Introduction to Management Science This page intentionally left blank Edition Introduction to Management Science 12 Global Edition Bernard W Taylor III Virginia Polytechnic Institute and State University Boston Columbus Indianapolis New York San Francisco Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Vice President, Business Publishing: Donna Battista Acquisitions Editor: Daniel Tylman Editorial Assistant: Linda Albelli Vice President, Product Marketing: Maggie Moylan Director of Marketing, Digital Services and Products: Jeanette Koskinas Senior Product Marketing Manager: Alison Haskins Executive Field Marketing Manager: Lori DeShazo Senior Strategic Marketing Manager: Erin Gardner Team Lead, Program Management: Ashley Santora Program Manager: Claudia Fernandes Team Lead, Project Management: Jeff Holcomb Project Manager: Meredith Gertz Acquisitions Editor, Global Edition: Vrinda Malik Senior Project Editor, Global Edition: Daniel Luiz Manager, Media Production, Global Edition: M Vikram Kumar Senior Manufacturing Controller, Production, Global Edition: Trudy Kimber Operations Specialist: Carol Melville Creative Director: Blair Brown Art Director: Jon Boylan Vice President, Director of Digital Strategy and Assessment: Paul Gentile Manager of Learning Applications: Paul DeLuca Digital Editor: Megan Rees Director, Digital Studio: Sacha Laustsen Digital Studio Manager: Diane Lombardo Digital Studio Project Manager: James Bateman Digital Content Team Lead: Noel Lotz Product Manager: James Bateman Full-Service Project Management and Composition: Lumina Datamatics, Inc Cover Designer: Lumina Datamatics, Inc Cover Art: © Kumpol Chuansakul\Shutterstock Microsoft and/or its respective suppliers make no representations about the suitability of the information contained in the documents and related graphics published as part of the services for any purpose All such 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and/or the program(s) described herein at any time Partial screen shots may be viewed in full within the software version specified Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U.S.A and other countries This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited 2016 The rights of Bernard W Taylor III to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States edition, entitled Introduction to Management Science, 12th edition, ISBN 978-0-13-377884-7, by Bernard W Taylor III, published by Pearson Education © 2016 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners ISBN 10: 1-29-209291-2 ISBN 13: 978-1-29-209291-1 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 14 13 12 11 10 Typeset in Times LT Std Roman by 10/12 Printed and bound by RR Donnelley Kendallville in the United States of America To Diane, Kathleen, and Lindsey This page intentionally left blank Brief Contents Preface 13 Management Science 21 Linear Programming: Model Formulation and Graphical Solution 51 Linear Programming: Computer Solution and Sensitivity Analysis 94 Linear Programming: Modeling Examples 133 Integer Programming 205 Transportation, Transshipment, and Assignment Problems 257 Network Flow Models 315 Project Management 366 Multicriteria Decision Making 435 10 Nonlinear Programming 506 11 Probability and Statistics 531 12 Decision Analysis 566 13 Queuing Analysis 627 14 Simulation 667 15 Forecasting 719 16 Inventory Management 785 Appendix A Normal and Chi-Square Tables 827 Appendix B Setting Up and Editing a Spreadsheet 829 Appendix C The Poisson and Exponential Distributions 833 Solutions to Selected Odd-Numbered Problems 835 Glossary 845 Index 850 The following items can be found on the Companion Web site that accompanies this text: Web Site Modules Module A: The Simplex Solution Method A-1 Module B: Transportation and Assignment Solution Methods B-1 Module C: Integer Programming: The Branch and Bound Method C-1 Module D: Nonlinear Programming Solution Techniques D-1 Module E: Game Theory E-1 Module F: Markov Analysis F-1 Contents Management Science Application: Preface 13 Management Science Allocating Seat Capacity on Indian Railways Using Linear Programming 56 Graphical Solutions of Linear Programming Models 56 21 The Management Science Approach to Problem Solving 22 Management Science Application: Renewable Energy Investment Decisions at GE Energy 68 A Minimization Model Example 68 Time Out: for Pioneers in Management Science 25 Management Science Application: Management Science Application: Room Pricing with Management Science at Marriott 26 Management Science and Business Analytics 27 Model Building: Break-Even Analysis 28 Computer Solution 32 Management Science Modeling Techniques 35 Determining Optimal Fertilizer Mixes at Soquimich (South America) 72 Irregular Types of Linear Programming Problems 74 Characteristics of Linear Programming Problems 77 Management Science Application: The Application of Management Science with Spreadsheets 36 Business Usage of Management Science Techniques 38 Management Science Application: Management Science in Health Care 39 Management Science Models in Decision Support Systems 40 Summary 41 • Problems 42 • Case Problems 48 Linear Programming: Computer Solution and Sensitivity Analysis 94 Computer Solution 95 Management Science Application: Scheduling Air Ambulance Service in Ontario (Canada) 100 Linear Programming: Model Formulation and Graphical Solution 51 Management Science Application: Model Formulation 52 A Maximization Model Example 52 Summary 113 • Example Problem Solutions 113 • Problems 116 • Case Problems 130 Time Out: for George B Dantzig Summary 78 • Example Problem Solutions 78 • Problems 82 • Case Problems 91 53 Improving Profitability at Norske Skog with Linear Programming 101 Sensitivity Analysis 102 contents 9 Linear Programming: Modeling Examples Management Science Application: A Set Covering Model for Determining Fire Station Locations in Istanbul 229 133 Summary 229 • Example Problem Solution 230 • Problems 230 • Case Problems 247 A Product Mix Example 134 Time Out: for George B Dantzig 139 A Diet Example 139 An Investment Example 142 Management Science Application: A Linear Programming Model for Optimal Portfolio Selection at GE Asset Management 147 A Marketing Example 148 A Transportation Example 152 A Blend Example 155 A Multiperiod Scheduling Example 159 257 The Transportation Model 258 Time Out: for Frank L Hitchcock and Tjalling C Koopmans 260 Management Science Application: Reducing Transportation Costs in the California Cut Flower Industry 261 Computer Solution of a Transportation Problem 261 Management Science Application: Linear Programming Blending Applications in the Petroleum Industry 160 Management Science Application: Employee Management Science Application: Analyzing Management Science Application: Management Science Application: Container Traffic Potential at the Port of Davisville (RI) 267 Scheduling with Management Science 162 A Data Envelopment Analysis Example 164 The Silk Road Once Again Unites East and West 271 The Assignment Model 271 Computer Solution of an Assignment Problem 272 Measuring Asian Ports’ Efficiency Using Dea 166 Summary 168 • Example Problem Solution 169 • Problems 171 • Case Problems 200 Transportation, Transshipment, and Assignment Problems Integer Programming Management Science Application: 205 Improving Financial Reporting with Management Science at Nestlé 275 Integer Programming Models 206 Management Science Application: Management Science Application: Selecting Assigning Umpire Crews at Professional Tennis Tournaments 276 Volunteer Teams at Eli Lilly to Serve in Impoversihed Communities 209 Integer Programming Graphical Solution 209 Computer Solution of Integer Programming Problems with Excel and QM for Windows 211 Time Out: for Ralph E Gomory 212 Management Science Application: Scheduling Appeals Court Sessions in Virginia with Integer Programming 215 Management Science Application: Planes Get a Lift from Integrated Solutions 220 0–1 Integer Programming Modeling Examples 220 Summary 277 • Example Problem Solution 277 • Problems 278 • Case Problems 306 Network Flow Models 315 Network Components 316 The Shortest Route Problem 317 The Minimal Spanning Tree Problem 325 Management Science Application: Determining Optimal Milk Collection Routes in Italy 328 The Maximal Flow Problem 329 www.downloadslide.net 844 25 27 29 31 33 35 Solutions to Selected Odd-Numbered Problems Q = 661,800.9 bales; TC = $10,158,664; shipments = 1.88; time between orders = 194 days (a) Q = 4,912.03, TC = $18,420.11; (b) Q = 3,833.19, TC = $17,249.36; select new location Cc = $950 take discount, Q = 300 Q = 500, TC = $64,424 Q = 6,000, TC = $85,230.33 37 Q = 30,000, TC = $14,140 39 Q = 20,000, TC = $893,368 41 91% 43 R190%2 = 74.61 gal; increase safety stock to 26.37 gal 45 254.4 gal 47 R = 24.38 49 120 pizzas 51 (a) 15.15%; (b) R = 6.977 pizzas www.downloadslide.net Glossary A B C activities in a CPM/PERT project network, the branches reflecting project operations activity slack in a CPM/PERT network, the amount of time that the start of an activity can be delayed without exceeding the critical path project time adjusted exponential smoothing the exponential smoothing forecasting technique adjusted for trend changes and seasonal patterns agile project management an incremental approach to project management that is more adaptable to change caused by uncertainty