Business analytics for decision making

326 Pages·2016·10.26 MB·English

by  Kimbrough, Steve, Lau, Hoong Chuin

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
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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