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Business Analytics for Decision Making TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk Business Analytics for Decision Making Steven Orla Kimbrough The Wharton School University of Pennsylvania Philadelphia, USA Hoong Chuin Lau School of Information Systems Singapore Management University Singapore CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20151019 International Standard Book Number-13: 978-1-4822-2177-0 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xi List of Figures xvii List of Tables xxi I Starters 1 1 Introduction 3 1.1 The Computational Problem Solving Cycle . . . . . . . . . . . . . . . . . . 3 1.2 Example: Simple Knapsack Models . . . . . . . . . . . . . . . . . . . . . . 6 1.3 An Example: The Eilon Simple Knapsack Model . . . . . . . . . . . . . . . 9 1.4 Scoping Out Post-Solution Analysis . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.3 Outcome Reach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.4 Opportunity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.6 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.7 Resilience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Parameter Sweeping: A Method for Post-Solution Analysis . . . . . . . . . 18 1.6 Decision Sweeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.7 Summary of Vocabulary and Main Points . . . . . . . . . . . . . . . . . . . 20 1.8 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.9 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 Constrained Optimization Models: Introduction and Concepts 25 2.1 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Classification of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 (1) Linear Program (LP) . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.2 (2) Integer Linear Program (ILP) . . . . . . . . . . . . . . . . . . . . 31 2.2.3 (3) Mixed Integer Linear Program (MILP) . . . . . . . . . . . . . . 31 2.2.4 (4) Nonlinear Program (NLP) . . . . . . . . . . . . . . . . . . . . . . 32 2.2.5 (5) Nonlinear Integer Program (NLIP) . . . . . . . . . . . . . . . . . 33 2.2.6 (6) Mixed Integer Nonlinear Program (MINLP) . . . . . . . . . . . . 33 2.3 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Computational Complexity and Solution Methods . . . . . . . . . . . . . . 35 2.5 Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.1 Greedy Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.2 Local Search Metaheuristics: Simulated Annealing . . . . . . . . . . 39 v vi Contents 2.5.3 Population Based Metaheuristics: Evolutionary Algorithms . . . . . 39 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.7 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.8 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3 Linear Programming 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Wagner Diet Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.3 Solving an LP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4 Post-Solution Analysis of LPs . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5 More than One at a Time: The 100% Rule . . . . . . . . . . . . . . . . . . 53 3.6 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.7 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 II Optimization Modeling 59 4 Simple Knapsack Problems 61 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 Solving a Simple Knapsack in Excel . . . . . . . . . . . . . . . . . . . . . . 61 4.3 The Bang-for-Buck Heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4 Post-Solution Analytics with the Simple Knapsack . . . . . . . . . . . . . . 64 4.4.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4.2 Candle Lighting Analysis . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 Creating Simple Knapsack Test Models . . . . . . . . . . . . . . . . . . . . 72 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.7 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.8 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5 Assignment Problems 81 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 The Generalized Assignment Problem . . . . . . . . . . . . . . . . . . . . . 82 5.3 Case Example: GAP 1-c5-15-1 . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4 Using Decisions from Evolutionary Computation . . . . . . . . . . . . . . . 86 5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.6 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.7 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6 The Traveling Salesman Problem 97 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.3 Solution Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.3.1 Exact Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.3.2 Heuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.3.2.1 Construction Heuristics . . . . . . . . . . . . . . . . . . . . 101 6.3.2.2 Iterative Improvement or Local Search . . . . . . . . . . . 102 6.3.3 Putting Everything Together . . . . . . . . . . . . . . . . . . . . . . 103 6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Contents vii 6.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7 Vehicle Routing Problems 111 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.3 Solution Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.3.1 Exact Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.3.2 Heuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.3.2.1 Construction Heuristics . . . . . . . . . . . . . . . . . . . . 115 7.3.2.2 Iterative Improvement or Local Search . . . . . . . . . . . 115 7.4 Extensions of VRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 8 Resource-Constrained Scheduling 119 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.2 Formal Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.3 Solution Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.3.1 Exact Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.3.2 Heuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8.3.2.1 Serial Method . . . . . . . . . . . . . . . . . . . . . . . . . 123 8.3.2.2 Parallel Method . . . . . . . . . . . . . . . . . . . . . . . . 123 8.3.2.3 Iterative Improvement or Local Search . . . . . . . . . . . 123 8.4 Extensions of RCPSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 9 Location Analysis 129 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9.2 Locating One Service Center . . . . . . . . . . . . . . . . . . . . . . . . . . 130 9.2.1 Minimizing Total Distance. . . . . . . . . . . . . . . . . . . . . . . . 130 9.2.2 Weighting by Population . . . . . . . . . . . . . . . . . . . . . . . . 