and risk analogue simulation replacement of an original physical system with an analogous physical system that is easier to test and manipulate analytical containing or pertaining to mathematical analysis using formulas or equations analytical hierarchy process (AHP) ranks decision alternatives according to multiple criteria a priori probability one of the two types of objective probabilities; given a set of outcomes for an activity, the ratio of the number of desired outcomes to the total number of outcomes arrival rate the number of arrivals at a service facility (within a queuing system) during a specified period of time artificial variable a variable that is added to an = or Ú constraint so that initial solutions in a linear programming problem can be obtained at the origin assignment model a type of linear programming model similar to a transportation model, except that the supply at each source is limited to one unit and the demand at each destination is limited to one unit average error the cumulative error, averaged over the number of time periods back order a customer order that cannot be filled from existing inventory but will be filled when inventory is replenished backward pass a means of determining the latest event times in a CPM/PERT network balanced transportation model a model in which supply equals demand basic feasible solution any solution in linear programming that satisfies the model constraints basic variables in a linear programming problem, variables that have values (other than zero) at a basic feasible solution point Bayesian analysis a method for altering marginal probabilities, given additional information; the altered probabilities are referred to as revised or posterior probabilities Bernoulli process a probability experiment that has the following properties: (1) each trial has two outcomes, (2) the probabilities remain constant, (3) the outcomes are independent, and (4) the number of trials is discrete beta distribution a probability distribution used in network analysis for determining activity times binomial distribution a probability distribution for experiments for which the Bernoulli properties hold branch in a network diagram, a line that represents the flow of items from one point (i.e., node) to another branch and bound method a solution approach whereby a total set of feasible solutions is partitioned into smaller subsets, which are then evaluated systematically; this technique is used extensively to solve integer programming problems break-even analysis the determination of the number of units that must be produced and sold to equate total revenue with total cost break-even point the volume of units that equates total revenue with total cost business analytics uses large amounts of data in combination with management science techniques and modeling to help managers make decisions calculus a branch of mathematics that is concerned with the rate of change of functions; the two basic forms of calculus are differential calculus and integral calculus calling population the source of customers to a waiting line carrying cost the cost incurred by a business for holding items in inventory causal forecasting methods a class of mathematical techniques that relate variables to other factors that cause forecast behavior classical optimization the use of calculus to find optimal values for variables classical probability an a priori probability coefficient of determination a measure of the strength of the relationship between the variables in a regression equation coefficient of optimism a measure of a decision maker’s optimism collectively exhaustive events all the possible events of an experiment concave curve a curve shaped like an inverted bowl conditional probability the probability that one event will occur, given that another event has already occurred constrained optimization model a model that has a single objective function and one or more constraints constraint a mathematical relationship that represents limited resources or minimum levels of activity in a mathematical programming model continuous distribution a probability distribution in which the random variables can equal an infinite number of values within an interval continuous random variable a variable that can take on an infinite number of values within some interval convex curve a curve shaped like an upright bowl correlation a measure of the strength of the causal relationship between the independent 844 www.downloadslide.net Glossary 845 and dependent variables in a linear regression equation critical path the longest path through a CPM/PERT network; it indicates the minimum time in which a project can be completed critical path method (CPM) a network technique that uses deterministic activity times for project planning and scheduling cumulative error a sum of the forecasted errors cumulative probability distribution a probability distribution in which the probability of an event is added to the sum of the probabilities of the previously listed events cycle movement up or down during a trend in a forecast D data pieces of information database an organized collection of numeric information data mining a process and set of tools used to categorize large amounts of data in order to identify patterns and relationships among variables decision analysis the analysis of decision situations in which certainty cannot be assumed decision support system (DSS) a computerbased information system that a manager can use to assist in and support decision making decision tree a graphical diagram for analyzing a decision situation decision variable a variable whose value represents a potential decision on the part of the manager Delphi method a procedure for acquiring informal judgments and opinions from knowledgeable individuals to use as a subjective forecast dependent demand typically, component parts used internally to produce a final product dependent events events for which the probability of one event is affected by the probability of occurrence of other events derivative in calculus, a transformed form of a mathematical function that defines the slope of the function deterministic characterized by the assumption that there is no uncertainty deviational variables in a goal programming model constraint, variables that reflect the possible deviation from a goal level differential the derivative of a function directed branch a branch in a network in which flow is possible in only one direction discrete distribution a probability distribution that consists of values for the random variable that are countable and usually integers dual an alternative form of a linear programming model that contains useful information regarding the value of resources, which form the constraints of the model dummy activity a branch in a CPM/ PERT network that reflects a precedence relationship but does not represent any passage of time E earliest activity times in a CPM/PERT network, the earliest start and earliest finish times at which an activity can be started without exceeding the critical path project time economic forecast a prediction of the state of the economy in the future economic order quantity (EOQ) the optimal order size that corresponds to total minimum inventory cost efficiency of sample information an indicator of how close to perfection sample information is; it is computed by dividing the expected value of sample information by the expected value of perfect information empirical consisting of (or based on) data or information gained from experiment and observation equal likelihood criterion a decision-making method in which all states of nature are weighted equally (also known as the LaPlace criterion) equilibrium point the outcome of a game that results from a pure strategy event the possible result of a probability experiment events in a CPM/PERT project network, the nodes that reflect the beginning and termination of activities expected monetary value the expected (average) monetary outcome of a decision, computed by multiplying the outcomes by their probabilities of occurrence and summing these products expected opportunity loss the expected cost of the loss of opportunity resulting from an incorrect decision by the decision maker expected value an average value computed by multiplying each value of a random variable by its probability of occurrence expected value of perfect information (EVPI) the value of information expressed as the amount of money that a decision maker would be willing to pay to make a better decision expected value of sample information (EVSI) the difference between the expected value of a decision situation with and without additional information experiment in probability, a particular action, such as tossing a coin exponential distribution a probability distribution often used to define the service times in a queuing system exponential smoothing a time series forecasting method similar to a moving average in which more recent data are weighted more heavily than past data extreme points the maximum and minimum points on a curve (also known as relative extreme points); in a linear programming problem, a protrusion in the feasible solution space F factorial for a value of n, n! = n(n - 1) (n - 2) g(2)(1) feasible solution a solution that does not violate any of the restrictions or constraints in a model feedback decision results