Part 1 Introduction to Management Science 1 Introduction to Management Science 1.1 Introduction A Problem Focus Use of a Quantitative Approach 1.2 Models Benefits and Risks of Using Models Assumptions of Models Deterministic Versus Probabilistic Models 1.3 The Management Science Approach Problem Definition Model Construction Model Analysis Implementation and Follow-Up 1.4 The Utilization of Decision Support Systems (DSS) in the Context of Management Science 1.5 Plan of the Book 1.6 Role of Computers and Spreadsheets in Management Science Getting Started with Excel Spreadsheet Engineering 1.7 Break-Even Analysis Introduction to Break-Even Analysis Components of Break-Even Analysis The Break-Even Point Assumptions of Break-Even Analysis Sensitivity Analysis Using Excel to Solve the Break-Even Model Using Excel’s Goal Seek to Compute the Break-Even Point
xv
1 2 4 4 4 5 7 8 8 9 9 10 11 11
12 14 14 17 20 21 21 22 25 26 27 27 28
1.8 The Importance and Impact of Management Science Canadian Management-ScienceBased Solution Providers Summary Glossary Discussion and Review Questions Problems Case 1: Green Daisy Company Case 2: Wood Made Co.
30 30 34 34 35 36 38 38
Part 2 Deterministic Decision Models 39 2 Linear Programming: Basic Concepts, Graphical Solution, and Computer Solution 2.1 Introduction Constrained Optimization Linear Programming A Simple Example 2.2 Components and Assumptions of LP Models Components of LP Models Assumptions of LP Models 2.3 Formulating LP Models 2.4 Graphical Method Plotting the Constraints and Determining the Feasible Region Finding the Optimal Solution: The Extreme Point Approach Finding the Optimal Solution: The Objective Function Approach 2.5 Solving LP Models with a Spreadsheet Setting up the Spreadsheet Model Using Solver 2.6 A Minimization Example 2.7 Slack and Surplus
2.8 Some Special Issues No Feasible Solutions Unbounded Problems Redundant Constraints Multiple Optimal Solutions 2.9 Comments About the Use of Excel Solver Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Son, Ltd. Case 2: ABC Company Case 3: ALN Motorcycles Canada
73 73 73 74 74 76 77 78 79 83 84 91 92 93
3 Linear Programming: Sensitivity Analysis and Computer Solution Interpretation 95 3.1 Introduction to Sensitivity Analysis 96 3.2 Graphical Approach to Sensitivity Analysis 97 A Change in the Value of an Objective Function Coefficient 98 A Change in the RHS Value of a Constraint 102 Minimization Problems 108 3.3 Sensitivity Analysis with Excel 108 3.4 Analyzing Multiple Changes 113 3.5 Interpretation and Managerial Use of Computer Solution Outputs 115 Summary 124 Glossary 125 Solved Problems 125 Discussion and Review Questions 130 Problems 131 Case 1: Red Brand Canners 153 Case 2: Staffing Nurse Personnel 155 Case 3: Ottawa Catholic School Board 157 4 Applications of Linear Programming 4.1 Introduction 4.2 Product-Mix Problems Problem Formulation Excel Solution of the Style and Comfort Furniture Company Example 4.3 Diet Problems 4.4 Blending Problems 4.5 Marketing Applications Media Selection Marketing Research
159 160 160 162 164 166 168 172 172 175
4.6 Financial Applications Financial Planning Problems for Banks Portfolio Selection Multiperiod Financial Planning Models 4.7 Production Applications Multiperiod Production Scheduling Workforce Scheduling Make-or-Buy Decisions 4.8 Agriculture Applications 4.9 Data Envelopment Analysis Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Direct Marketing Case 2: Quota Allocation by Linear Programming Case 3: Shipping Wood to Market Case 4: Workforce Scheduling at ASC Case 5: Ottawa Catholic School Board (Revisited) 5 Distribution and Network Flow Models 5.1 Introduction 5.2 Transportation Problems Formulating the Model Special Cases of Transportation Problems A General Linear Formulation of a Transportation Problem Solving Transportation Problems Using Excel Other Applications 5.3 Transshipment Problems Linear Programming Formulation of the Transshipment Problem Solving the Transshipment Problem Using Excel Special Cases of Transshipment Problems 5.4 Assignment Problems Linear Programming Formulation of the Assignment Problem Solving the Assignment Problem Using Excel Special Cases of Assignment Problems 5.5 The Shortest-Route Problem Linear Programming Formulation of the Shortest-Route Problem
