCom project 492 simulation 493–502 what-if analysis 492–3 risk profile 562–4 River City Fire Department 448–9 RMC Corporation 73, 250–1, 627–9 Robotics Manufacturing Company problem 484–5 Romans Food Market (Italy) problem 195 Romero Department Store problem 582 Round Tree Manor problem 133 route capacities and/or minimums 285 unacceptable 285 Ruiters’ Manufacturing Company problem 628–9 Russo Manufacturing Company problem 583–4 Ryan Pharmaceuticals 314–20 safety stock 406–7, 436–7 sample information 556 decision strategy 558–62 decision tree 556–8 efficiency of 565–6 expected value of 564–5 risk profile 562–4 Samsung scheduling 143–50 change-in-production-level costs 145–6 inventory, stock, holding cost 145 production cost 145 workforce 204–5 school meals 96 scoring model 594, 609–14 Scot Air problem 579–80 Scott and Associates Inc problem 332 Seasongood & Mayer (Cincinnati, Ohio) 381 Seastrand Oil Company problem 195 secondary goal (priority level 2) 595, 603 sensitivity analysis 86–8 computer solution 97–105 decision making 552–5 EOQ model 414–15 graphical solution 88–95 more than two decision variables 105–15 with Simplex tableau 255–65 Taiwan Electronic Communications problem 115–20 service level 504 service rate 453 setup cost 418 shadow price 95 Shimla Textile Mill (India) 202–3 shortage 421 shortest route 345–6 shortest route algorithm 346–53 Silver Star Bicycle Company problem 197 Simplex method 212 algebraic overview 212–16 calculating next tableau 222–9 duality 266–72 general case 230–7 improving solution 218–22 minimization problem 237–9 sensitivity analysis 255–65 setting up initial tableau 217–18 special cases 239–48 summary of 228–9 tableau form 216–17 transportation problem 286–302 simulation 7, 21, 490 advantages/disadvantages 522 computer implementation 520–1 flows 491 inventory systems 490, 504–8 new product development 490 queuing systems 491, 509–19 reservation systems 490 risk analysis 492–504 spreadsheets 520 verification/validation 521–2 simultaneous changes 92–3, 99–101, 265 single-channel queue 454 with Poisson arrivals and arbitrary service times 471–2 with Poisson arrivals and exponential service times 456–61 single-period inventory model with probabilistic demand 427–32 slack variables 51–2 soft MS 10 solutions 11 Souk al Bustan Shopping Centre (Dubai) 372–3 South Central Airlines problem 528–9 spreadsheets 18, 520 Stad National Bank problem 481–2 staff 157 staff selection 632–3 standard form 52 states of nature 541 static simulation models 509 steady-state operation 456 stepping-stone method 293–6 stock investment 632 stock-out 421 stock-out cost 408 Stockholm Construction Company 587 Suncoast Office Supplies 602–7 sunk cost 104 687 surplus variables 59–61 Suyuti Auto problem 443–5 Swofford real estate investment 569–74 synthesization 619–20 tableau form 216–17 calculating next tableau 222–9 eliminating negative right-hand side values 235 equality constraints 234–5 general case 230–7 greater-than-or-equal-to constraints 230–4 initial setup 217–18 summary 236–7 Taiwan Electronic Communications 115–20 tea production/distribution 119 time series models 21 total cost model 418–20 traffic control 71 training 157 transient period 456 transportation 8, 20 transportation problem Excel solution 338–9 general linear programming model 285–6 maximization objective function 285 network model 280–5 route capacities and/or route minimums 285 total supply not equal to total demand 284–5 unacceptable routs 285 variations 283–4 transportation Simplex method 286–7 finding initial feasible solution 288–91 iterating to optimal solution 291–300 problem variations 302 summary 300–2 transportation tableau 287 transshipment problem Excel solution 341–3 general linear programming model 320 network model 314–19 production and inventory application 320–4 TreePlan 587–92 trend projecting 22 Tri-County Utilities problem 329 truck leasing strategy 136 Tucker Inc problem 131–2 Two-Rivers Oil Company (Pittsburgh) problem 196–7 Uforia Corporation problem 252–3 Uhuru Craft Cooperative (Tanzania) 27 UK Oil 594–601 UltraPortable model 212 unacceptable assignments 314 unacceptable routes 302 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.freebookslides.com 688 INDEX unbounded problems 64–6, 240–1 uncertain activity times 382–5 unit columns 217 unit vectors 217 Uppsala Chamber of Commerce 191 UPS 287 utility 568–9 definition/concept 569–71 developing for payoffs 571–3 expected 573–4 utilization factor 458 validation 521 vehicle fleet management (Quebec) 608 verification 521 Vipac (Mexico) 524 Voilmer Manufacturing (Germany) 121–2 VOLCANO (Volume, Location and Aircraft Network Optimizer) 287 Wagner Fabricating Company (Germany) 447–8 waiting line system 481 see also queuing Welte Mutual (Berlin) 170–3, 193 Western Family Restaurant problem 199 what-if analysis 492–3 when-to-order decision 413-14, 435–7 workforce assignment 150–6 workforce scheduling 204–5 workload balancing 76–7 Zondo Industries problem 584–5 Copyright 2014 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it ... right to remove additional content at any time if subsequent rights restrictions require it An Introduction to Management Science: Quantitative Approaches to Decision Making, 2nd Edition Anderson, ... qualitative and quantitative approaches to managerial decision making Why is it important for a manager or decision maker to have a good understanding of both of these approaches to decision making? ... your bank or finance company had to decide what credit limit to give you when you took out the card Too little and you might use a card from another bank Too much and you may get into debt and