that are fed back into a management information system to be used as data finite calling population a source of customers for a queuing system limited to a finite number finite queue a queue with a limited (maximum) size fixed costs costs that are independent of the volume of units produced forecast a prediction of what will occur in the future forecast error the difference between actual and forecasted demand forecast reliability a measure of how closely a forecast reflects reality forecast time frame how far in the future a forecast projects forward pass a method for determining earliest activity times in a CPM/PERT network frequency distribution the organization of events into classes, which shows the frequency with which the events occur functional relationship an equation that relates a dependent variable to one or more independent variables G Gantt chart a graph or bar chart with a bar for each activity in a project, showing the passage of time goal constraint a constraint in a goal programming model that contains deviational variables goal programming a linear programming technique that considers more than one objective in the model goals the alternative objectives in a goal programming model www.downloadslide.net 846 Glossary Glossary H Hurwicz criterion a method for making a decision in a decision analysis problem; the decision is a compromise between total optimism and total pessimism I identity matrix a matrix containing ones along the diagonal and zeros elsewhere implementation the use of model results implicit enumeration a method for solving integer programming problems in which obviously infeasible solutions are eliminated and the remaining solutions are systematically evaluated to see which one is best independent demand final product demanded by an external customer independent events events for which the probability of occurrence of one event does not affect the probability of occurrence of the other events inequality a mathematical relationship containing a Ú or … sign infeasible problem a linear programming problem with no feasible solution area and thus no solution instantaneous receipt the assumption that once inventory level reaches zero, an order is received after the passage of an infinitely small amount of time integer programming a form of linear programming that generates only integer solution values for the model variables inventory a stock of items kept on hand by an organization to use to meet customer demand inventory analysis the analysis of the problems of inventory planning and control, with the objective of minimizing inventoryrelated costs J joint probability the probability of several events occurring jointly in an experiment L LaPlace criterion a decision-making method in which all states of nature are weighted equally (more commonly known as the equal likelihood criterion) latest activity times in a CPM/PERT network, the latest start and latest finish times at which an activity can be started without exceeding the critical path project time linear programming a management science technique used to determine the optimal way to achieve an objective, subject to restrictions, in cases in which all the mathematical relationships are linear linear (simple) regression a form of regression that relates a dependent variable to one independent variable linear trend line a forecast that uses the linear regression equation to relate demand to time long-range forecast a forecast that typically encompasses a period of time longer than 1 or 2 years M management science the application of mathematical techniques and scientific principles to management problems to help managers make better decisions marginal probability the probability that a single event will occur marginal value also known as dual value and shadow price, the dollar value of obtaining one additional resource unit maximal flow problem a network problem in which the objective is to maximize the total amount of flow from a source to a destination maximax criterion a method for making a decision in a decision analysis problem; the decision will result in the maximum of the maximum payoffs maximin criterion a method for making a decision in a decision analysis problem; the decision will result in the maximum of the minimum payoffs maximization problem a linear programming problem in which an objective, such as profit, is maximized mean absolute deviation (MAD) a measure of the difference between a forecast and what actually occurs mean absolute percent deviation (MAPD) the absolute forecast error, measured as a percentage of demand mean squared error (MSE) the average of the squared forecast errors medium-range forecast a forecast that encompasses anywhere from month to 1 year minimal spanning tree problem a network problem in which the objective is to connect all the nodes in a network so that the total branch lengths are minimized minimax regret criterion a method for making a decision in a decision analysis problem; the decision will minimize the maximum regret minimization problem a linear programming problem in which an objective, such as cost, is minimized minimum cell cost method a method for determining the initial solution to a transportation model mixed constraint problem a linear programming problem with a mixture of … , = , and Ú constraints mixed integer model an integer linear programming model that can generate a solution with both integer and non-integer values model an abstract (mathematical) representation of a problem Monte Carlo process a technique used in simulation for selecting numbers randomly from a probability distribution most likely time one of three time estimates used in a beta distribution to determine an activity time; the time that would occur most frequently if the activity was repeated many times moving average a time series forecasting method that involves dividing values of a forecast variable by a sequence of time periods multiple optimum solutions alternative solutions to a linear programming problem, all of which achieve the same objective function value multiple regression a form of regression that relates a dependent variable to two or more independent variables multiple-server queuing system a system in which a single waiting line feeds into two or more servers in parallel mutually exclusive events in a probability experiment, events that can occur only one at a time N network an arrangement of paths connected at various points (drawn as a diagram), through which an item or items move from one point to another network flow models a model that represents the flow of items through a system node in a network diagram, a point that represents a junction or an intersection; it is represented by a circle noninstantaneous receipt the gradual receipt of inventory over time nonlinear programming a form of mathematical programming in which the objective function or constraints (or both) are nonlinear functions normal distribution a continuous probability distribution that has the shape of a bell O objective function a mathematical relationship that represents the objective of a problem solution objective probability the relative frequency with which a specific outcome in an www.downloadslide.net Glossary 847 experiment has been observed to occur in the long run operating characteristics average values for characteristics that describe a waiting line opportunity cost table a table derived in the solution to an assignment problem optimal solution the best solution to a problem optimistic time one of three time estimates used in a beta distribution to determine an activity time; the shortest possible time it would take to complete an activity if everything went right order cycle the time period during which a maximum inventory level is depleted and a new order is received to bring inventory back to its maximum level ordering cost the cost a business incurs when it makes an order to replenish its inventory P pairwise comparison in AHP the comparison of two alternatives according to a criterion parameter a constant value that is generally a coefficient of a variable in a mathematical equation payoff table a table used to show the payoffs that can result from decisions under various states of nature penalty cost the penalty (or regret) suffered by a decision maker when a wrong decision is made periodic inventory system a system in which an order is placed for a variable amount at fixed time intervals permanent set in a shortest route network problem, a set of nodes to which the shortest route from the start node has been determined pessimistic time one of three time estimates used in a beta distribution to determine an activity time; the longest possible time it would take to complete an activity if everything went wrong pivot column the column corresponding to the entering variable Poisson distribution a probability distribution that describes the occurrence of a relatively rare event in a fixed period of time; often used to define arrivals at a service facility in a queuing system political/social forecast a prediction of political and social changes that may occur in the future population mean the mean of an entire set of data being analyzed posterior probability the altered marginal probability of an event based on additional information precedence relationship the relationship exhibited by events that must occur in sequence; such