Solving the Shortest-Route Problem Using Excel 5.6 The Maximum Flow Problem Linear Programming Formulation of the Maximum Flow Problem General Linear Formulation of Flow a Maximum Problem Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Sunshine Tomato Inc. Case 2: Furnace County Emergency Response Routes 6 Integer Programming Methods 6.1 Introduction to Integer Programming 6.2 Types of Integer Programming Problems Pure-Integer Problems Mixed-Integer Problems 0–1 Integer Problems 6.3 Graphical Representation of Integer Programming Problems 6.4 Solving Integer Programming Problems Using Excel 6.5 A Comment About Sensitivity 6.6 Formulating Integer Programming Problems with 0–1 Constraints Either-Or Alternatives k-Out-of-n Alternatives If-Then Alternatives Either-Or Constraints Variables That Have Minimum Level Requirements 6.7 Specialized Integer Programming Problems Fixed-Charge Problem Set Covering Problem Knapsack Problem Facility Location Problem Travelling Salesperson Problem 6.8 Difficulties in Solving Integer Programming Problems Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Suburban Kelowna
Case 2: City Hall of Ottawa (CHO) Case 3: Ottawa Catholic School Board (Revisited)
313
7 Nonlinear Programming 7.1 Introduction 7.2 Models with One Decision Variable Unconstrained Problem with One Decision Variable Solution of One-Decision-Variable, Unconstrained Problem with Excel Constrained Problem with One Decision Variable Solution of One-Decision-Variable, Constrained Problem with Excel 7.3 Models with Two Decision Variables, Unconstrained Problem Solution of Unconstrained Problems with Two Decision Variables Using Excel 7.4 Models with Two Decision Variables and an Equality Constraint (Lagrange Multipliers) Interpreting λ Solution of Problems with Two Decision Variables and a Single Equality Constraint Using Excel 7.5 Models with Two Decision Variables and a Single Inequality Constraint Solution of Problems with Two Decision Variables and Multiple Constraints Using Excel Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Koch International Incorporated
317 318 319
8 Project Scheduling: PERT/CPM 8.1 Introduction 8.2 A Project Example: Replacement of an Airport Gate-Management System 8.3 Project Network Representation 8.4 Project Scheduling with Deterministic Activity Durations 8.5 Project Scheduling with Probabilistic Activity Durations Probability of Whether a Project Can Be Completed or Not by a Specific Deadline
359 360
315
319 323 327 330 332
336
338 340
340 343
345 348 349 349 355 355 357
361 361 364 368
370
ste13809_fm_i-xxvi.qxd
xii
1/27/09
2:29 AM
Page xii
Contents
Project Completion Time Given a Certain Probability 8.6 Uses of Simulation in Project Scheduling 8.7 Project Crashing Using Linear Programming to Make Crashing Decisions 8.8 Using Linear Programming in Project Scheduling 8.9 Project Scheduling Software Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Fantasy Products 9 Multicriteria Decision-Making Models 9.1 Introduction 9.2 Goal Programming Models Deviation Variables Model Formulation Graphical Solutions Solving Goal Programming Problems Using Excel Weighted Goals 9.3 Analytical Hierarchy Process Pairwise Comparisons Normalized Pairwise Comparison Matrix Consistency Check for Criteria Analytical Hierarchy Process Using Excel 9.4 Scoring Models The Steps for the Scoring Model Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Hi-Tech Incorporated
Part 3 Probabilistic Decision Models 447 10 Decision Analysis 10.1 Introduction List of Alternatives States of Nature Payoffs Degree of Certainty Decision Criterion 10.2 The Payoff Table 10.3 Decision Making Under Certainty
449 450 451 452 452 452 452 453 454