132 9.3 A Na¨ıve Greedy Heuristic for Locating n Centers . . . . . . . . . . . . . . 132 9.4 Using a Greedy Hill Climbing Heuristic . . . . . . . . . . . . . . . . . . . . 136 9.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 9.6 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 9.7 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 10 Two-Sided Matching 149 10.1 Quick Introduction: Two-Sided Matching Problems . . . . . . . . . . . . . 149 10.2 Narrative Description of Two-Sided Matching Problems . . . . . . . . . . . 150 10.3 Representing the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 10.4 Stable Matches and the Deferred Acceptance Algorithm . . . . . . . . . . . 154 10.5 Once More, in More Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 10.6 Generalization: Matching in Centralized Markets . . . . . . . . . . . . . . . 156 10.7 Discussion: Complications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 10.8 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 viii Contents III Metaheuristic Solution Methods 161 11 Local Search Metaheuristics 163 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 11.2 Greedy Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 11.2.1 Implementation in Python . . . . . . . . . . . . . . . . . . . . . . . . 165 11.2.2 Experimenting with the Greedy Hill Climbing Implementation . . . 167 11.3 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 11.4 Running the Simulated Annealer Code . . . . . . . . . . . . . . . . . . . . 172 11.5 Threshold Accepting Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 172 11.6 Tabu Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 11.7 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 11.8 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 12 Evolutionary Algorithms 179 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 12.2 EPs: Evolutionary Programs . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.2.1 The EP Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.2.2 Applying the EP Code to the Test Problems . . . . . . . . . . . . . 184 12.2.3 EP Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 12.3 The Basic Genetic Algorithm (GA) . . . . . . . . . . . . . . . . . . . . . . 188 12.3.1 The GA Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 12.3.2 Applying the Basic GA Code to a Test Problem . . . . . . . . . . . 193 12.3.3 GA Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 12.4 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 12.5 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 13 Identifying and Collecting Decisions of Interest 197 13.1 Kinds of Decisions of Interest (DoIs) . . . . . . . . . . . . . . . . . . . . . . 197 13.2 The FI2-Pop GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 13.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 13.4 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 13.5 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 IV Post-Solution Analysis of Optimization Models 203 14 Decision Sweeping 205 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 14.2 Decision Sweeping with the GAP 1-c5-15-1 Model . . . . . . . . . . . . . . 205 14.3 Deliberating with the Results of a Decision Sweep . . . . . . . . . . . . . . 207 14.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 14.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 14.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Contents ix 15 Parameter Sweeping 219 15.1 Introduction: Reminders on Solution Pluralism and Parameter Sweeping . 219 15.2 Parameter Sweeping: Post-Solution Analysis by Model Re-Solution . . . . 220 15.2.1 One Parameter at a Time . . . . . . . . . . . . . . . . . . . . . . . . 221 15.2.2 Two Parameters at a Time . . . . . . . . . . . . . . . . . . . . . . . 222 15.2.3 N Parameters at a Time . . . . . . . . . . . . . . . . . . . . . . . . 222 15.2.4 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 15.2.5 Active Nonlinear Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 225 15.3 Parameter Sweeping with Decision Sweeping . . . . . . . . . . . . . . . . . 225 15.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 15.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 15.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 16 Multiattribute Utility Modeling 229 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 16.2 Single Attribute Utility Modeling . . . . . . . . . . . . . . . . . . . . . . . 230 16.2.1 The Basic Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 230 16.2.2 Example: Bringing Wine . . . . . . . . . . . . . . . . . . . . . . . . . 231 16.3 Multiattribute Utility Models . . . . . . . . . . . . . . . . . . . . . . . . . . 234 16.3.1 Multiattribute Example: Picking a Restaurant . . . . . . . . . . . . 235 16.3.2 The SMARTER Model Building Methodology. . . . . . . . . . . . . 236 16.3.2.1 Step 1: Purpose and Decision Makers . . . . . . . . . . . . 236 16.3.2.2 Step 2: Value Tree . . . . . . . . . . . . . . . . . . . . . . . 236 16.3.2.3 Step 3: Objects of Evaluation . . . . . . . . . . . . . . . . . 236 16.3.2.4 Step 4: Objects-by-Attributes Table . . . . . . . . . . . . . 237 16.3.2.5 Step 5: Dominated Options . . . . . . . . . . . . . . . . . . 237 16.3.2.6 Step 6: Single-Dimension Utilities . . . . . . . . . . . . . . 237 16.3.2.7 Step 7: Do Part I of Swing Weighting . . . . . . . . . . . . 238 16.3.2.8 Step 8: Obtain the Rank Weights . . . . . . . . . . . . . . 238 16.3.2.9 Step 9: Calculate the Choice Utilities and Decide. . . . . . 239 16.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 16.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 16.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 17 Data Envelopment Analysis 243 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 17.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 17.3 Demonstration of DEA Concept . . . . . . . . . . . . . . . . . . . . . . . . 247 17.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 17.5 For Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 17.6 For More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 18 Redistricting: A Case Study in Zone Design 253 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 18.2 The Basic Redistricting Formulation . . . . . . . . . . . . . . . . . . . . . . 254 18.3 Representing and Formulating the Problem . . . . . . . . . . . . . . . . . . 255 18.4 Initial Forays for Discovering Good Districting Plans . . . . . . . . . . . . 258

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