events can be represented by a CPM/PERT network preference scale in AHP assigns a value to different levels of preference primal the original form of a linear programming model priority the importance of a goal relative to other goals in a goal programming model probabilistic techniques management science techniques that take into account uncertain information and give probabilistic solutions probability distribution a distribution showing the probability of occurrence of all events in an experiment probability tree a diagram showing the probabilities of the various outcomes of an experiment production lot size model an inventory model for a business that produces its own inventory at a gradual rate (also known as the noninstantaneous receipt model) prohibited route in a transportation model, a route (i.e., variable) to which no allocation can be made project crashing a method for reducing the duration of a CPM/PERT project network by reducing one or more critical path activities and incurring a cost project evaluation and review technique (PERT) a network technique, designed for project planning and scheduling, that uses probabilistic activity times pseudorandom numbers random numbers generated by a mathematical process rather than by a physical process Q qualitative forecast methods nonquantitative, subjective forecasts based on judgment, opinion, experience, and expert opinion quantitative forecast methods forecasts derived from a mathematical formula quantity discount model an inventory model in which a discount is received for large orders queue a waiting line queue discipline the order in which customers waiting in line are served queuing analysis the probabilistic analysis of waiting lines R random number table a table containing random numbers derived from some artificial process, such as a computer program random numbers numbers that are equally likely to be drawn from a large population of numbers random variable a variable that can be assigned numeric values reflecting the outcomes of an event; because these values occur in no particular order, they are said to be random random variations movements in a forecast that are not predictable and follow no pattern regression a statistical technique for measuring the relationship of one variable to one or more other variables; this method is used extensively in forecasting regression equation an equation derived from historical data that is used to forecast regret a value representing the regret the decision maker suffers when a wrong decision is made relative frequency probability another name for an objective (a posteriori) probability; it represents the relative frequency with which a specific outcome has been observed to occur in the long run reorder lead time the time between the placement of an order and its receipt of inventory reorder point the inventory level at which an order is placed responsibility assignment matrix a chart showing who is responsible for project work return on investment (ROI) a measure used to evaluate projects by dividing the gain minus the cost by the cost rim requirements the supply and demand values along the outer row and column of a transportation tableau risk averter a person who avoids taking risks risk taker a person who takes risks in the hope of achieving a large return row operations method used to solve simultaneous equations in which equations are multiplied by constants and added or subtracted from each other run a sequence of sample values that displays the same tendency in a control chart S safety stock a buffer of extra inventory used as protection against a stockout (i.e., running out of inventory) sample a portion of the items produced used for inspection sample mean the mean of a subset of the population data satisfactory solution in a goal programming model, a solution that satisfies the goals in the best way possible scatter diagram a diagram used in forecasting that shows historical data points scientific method a method for solving problems that includes the following steps: (1) observation, (2) problem definition, www.downloadslide.net 848 Glossary Glossary (3) model construction, (4) model solution, and (5) implementation scope statement a document that states the justification for, and expected results of, a project search techniques methods for searching through the solutions generated by a simulation model to find the best one seasonal factor a numeric value that is multiplied by a normal forecast to get a seasonally adjusted forecast seasonal pattern in a forecast, a movement that occurs periodically and is repetitive seed value a number selected arbitrarily from a range of numbers to begin a stream of random numbers generated by a computerized random number generator sensitivity analysis the analysis of changes in the parameters of a linear programming problem sequential decision tree a decision tree that analyzes a series of sequential decisions service level the percentage of orders a business is able to fill from inventory in stock during the reorder period service rate the average number of customers that can be served from a queue in a specified period of time shadow price the price one would be willing to pay to obtain one more unit of a resource in a linear programming problem shared slack in a CPM/PERT network, slack that is shared among several adjacent activities shortest route problem a network problem in which the objective is to determine the shortest distance between an originating point and several destination points short-range forecast a forecast of the immediate future that is concerned with daily operations simple regression a form of regression that relates a dependent variable to one independent variable simplex method a tabular approach to solving linear programming problems simplex tableau the table in which the steps of the simplex method are conducted; each tableau represents a solution simulated time the representation of real time in a simulation model simulation the replication of a real system with a mathematical model that can be analyzed with a computer simulation language a computer programming language developed specifically for performing simulation single-server waiting line a waiting line that contains only one service facility at which customers can be served slack variable a variable representing unused resources that is added to a … inequality constraint to make the constraint an equation slope the rate of change in a linear mathematical function smoothing constant a weighting factor used in the exponential smoothing forecasting technique standard deviation a measure of dispersion around the mean of a probability distribution states of nature in a decision situation, the possible events that may occur in the future steady state a constant value achieved by a system after an extended period of time steady-state probability a constant probability that a system will end up in a particular state after a large number of transition periods stockout running out of inventory subjective probability a probability that is based on personal experience, knowledge of a situation, or intuition rather than on a priori or a posteriori evidence substitution method a method for solving nonlinear programming problems that contain only one equality constraint; the constraint is solved for one variable in terms of another and is substituted into the objective function surplus variable a variable that reflects the excess above a minimum resource requirement level; it is subtracted from a Ú inequality constraint in a linear programming problem synthesization in AHP a step where decision alternatives are prioritized within each criterion system a set or an arrangement of related items that forms an organic whole U unbalanced transportation model a transportation model in which supply exceeds demand or demand exceeds supply unbounded problem a linear programming problem in which there is no completely closed-in feasible solution area and therefore the objective function can increase infinitely unconstrained optimization model a model with a single objective function and no constraints undirected branch a branch in a network that allows flow in both directions utiles the units in which utility is measured utility a numeric measure of the satisfaction a person derives from money utilization factor the probability that a server in a queuing system will be busy V validation the process of making sure model solution results are correct (valid) variable within a model, a mathematical symbol that can take on different values variable costs costs that are determined on a per unit basis variance a measure of how much the values in a probability distribution vary from the mean Venn diagram a pictorial representation of mutually exclusive or nonmutually exclusive events W T technological forecast a prediction of what types of technology may be available in the future time series methods statistical forecasting techniques that are based solely on historical data accumulated over a period of time total revenue the volume of units produced multiplied by price per unit transportation model a type of linear programming problem in which a product is to be transported from a number of sources to a number of destinations at the minimum cost transshipment model an extension of the transportation model that includes intermediate