10.4 Decision Making Under Complete Uncertainty Maximin Maximax Minimax Regret The Hurwicz (Realism) Criterion Equal Likelihood Criterion Using Excel for Decision Making Under Complete Uncertainty 10.5 Decision Making Under Risk Expected Monetary Value Expected Opportunity Loss Expected Value of Perfect Information Using Excel for Decision Making Under Risk 10.6 Decision Trees Using TreePlan to Develop Decision Trees with Excel 10.7 Decision Making with Additional Information Efficiency of Sample Information Computing the Probabilities Computing Revised Probabilities with Excel 10.8 Sensitivity Analysis 10.9 Utility Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: MKGP Construction Company Case 2: Cerebrosoft Inc. 11 Markov Analysis 11.1 Introduction 11.2 Transition Probabilities 11.3 System Behaviour 11.4 Methods of Analysis Tree Diagram Matrix Multiplication Algebraic Solution 11.5 Using Excel for Markov Analysis 11.6 Analysis of a 3 ⫻ 3 Matrix Tree Diagram Matrix Multiplication Algebraic Solution 11.7 Cyclical, Transient, and Absorbing Systems Analysis of Accounts Receivable
11.8 Analysis of Absorbing States Using Excel 11.9 Assumptions of Markov Analysis Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Montreal Heart Institute
539 542 542 543 543 548 550 555
12 Waiting-Line Models 556 12.1 Introduction 557 12.2 Goals of Queuing System Design 557 12.3 Elements and Characteristics of Waiting-Line Systems 559 Calling Population 559 Customer Arrivals 560 Poisson Distribution 561 Calculation of Poisson Probability Using Excel 563 The Waiting Line 565 Processing Order 565 Service 565 Exponential Distribution 567 Calculation of Exponential Probability Using Excel 570 Exit 571 12.4 Measures of System Performance 571 Basic Relationships 572 12.5 Queuing Models 574 Basic Single-Channel (M/M/1) Model 574 Basic Single-Channel Model with Poisson Arrival and Exponential Service Rate (M/M/1 Model) with Excel 576 Multiple-Channel Model (M/M/s) 578 Multiple-Channel Model with Poisson Arrival and Exponential Service Rate (M/M/s Model) with Excel 581 Determining Maximum Length of Waiting Lines 581 12.6 Cost Considerations 584 12.7 Other Queuing Models 586 Model Variation I: Poisson Arrival Rate with Any Service Distribution (M/G/1) 586 Model Variation II: Poisson Arrival Rate, Constant Service Time (M/D/1) 587 Model Variation III: Finite Queue Length 588 Model Variation IV: Finite Calling Population 589
Model Variation V: Multiple-Server, Priority Servicing Model Revising Priorities Utilization of Excel’s Goal Seek Function 12.8 The Psychology of Waiting-Line Models 12.9 The Value of Waiting-Line Models Summary Glossary Solved Problems Discussion and Review Questions Problems Case 1: Big Bank Case 2: Adjusting Centralized Appointment Scheduling at the Ottawa General Hospital 13 Simulation 13.1 Introduction 13.2 Types of Simulation Discrete Versus Continuous Simulations Fixed-Interval Versus Next-Event Simulations Deterministic Versus Probabilistic Simulations Static Versus Dynamic Simulations 13.3 Steps in Simulation Defining the Problem and Setting Objectives Developing a Model Gathering Data Validating the Model Designing Experiments Running Simulations Analyzing and Interpreting the Results 13.4 The Monte Carlo Simulation Method Simulation Using Empirical Distributions Simulation Using a Theoretical Distribution The Uniform Distribution The Exponential Distribution The Normal Distribution 13.5 Multiple-Variable Simulations 13.6 Computer Simulation Using Excel Random Number Generation with Probability Distributions Using Excel A Discrete Distribution with Two Outcomes
A Discrete Distribution with More Than Two Outcomes Simulation of Waiting Lines with Excel Simulation of Inventory Systems with Excel Simulation of Financial Applications with Excel Scenario Manager 13.7 Computer Simulation Using Crystal Ball Define and Enter the Assumptions Define Forecast Set the Run Preferences Run the Simulation 13.8 Simulation Languages 13.9 Pseudo-Random Numbers 13.10 Advantages and Limitations of Simulation 13.11 When to Use Simulation Summary Glossary Solved Problems
Discussion and Review Questions Problems Case 1: Krohler Supermarkets Case 2: CerebroTech Inc.
The following chapters can be found on the text OLC at www.mcgrawhill.ca/olc/stevensonmgmtsci: 14 15 16 17
Forecasting Linear Programming: The Simplex Method Procedures for Solving Network Models Methods of Solving Integer Programming Problems 18 Mini Review of Differential Arithmetic Answers to Most Odd-Numbered Problems can be found on the text OLC at www.mcgrawhill.ca/olc/stevensonmgmtsci. Appendix: Tables Index