points between sources and destinations trend a long-term movement of an item being forecasted weighted moving average a time series forecasting method in which the most recent data are weighted what-if? analysis a form of interactive decision analysis in which a computer is used to determine the results of making various changes in a model work breakdown structure (WBS) a structure that breaks down a project into its major subcomponents, components, activities, and tasks Z zero–one integer model an integer programming model that can have solution values of only zero or one www.downloadslide.net Index A A priori probability, 532 Absorbing state, F13 Abu Dhabi (Health Centers), 637 Activities, 377 Activity-on-Arrow (AOA) networks, 377–378 Activity-on-Node (AON) networks, 378–379 Activity scheduling, 380–383 backward pass, 382 critical path, 379–380, 383 earliest finish time, 381 earliest start time, 380 forward pass, 382 latest finish time, 382 latest start time, 382 shared slack, 384 slack, 383–384 Activity slack, 383–384 Adjusted exponential smoothing, 730–731 Agile project management, 376 Alternate optimal solution, 75 Amazon.com, 752 American Red Cross, 35, 166 Analogue simulation, 668 Analytical hierarchy process (AHP), 450–460 consistency index, 456 Excel, 458–460 normalized matrix, 453 pairwise comparisons, 451–452 preference scale, 451 preference vector, 453 random index, 457 Saaty, Thomas, 459 summary steps, 455 synthesization, 452 Analytics, 27 AOA (Activity-on-Arrow) networks, 377–378 AON (Activity-on-Node) networks, 378–379 Apple, 369 Arrival rate, 630 Poisson distribution, 630, 833 Artificial variable, A18, A22 Assignment model, 271–276 balanced model, 272 Excel, 272–273 Excel QM, 273–274 QM for Windows, 275–276 850 unbalanced model, 272 Assignment solution method, B22–B25 column reductions, B23 dummy column, B24 dummy row, B25 multiple optimal solutions, B24 opportunity cost table, B22 optimal solution, B24 prohibited assignment, B25 row reductions, B23 summary steps, B25 unbalanced, B24 ASSO.LA.C, 328 Association rule learning, 753 AT&T, 650 Average error (bias), 738 B Backward pass, 382 Bad debt example (see debt example), F13–F16 Balanced assignment problem, 272 Balanced transportation problem, 260 Bar chart, 373 Basic feasible solution, A6 Basic variables, A6 Battle of Britain, 25 Bayes, Thomas, 543 Bayes’s rule, 544, 591, 594 Bayesian analysis, 543–544, 589–591 Beer, Stafford, 25 Bernoulli process, 539 Beta distribution, 385, 387 mean, 387 variance, 387 Bias (see average error), 738 Binomial distribution, 538–540 Blackett, P.M S., 25 Blackett’s Circus, 25 Blend example (linear programming), 155–159 Booz, Allen, Hamilton, 378 Branch and bound method, C2–C9, 211 Branches, 316, 377 Brand-switching problem, F2 Break-even analysis, 28–32 Excel, 32, 33 Excel QM, 34 fixed costs, 28 graphical solution, 30–32 profit, 29 profit analysis, 28, 29 QM for Windows, 32, 34 sensitivity analysis, 30, 31 simulation, total cost, 28 variable costs, 28 volume, 28, 29, 30 Break-even point, 29 Break-even volume, 28, 29, 30 British Petroleum (BP), 160 Buffer stock, 786 Bush, Vannevar, 25 Business analytics, 22, 27 C California Cut Flower Commission, 261 Calling population, 630 Canadian Army, 35 Capacity-planning problem, 162 Capital budgeting example (0–1 integer programming), 221–222 Carrying costs, 791–793 Causal forecasting methods, 721 Centers for Disease Control and Prevention (CDC), 35, 575, 681 Charnes, Abraham, 447 Chi-square table, 828 Chi-square test, 552–555, 828 Classical optimization, 510 Classical probability, 532 Classification (in data mining), 753 Clustering analysis, 753 Coefficient of determination, 746 Coefficient of optimism, 571 Coefficient of pessimism, 571 Collectively exhaustive (events), 535 Compana Sud Americana de Vapores (CSAV), 727 Complete enumeration, C11 Conant, James B., 25 Concurrent activities, 377 Conditional constraint, 208 www.downloadslide.net Index 851 Conditional probability, 537 Confidence limits, 687 Conservation of flow (networks), 322 Consistency index, 456 Constant service times, 638–639 Constrained optimization, 510–512 Constraints, 24, 52, 54, 55, 70 Constraints (in linear programming), 52, 54, 55, 70 Contingency constraint, 207 Continuous inventory system, 789–790 Continuous probability distribution, 546, 682–686 Continuous random variable, 546 Cook County Hospital, 39 Cooper, William W., 447 Corequisite constraint, 208 Correlation, 745–746 Cost management (in a project), 374 Cost variance, 375 Covariance, 520 CPM (critical path method), 367, 373, 376, 378 CPM/PERT, 38, 367, 373, 374, 376–392 activity scheduling, 380–383 backward pass, 382 beta distribution, 385 branches, 377 concurrent activities, 377 crashing, 396–400 critical path, 379–380, 383 dummy activities, 378 earliest finish time, 381 earliest start time, 380 Excel, 403–405 Excel QM, 391–392 forward pass, 382 latest finish time, 382 latest start time, 382 linear programming formulation, 401–406 Microsoft Project, 392–396 most likely time estimate, 385, 387 nodes, 377 optimistic time estimate, 385, 387 pessimistic time estimate, 385, 387 precedence relationships, 377 probabilistic activity times, 385, 387 probability analysis, 389–391 project variance, 389 QM for Windows, 391–392 shared slack, 384 slack, 383–384 Crash cost, 397 Crash time, 397 Crashing (a project), 396–401, 405–408 crash costs, 397 crash times, 397 Excel, 406–408 linear programming, 405–406 normal activity costs, 397 normal activity times, 397 QM for Windows, 399–400 Criteria preference matrix, 453 Critical path, 379–380, 383 Critical path method (CPM), 367, 373, 374, 376–392 Crystal Ball, 689–696 CSX Transportation, 331 Cumulative error, 737–738 Cumulative probability distribution, 537 Cycles (in forecasting), 720 Cyclic (transition) matrix, F13 D Dantzig, George B., 53, 139, 330 Data, 24 Database, 40, 752 Data mart, 752, 753 Data warehouse, 752, 753 Data envelopment analysis (DEA) example (linear programming), 164–168 DEA (data envelopment analysis) example (linear programming), 164–168 Data mining, 723, 752–753 Debt example, F13 Decision analysis, 566–597 criteria, 569–574 dominant decision, 572 Excel, 574, 577, 580, 583–585, 589, 594 Excel QM, 577, 578, 581–583, 588–589 expected opportunity loss, 576–577 expected value, 575–578 payoff, 567 payoff table, 567 QM for Windows, 573–574, 577 states of nature, 567 Treeplan, 583–585 with additional information, 589–596 with probabilities, 575–589 without probabilities, 568–574 Decision-making criteria, 569–573, 575–577 equal likelihood, 572 expected opportunity loss, 576–577 expected value, 575–576 Hurwicz, 571–572 maximax, 569 maximin, 570 minimax regret, 570–571 minimin, 569 Decision sciences, 22 Decision strategies, 593 Decision support systems (DSS), 40–41 Decision trees, 579–589 Excel, 583–585 Excel QM, 581–583, 588 sequential, 585–589 TreePlan, 583–585, 589 with posterior probabilities, 591–593 Decision variables, 52, 54, 69 Degeneracy (in linear programming), A27–A29 Degeneracy (in transportation problem), B20–B22 Dell, 802 Delphi method, 723 Demand, 787 Dependent demand, 787 Dependent events, 540–543 Dependent variable, 64 Descriptive results, 25 Deterministic techniques, 37 Deviational variables, 437 Diet example (linear programming), 139–142 Dijkstra, E.W., 330 Directed branch, 329 Discrete probability distribution, 539 Discrete values, 546 Doig, A.C., 212 Dominant decisions, 572 Dominant strategies, E5–E6 Dual, 100, 111–113, 138, 146 Dual value, 100, 111–113, 138, 146 Dummy activities, 378 E Earliest event times, 401 Earliest finish time, 381 Earliest start time, 380 Earned value analysis (EVA), 375 East Carolina University Student Health Service, 39 Economic order quantity (EOQ), 790–804 assumptions of, 791 basic model, 791–796 carrying costs, 791–792 Excel, 803 Excel QM, 803 gradual usage model, 796 lead time, 808 noninstantaneous receipt model, 796–799 ordering cost, 793 production lot size model, 796 QM for Windows, 802, 807 reorder point, 808–809 robustness, 795 with safety stocks, 809 service level, 810–812 with shortages, 799–801 time, 795–796 total cost, 793–795 Efficiency of sample information, 596 Electronic data interchange (EDI), 41 Eli Lilly and Company, 209 Employee scheduling, 162 Entering nonbasic variable, A9, B13 Enterprise resource planning (ERP), 41 EOQ (economic order quantity), 790–804 assumptions of, 791 basic model, 791–796 carrying costs, 791–792 Excel, 803 Excel QM, 803 gradual usage model, 796 lead time, 808 noninstantaneous receipt model, 796–799 www.downloadslide.net 852 Index EOQ (economic order quantity) (continued) ordering cost, 793 production lot size model, 796 QM for Windows, 802, 807 reorder point, 808–809 robustness, 795 with safety stocks, 809 service level, 810–812 with shortages, 799–801 time, 795–796 total cost, 793–795 Equal likelihood criterion, 572 Equation of a line, 64, 732, 743 Equilibrium point, E5 Erlang, A.K., 630 Error (in forecasting), 737–738 EVA (earned value analysis), 375 Events, 534 collectively exhaustive, 535 dependent, 540–543 independent, 537–538 mutually exclusive, 534 EVPI (expected value of perfect information), 578 EVSI (expected value of sample information), 595–596 Excel, 32, 33, 40, 95–98, 106–107, 109, 111, 112, 136–137, 141, 144–145, 146, 149, 150, 151, 153–154, 157–158, 159, 162– 163, 167–168, 210, 211–214, 216–219, 221–222, 224–225, 227–228, 261–263, 269–270, 272–273, 322–324, 333–336, 403–405, 406–408, 445–449, 458–460, 461, 512–516, 517–518, 519–520, 522–523, 555–556, 574, 577, 580, 583–585, 589, 594, 637, 640–641, 643, 646, 651, 674–678, 680–682, 685–689, 739–741, 746–749, 749–752, 803, 807–808, 811, 813–814 analytical hierarchy process (AHP), 458–460 assignment problem, 272–273 break-even analysis, 32, 33 CPM/PERT, 403–405 crashing, 406–408 decision analysis, 574, 577, 580, 583–585, 589, 594 EOQ analysis, 803 expected value, 577 forecasting, 739–741, 746–749, 749–752 goal programming, 445–449 integer programming, 150–151, 210, 211–214, 216–219, 221–222, 224–225, 227–228 inventory management, 803, 807–808, 811, 813–814 linear programming, 95–98, 106–107, 109, 111, 112, 136–137, 141, 144–145, 146, 149, 150, 151, 153–154, 157–158, 159, 162–163, 167–168 linear regression, 746–749 Markov analysis, F16 maximal flow problem, 333–336 multiple regression, 749–752 nonlinear programming, 512–516, 517–518, 519–520, 522–523 posterior probabilities, 594 queuing analysis, 637, 640–641, 643, 646, 651 scoring model, 461 sensitivity analysis, 106–107, 109–113 shortest route problem, 321–324 shadow price, 111–112 simulation, 674–678, 680–682, 685–689 Solver, 96, 106 statistical analysis, 555–556 time series forecasting, 739–741 total integer programming problem, 216–219 transportation problem, 153–154, 261–263 transshipment problem, 269–270 TreePlan, 583–585 tutorial on, 829–832 Excel QM, 32, 34, 263–264, 272–273, 391–392, 577, 578, 581–583, 588–589, 638, 646, 651–652, 741–742, 803 Expected gain and loss method, E8 Expected opportunity loss, 576–587 Expected utility, 597 Expected value, 544–546, 575–578, 672 Expected value given perfect information, 579 Expected value of perfect information (EVPI), 578–579 Expected value of sample information (EVSI), 595–596 Expected value without perfect information, 579 Experiment (in probability), 534 Exponential distribution, 631, 834 Exponential service times, 631 Exponential smoothing, 726–730 smoothing constant, 727 Extranet, 41 Extreme points (in linear programming), 62 accuracy, 735–739 adjusted exponential smoothing, 730–731 average error (bias), 738 coefficient of determination, 746 correlation, 745–746 cumulative error, 737–738 cycles, 720 data mining, 723, 752–753 Delphi method, 723 error, 737–738 Excel, 739–741, 746–749, 749–752 Excel QM, 741–742 exponential smoothing, 726–730 linear regression, 743–745 linear trend line, 732–734 long-range forecasts, 720 mean absolute deviation (MAD), 736–737 mean absolute percentage deviation (MAPD), 737 mean squared error (MSE), 738 medium-range forecasts, 720 moving averages, 723–726 multiple regression, 749–752 QM for Windows, 742–743, 749, 750 qualitative methods, 721–723 random variations, 720 regression methods, 743–753 seasonal adjustments, 734–735 seasonal factor, 734 seasonal patterns, 720 short-range forecasts, 720 simple exponential smoothing, 726 smoothing constant, 727 time series methods, 723–735 trend, 720 weighted moving averages, 726 Forward pass, 382 Frequency distribution, 534 Fulkerson, D.R., 330 Functional relationship, 24 Fundamental matrix, F15 F G Facebook, 369 Facility location example, 223–226 0–1 integer programming, 223–226 nonlinear programming, 519–520 Factorials, 539 Feasible solution (in linear programming), 55, 71 Finite calling population, 644–647 Finite queue, 641–643 Fixed charge example (0–1 integer programming), 223–226 Fixed costs, 28 Fixed-order quantity system, 789 Fixed-time period system, 790 Ford, L.R., Jr., 330 Forecast accuracy, 735–739 Forecast error, 737–738 Forecasting, 38, 719–753 Game theory, E2–E10 closed loop, E8 dominant strategies, E5–E6 equilibrium point, E6 expected gain and loss method, E8–E10 maximin strategy, E4 minimax strategy, E4 mixed strategy game, E6–E8 n-person game, E2 optimal strategy, E3 payoff table, E3 pure strategy game, E3 QM for Windows, E5, E10 saddle point, E5 strategies, E3 two-person game, E2–E3 value of the game, E3 zero-sum game, E2 www.downloadslide.net Index 853 Gantt, Henry, 373 Gantt chart, 373–374 GE Asset Management, 147 GE Energy, 68 Global optimal, 507 Goal constraint, 437 Goal programming, 436–449 deviational variables, 437 Excel, 445–449 goals, 437 graphical solution, 440–443 model formulation, 436 objective function, 439, 440 priorities, 438 QM for Windows, 444–445 satisfactory solution, 443 Gomory, Ralph E., 212 Goodness-of-fit, 552 Gradual usage model, 796 Graphical solution, 30–32, 56–67, 70–74, 210–211, 440–443 break-even analysis, 30–32 goal programming, 440–443 infeasible problem, 75 integer programming model, 210–211 linear programming, 56–67, 70–74 maximization model, 57–67 minimization model, 70–74 multiple optimal solutions, 75 nonlinear programming, 508–510, 511–512 sensitivity analysis, 102–106 slack variable, 67 surplus variables, 74 summary steps, 67 unbounded problem, 76 Google, 369 H Harris, Ford, 790 Heineken USA, 732 Hewlett-Packard, 35 Hitchcock, Frank L., 260 Hurwicz criterion, 571–572 Hypo Real Estate Bank, 35 I Identity matrix, F15 Ijiri, Yuri, 447 Implementation, 22, 23, 27 Implicit enumeration, C11 Independent demand, 787 Independent events, 537–538 Independent variable, 64 Indian Railways, 56 Indiana University, 220 Infeasible problem (in linear programming), 75, A25–A26 Instantaneous receipt, 792 Institute for Operations Research and Management Sciences (INFORMS), 40 Integer programming, C1–C11, 150–151, 206–229 branch and bound method, C2–C9, 211 capital budgeting example, 221–222 complete enumeration, C11 conditional constraint, 208 contingency constraint, 207 corequisite constraint, 208 Excel, 150–151, 210, 211–214, 216–219, 221–222, 224–225, 227–228 facility location example, 223–226 fixed charge example, 223–226 graphical solution, 210–211 mixed integer model, 208–209, 216–219 multiple-choice constraint, 207 mutually exclusive constraint, 207 optimal solution, 211 QM for Windows, 213–215, 219, 230 relaxed solution, C3 rounded down solution, 210 set covering example, 226–228 total integer model, 206–207, 216 0–1 integer model, 207–208, 211–215 Interfaces, 38, 40 Internet, 41 Intranets, 41 Inventory, 786 average level, 792 buffer stock, 786 carrying costs, 791–793 costs, 791–795 definition of, 786 ordering costs, 787–788 role of, 796–797 safety stock, 786, 809, 810–812 shortage costs, 800 total cost, 793–795 Inventory control, 789–790 Inventory management, 785–814 certain demand, 791 control systems, 789–790 continuous system, 789–790 costs, 787–789 dependent demand, 787 elements of, 786–789 economic order quantity (EOQ), 790–796 Excel, 803, 807–808, 811, 813–814 Excel QM, 803 fixed-order quantity system, 789 fixed-time period system, 790 gradual usage, 796 independent demand, 787 instantaneous receipt, 792 noninstantaneous receipt, 798 periodic system, 790, 812–814 production lot size, 796 QM for Windows, 802, 807 quantity discounts, 804–808 reorder point, 808–809 role of, 786–787 safety stocks, 809, 810–812 shortages, 799–801 simulation, 668–678 Inverse (of a matrix), F15 Investment example (linear programming), 142–147 Investment portfolio selection example (nonlinear programming), 520–523 Irregular types of linear programming problems, 74 Istanbul Metropolitan Municipality, 229 J Joint probability, 535 Joint probability table, 542, 543 K Kelley, James E., Jr., 378 Koopmans, T.C., 260 L Lagrange multipliers method, 514, 516, D4–D6 Lagrangian function, D5 Land, A.H., 212 Lands’ End, 644 LaPlace criterion, 572 Latest finish time, 382 Latest start time, 382 Lead time, 808, 810, 811, 813 Least squares formula, 744 Linear equation, 64, 732, 743 Linear programming, 36, 37, 52–78, 94–113, 133–168, 322–323, 333–334, 401–406 assignment problem, 272 basic feasible solution, A6 basic variables, A6 blend example, 155–159 characteristics, 77 computer solution, 94–113, 136–138, 139, 141, 144–145, 146, 149–151, 153–154, 157–158, 159, 162–163, 167–168 constraints, 52, 54, 55, 70, 136 CPM/PERT, 401–406 crashing, 405–406 data envelopment analysis (DEA) example, 164–168 decision variables, 52, 54, 69 degeneracy, A27 diet example, 139–142 dual, 100, 111–113 dual value (see also shadow price), 100, 111–113, 138, 146 Excel, 95–98, 106–107, 109, 111, 112, 136–137, 141, 144–145, 146, 149, 150, 151, 153–154, 157–158, 159, 162–163, 167–168, 401–406 extreme points, 62 feasible solution, 55, 71 www.downloadslide.net 854 Index Linear programming (continued) feasible solution area, 59, 71 graphical solution, 56–67, 70–74 infeasible problem, 75 integer solutions, 150 investment example, 142–147 irregular types of problems, 74 marginal value, 100 marketing example, 148–151 maximal flow problem, 329–336, 333–334 maximization model, 52–56 minimization model, 68–70 mixed constraint problem, A21 model formulation, 52, 54, 69, 135 modeling examples, 134–168 multiple optimal solutions, 74 multiperiod scheduling example, 159–164 objective function, 52, 54, 70 optimal solution, 60, 73 parameters, 52, 102 project crashing, 405–406 primal, A30, A32 product mix example, 134–139 properties, 77 QM for Windows, 98–101, 107, 109, 137, 138, sensitivity analysis, 65, 102–113, 138, 142, 145–147, 158–159, 164 shadow price (see also dual value), 111–113, 146 shortest route problem, 322–323 simplex method, A1, 95 simplex tableau, A5 slack variables, 65 standard model form, 67 summary steps (graphical solution), 67 summary steps (model formulation), 54, 69, 135 surplus variables, 73 transportation problem, 152–154 transshipment problem, 268–269 unbounded problem, 76 Linear regression, 743–745 Linear trend line, 732–734 L.L Bean, 644 Local optimal, 507 Lockheed Martin, 517 London Crossrail, 391 Long-range forecasts, 720 M MAD (mean absolute deviation), 736–737 Malcolm, D.G., 378 Management science, 22 definition, 22 “Management Science Application” (box), 26, 35, 39, 56, 68, 72, 99, 101, 147, 160, 162, 166, 209, 215, 220, 229, 261, 271, 275, 276, 328, 331, 369, 375, 391, 400, 443, 450, 457, 462, 517, 536, 545, 575, 595, 637, 644, 650, 681, 688, 722, 727, 732, 740, 747, 788, 802, 807 Abu Dhabi (Health Centers), 637 American Red Cross, 35, 166 Apple, 369 ASSO.LA.C, 328 AT&T, 650 British Petroleum (BP), 160 Californic Cut Flower Commission, 261 Canadian Army, 35 Centers for Disease Control and Prevention (CDC), 35, 575, 681 Compana Sud Americana de Vapores (CSAV), 727 CSX Transportation, 331 Dell, 802 East Carolina University Student Health Services, 39 Eli Lilly and Company, 209 employee scheduling, 162 Facebook, 369 GE Asset Management, 147 GE Energy, 68 Google, 369 Heineken USA, 732 Hewlett-Packard, 35 Hypo Real Estate Bank, 35 Indian Railways, 56 Indiana University, 220 Istanbul Metropolitan Municipality, 229 John H Stroger Hospital (Chicago), 39 Lands’ End, 644 L.L Bean, 644 Lockheed Martin, 517 Lockheed Martin Space Systems, 35 London Crossrail, 375 Marriott, 26 Mars, 807 Memorial Sloan-Kettering Cancer Center, 39 Merrill Lynch Bank USA, Microsoft Excel, 35 Mount Sinai Medical Center (NY), 39 NBC, 443, 722 New York Power Authority, 595 Norske Skog (Norway), 101 Ornge, 99 Pentagon, 400 petroleum industry, 160 Proctor & Gamble, 35, 788 Pyrenees transportation routes, 450 Sloan-Kettering Cancer Center, 39 Somali pirates, 688 Soquimich (SA), 72 S.S Central America, 536 Transportation Security Administration (TSA), 747 Union Pacific Railroad, 275 University of Toronto, 35 U.S Army, 462 U.S Coast Guard, 545 U.S Commercial Aviation Partnership (USCAP), 747 U.S Postal Service, 271 Virginia Court of Appeals, 215 Virginia Department of Transportation (VDOT), 375 World War II generals, 457 Zara, 740 Management scientist, 23 MAPD (mean absolute percentage deviation), 737 Marginal probability, 535 Marginal value, 100 Marketing example (linear programming), 148–151 Markov analysis, F1–F17 absorbing state, F13 cyclic (transition) matrix, F13 debt example, F13–F16 Excel, F16 properties, F3 QM for Windows, F11 steady-state probabilities, F8 system state, F3 transient state, F13 transition matrix, F5–F8 transition probabilities, F3 Markov, Andrey A., F4 Markov process, F3 Markowitz, Harry, 520 Marriott, 26 Mars, 807 Matrix algebra, F5 Maximal flow problem, 329–336 directed branch, 329 Excel, 333–336 linear programming formulation, 333–334 net flow, 330 QM for Windows, 333 solution steps, 333 undirected branch, 329 Maximax criterion, 569 Maximin criterion, 570 Maximin strategy, E4 Maximization model (in linear prorgmming), 52–56, A5 Mean, 545, 547, 550 Mean absolute deviation (MAD), 736–737 Mean absolute percentage deviation (MAPD), 737 Mean squared error (MSE), 738 Medium-range forecasts, 720 Memorial Sloan Kettering Cancer Center, 39 Microsoft Excel, 35 Microsoft Project, 392–396 Middleton, Michael, 583 Minimal spanning tree problem, 325–328 QM for Windows, 328 solution steps, 327 Minimin criterion, 560 Minimax regret criterion, 570–571 Minimax strategy, E4 Minimization model (linear programming), 68–70, A16 Minimum cell cost method, B5–B6 Mixed constraint problem, A20, A21–A23 www.downloadslide.net Index 855 Mixed integer model, 208–209, 216–219 Mixed strategy game, E3, E6 Model, 23, 24 constraints, 24 construction, 23 formulation, 52, 54, 69 implementation, 22, 23, 27 linear programming, parameters, 23 variables, 23 solution, 22, 23, 24 Modified distribution method (MODI), B15–B19 summary steps, B19 Monte Carlo process, 668–673 Monte Carlo simulation, 668–673 Morgenstern, Oskar, E7 Most likely time estimate, 385, 387 Mount Sinai Hospital (Toronto), Moving averages, 723–726 MSE (mean squared error), 738 Multicollinearity, 752 Multicriteria decision making, 38, 435–462 analytical hierarchy process (AHP), 450–460 goal programming, 436–449 scoring model, 460–462 Multiperiod scheduling example (linear programming), 159–164 Multiple-choice constraint, 207 Multiple optimal solutions, 74, 264, A24–A25, B15 assignment problem, B24 linear programming, 74, A24–A25 transportation problem, 264, B15 Multiple regression, 749–752 Multiple-server waiting line, 647–652 Mutually exclusive constraint, 207 Mutually exclusive events, 534 N Naïve forecasting, 723 NBC, 722 Net (branch) flow, 330 Network, 37, 316 Network flow models, 315–336 components, 316 Excel, 322–324, 333–336 maximal flow, 329–336 minimal spanning tree, 325–328 QM for Windows, 321–322, 328, 333 shortest route, 317–324 New York Power Authority, 595 Nodes, 316, 377 Nonbasic variable, A9 Noninstantaneous receipt model, 798 Nonlinear profit analysis, 507–512 Nonlinear programming, 506–522 constrained optimization, 510–512 Excel, 512–516, 517–518, 519–520, 522–523 Lagrange multipliers, 514, 516 substitution method, D2–D4 Nonnegativity constraints, 55 Non-zero-sum game, E2 Normal activity costs, 397 Normal activity times, 397 Normal distribution, 389–391, 546–550 CPM/PERT network, 389–391 mean, 545, 547, 550 reorder point, 810 standard deviation, 546, 547, 548 table, 827 Normal table, 827 Normalized matrix (AHP), 453 Norske Skog (Norway), 101 Northwest corner method, B4–B5 N-person game, E2 O Objective function, 52, 54, 70, 439, 440 Objective probability, 532–533 OBS (organizational breakdown structure), 372 Online analytical processing (OLAP), 41 Operating characteristics (queuing), 628 Operations research, 22, 25 Opportunity loss, 570 Opportunity loss table, 570 Optimal solution (in linear programming), 60, 61, 73, 262, A14–A15, B13 Optimistic time estimate, 385, 387 Ordering cost, 787–788 Organizational breakdown structure (OBS), Ornge, 99 P Pairwise comparisons, 451–452 Parameters, 23, 52, 102 Payoff, 567 Payoff table, 567 Penalty cost (VAM), B6 Pentagon, 400 Performance management, 374–375 Periodic inventory system, 790, 812–814 with variable demand, 813 Permanent set, 318 PERT (project evaluation and review technique), 367, 373, 374, 376–392 Pessimistic time estimate, 385, 387 Pivot column, A10 Pivot column tie, A27 Pivot number, A12 Pivot row, A12 Pivot row tie (degeneracy), A27–A29 Poisson arrival rate, 630 Poisson distribution, 630, 833 Polaris missile project, 378 Population mean, 550 Population variance, 550 Posterior probability, 543 table, 593–594 Precedence relationships, 377 Preference scale, 451 Preference vector, 453 Primal, A30, A32 Prior probability, 532 Priorities (in goal programming), 438 Probabilistic activity times, 385, 387 Probabilistic techniques, 36, 37 Probability, 389–391, 531– 556 a priori, 532 binomial distribution, 538–540 chi-square test, 552–555 classical, 532 collectively exhaustive events, 535 conditional, 537 continuous distribution, 546 cumulative distribution, 537 dependent events, 540–543 discrete distribution, 539 distribution, 534 events, 534 Excel, 555–556 expected value, 544–546 experiment, 534 frequency distribution, 534 fundamentals of, 532, 534–537 goodness-of-fit, 552 independent events, 537–538 joint, 535 joint probability table, 542, 543 marginal, 535 mean, 545, 547, 550 mutually exclusive events, 534 normal distribution, 546–550 objective, 532–533 posterior, 543 prior, 532 probability distribution, 534 relative frequency, 532 revised, 543 standard deviation, 546, 547, 548, 552 subjective, 533 tree, 538 unconditional, 541 variance, 389, 545, 550 Venn diagram, 535, 536 Problem definition, 22, 23 Proctor & Gamble, 35, 788 Product mix (linear programming) model, 134–139 Production lot size model, 796 Profit, 29 Profit analysis (see break-even analysis), 28 Prohibited assignment, B25 Prohibited transportation route, 260, B22 Project control, 374–375 Project crashing (see crashing), 396–401, 405–408 Project evaluation and review technique (PERT), 376 Project management, 366–408 control, 374–375 cost management, 374 www.downloadslide.net 856 Index Project management (continued) CPM, 367, 373, 374, 376–392 crashing, 396–400 critical path, 379–380, 383 earned value analysis (EVA), 375 elements of, 367–376 Gantt chart, 373–374 organizational breakdown structure (OBS), 372 performance management, 374–375 PERT, 367, 373, 374, 376–392 planning, 367 project manager, 370 project network, 377–379 project return, 368 project team, 369–370 responsibility assignment matrix (RAM), 372 return on investment (ROI), 368 scope statement, 370 statement of work, 370 time management, 374 work breakdown structure (WBS), 370–372 Project manager, 370 Project planning, 367 Project team, 369–370 Project variance, 389 Properties (of linear programming), 77 Proportionality, 77 Pseudorandom numbers, 673 Pure strategy game, E3 Q QM for Windows, 32, 34, 98–101, 107, 109, 137, 138, 211, 213–215, 219, 230, 265–266, 275–276, 321–322, 328, 333, 391–392, 399–400, 444–445, 573–574, 577, 638, 641, 643, 647, 652, 742–743, 749, 750, 802, 807 assignment problem, 275–276 break-even analysis, 32, 34 CPM/PERT, 391–392 crashing, 399–400 decision analysis, 573–574, 577 EOQ analysis, 802 EOQ with quantity discounts, 807 expected value, 577 forecasting, 742–743, 749, 750 game theory, E5, E10 goal programming, 444–445 integer programming, 211, 213–215, 219, inventory, 802, 807 linear programming, 98–101, 107, 109, 137, 138 linear regression, 749 Markov analysis, F11 maximal flow problem, 333 minimal spanning tree problem, 328 mixed strategy game, E10 quantity discounts, 807 queuing analysis, 638, 641, 643, 647, 652 sensitivity analysis, 107, 110, 139 shortest route problem, 321–322 time series forecasting, 742–743 transportation problem, 265–266 0–1 integer programming problem, 213–215 Qualitative forecasting methods, 721–723 Quantitative analysis, 22 Quantitative methods, 22 Quantity discounts, 804–808 carrying costs as a percentage of price, 805 constant carrying costs, 804–805 Queue, 629 Queue discipline, 630 Queuing analysis, 627–653 arrival rate, 630 calling population, 630 constant service times, 638–639 cost trade-off, 636 Excel, 637, 640–641, 643, 646, 651 Excel QM, 638, 646, 651–652 exponential distribution, 631, 834 finite calling population, 644–647 finite queue, 641–643 multiple-server waiting line, 647–652 operating characteristics, 628 Poisson distribution, 630, 833 QM for Windows, 638, 641, 643, 647, 652 queue, 629 queue discipline, 630 service rate, 631 simulation, 678–682 single-server waiting line, 629–633 steady-state, 633 undefined service times, 638–639 utilization factor, 632 Queuing theory, 630 R RAM (responsibility assignment matrix), 372 RAND, 25, 330 Random index, 457 Random numbers, 670 Random number table, 670, 671 Random variations (in forecasts), 720 Regression methods, 743–753 Regret, 570 Regret table, 571 Relative frequency, 532 Relaxed solution (integer programming), C3 Reorder point, 808–809 with variable demand, 810–812 with variable demand and lead time, 812 with variable lead time, 811 Responsibility assignment matrix (RAM), 372 Return on investment (ROI), 368 Revised probability, 543 Rim requirements, B3 Risk averters, 597 Risk takers, 597 ROI (return on investment), 368 Rounded down solution (in integer programming), 150, 210 Row operations, A5 S Saaty, Thomas, 459 Saddle point, E5 Safety stocks, 809, 810–812 Sample mean, 550 Sample variance, 550 Satisfactory solution (goal programming), 442, 443 Scheduling (LP) example, 159–164 Scientific method, 22 Scope statement, 370 Scoring models, 460–461 Excel, 461 Seasonal adjustments, 734–735 Seasonal factor, 734 Seasonal patterns, 720 Sensitivity analysis, 30, 31, 65, 102–113, 266, A34 Sensitivity analysis (in linear programming), 65, 102–113, 138, 142, 145–147, 158– 159, 164, A34 blend example, 158 changes in constraint quantity values, 107–109 changes in objective function coefficients, 102–107 computer analysis, 106–107, 109, 110 diet example, 142 Excel, 106–107, 109, 110 graphical analysis, investment example, 146 multiperiod scheduling example, 164 product mix example, 138 QM for Windows, 107, 110, 139 Sensitivity analysis (in transportation problem), 266 Sequential decision trees, 585–589 Server, 629 Service level, 810–812 Service rate, 631 Service times, 631 exponential distribution, 631, 834 Set covering example (0–1 integer programming), 226–228 Shadow price (see also dual value), 111–113, 146 Shared slack, 384 Shortage costs, 800 Shortest route problem, 317–324 Excel, 322–324 linear programming formulation, 322–323 permanent set, 318 QM for Windows, 321–322 solution steps, 321 Short-range forecasts, 720 Simple exponential smoothing, 726 Simplex method, 95, A1, A5–A30 artificial variable, A18, A22 basic variables, A6 degeneracy, A27–A29 entering nonbasic variable, A9 infeasible problem, A25–A26 www.downloadslide.net Index 857 leaving basic variable, A10 maximization problem, A5 minimization problem, A16 mixed constraint problem, A20, A21–A23 multiple optimal solutions, A25–A25 negative quantity values, A29–A30 nonbasic variables, A9 optimal solution, A14–A15 pivot column, A10 pivot column tie, A27 pivot number, A12 pivot row, A12 pivot row tie (degeneracy), A27–A29 sensitivity analysis, A34 summary steps, A16 tableau, A5 unbounded problem, A26–A27 Simplex tableau, A5 Simulated time, 669 Simulation, 38, 667–698 applications, 696–698 continuous probability distributions, 682–686 Crystal Ball, 689–696 environmental and resource analysis, 697 Excel, 674–678, 680–682, 685–689 finance, 697 inventory control, 697 marketing, 697 Monte Carlo process, 668–673 production and manufacturing, 697 public service operations, 697 pseudorandom numbers, 673 of a queuing system, 678–682 random numbers, 670 statistical analysis, 687–689 trials, 672 verification, 696 Simultaneous solution (of linear equations), 63 Single-server waiting line system, 629–633 formulas, 631–632 Slack, 65, 383–384 Slack variables, 65 Slope of a line, 64, 104 Smoothing constant, 727 Solver (Excel), 96–98 Somali pirates, 688 Soquimich (SA), 72 Spanning tree, 325 S.S Central America, 536 Standard deviation, 546, 547, 548, 552 Standard model form (in linear programming), 67 Standard normal distribution, 548 State (of a system), F3 Statement of work (SOW), 370 States of nature, 567 Statistical dependence, 537, 540 Statistical independence, 537 Statistics, 531–556 Steady-state, 633 Stepping stone method, B9–B15, closed path, B11 iteration, B13 summary steps, B15 Stigler, George, 139 Strategies (in game theory), E3–E4 Subjective probability, 533 Suboptimal solution, 210 Substitution method (in nonlinear programming), D2–D4 Surplus variables, 73 Symmonds, Gifford, 160 Synthesization (AHP), 452 T Time management (in project management), 374 “Time Out” (box), E7, F4, 25, 53, 139, 212, 260, 330, 373, 378, 447, 630, 673, 790 Beer, Stafford, 25 Blackett, P.M.S., 25 Bush, Vannevar, 25 Charnes, Abraham, 447 Conant, James B., 25 Cooper, William W., 447 Dantzig, George B., 53, 139, 330 Dijkstra, E.W., 330 Doig, A.C., 212 Erlang, Agner Krarup, 630 Ford, L.R., Jr., 330 Fulkerson, D.R., 330 Gantt, Henry, 373 Gomory, Ralph E., 212 Harris, Ford, 790 Hitchcock, Frank L., 260 Ijiri, Yuji, 447 Kelley, James E., Jr., 378 Koopmans, T.C., 260 Land, A.H., 212 Malcolm, D.G., 378 Markov, Andrey A., F4 Morgenstern, Oskar, E7 pioneers in management science, 25 Ulam, Stanislas, 673 Von Neumann, John, 673 Walker, Morgan R., 378 Time series methods, 723–735 adjusted exponential smoothing, 730–731 exponential smoothing, 726–730 linear trend line, 732–734 moving averages, 723–726 seasonal adjustments, 734–735 weighted moving averages, 726 Total integer model, 206–207, 216 Total revenue, 29 Transient state, F13 Transition matrix, F5–F8 Transition probability, F3 Transportation problem, 152–154, 258–266 balanced, 260 degeneracy, B20–B22 entering nonbasic variable, B13 Excel, 153–154, 261–263 Excel QM, 263–264 minimum cell cost method, B5–B6 modified distribution method (MODI), B15–B19 multiple optimal solutions, 264, B15 northwest corner method, B4–B5 optimal solution, B13, 262 prohibited route, B22, 260 QM for Windows, 265–266 sensitivity analysis, 266 stepping stone method, B9–B15 tableau, B3 unbalanced transportation problem, 260 Vogel’s approximation method (VAM), B6–B9 Transportation Security Administration (TSA), 747 Transportation tableau, B3 Transshipment model, 266–271 TreePlan, 583–585 Trend factor, 730 Trends (in forecasting), 720 Trials, 672 Two-person game, E2 U Ulam, Stanislaw, 673 Unbalanced assignment problem, 272 Unbalanced transportation problem, 260, B19 Unbounded problem (in linear programming), 76, A26–A27 Unconditional probability, 541 Unconstrained optimization, 510 Undefined service times, 638–639 Undirected branch, 329 Uniform distribution, 689, 691 Union Pacific Railroad, 275 Universal product code (UPC), 790 U.S Army, 457, 462 U.S Coast Guard, 545 U S Commercial Aviation Partnership (USCAP), 747 U.S Postal Service, 271 U.S Tennis Association, 276 User interface, 40 Utiles, 597 Utility, 596–597 Utilization factor, 632 V Value of the game, E3 Variable, 23 artificial, A18 decision, 52, 54 dependent, 23 deviational, 437 independent, 23 www.downloadslide.net 858 Index Variable (continued) slack, 65 surplus, 73 Variable costs, 28 Variance, 389, 520, 545, 550 Venn diagram, 535, 536 Verification (of simulation), 696 Virginia Court of Appeals, 215 Virgnia Department of Transportation (VDOT), 375 Vogel’s approximation method (VAM), B6–B9 Volume (break-even analysis), 28 Von Neumann, John, 673 W Z Waiting lines (see queuing analysis), 627–653 Walker, Morgan R., 378 WBS (work breakdown structure), 370–372 Weighted moving average, 726 Weiss, Howard, 32 Work breakdown structure (WBS), 370–372 World War II, 25, 457 World War II generals, 457 Zappos, 752 Zara, 740 0–1 integer model, 207–208, 211–215, 221–228 capital budgeting problem, 221–222 Excel, 221–222, 223–226, 226–228 facility location problem, 223–226 fixed charge problem, 223–226 QM for Windows, 230 set covering problem, 226–228 Zero-sum game, E2 .. .Introduction to Management Science This page intentionally left blank Edition Introduction to Management Science 12 Global Edition Bernard W Taylor III Virginia Polytechnic... Out: for Pioneers in Management Science 25 Management Science Application: Management Science Application: Room Pricing with Management Science at Marriott 26 Management Science and Business... Problems 77 Management Science Application: The Application of Management Science with Spreadsheets 36 Business Usage of Management Science Techniques 38 Management Science Application: Management Science