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Part I Linear Optimization and Heuristics
The Decision Tree Procedure . . . . . 3
Katharina Völker & Maresa Hümmer
1 Introduction . . . . . . 3
1.1 Theoretical Classification of the Decision Tree Procedure 4
1.2 Basic Structure of a Decision Model . . 4
1.3 The Decision Tree . 6
1.4 Process of Decision-Making with the Decision Tree . . . . . 7
2 Methods of Decision Tree Procedure . 9
2.1 Complete Enumeration . . . . . 10
2.2 Incomplete Enumeration. . . . 10
2.3 Dynamic Optimization . . . . . 11
2.4 Branching and Bounding . . . 12
3 Economic Relevance and Critical Appraisal . . . 14
3.1 Economic Relevance . . . . . . . 14
3.2 Critical Appraisal . 15
4 Case Studies and Software . . 16
4.1 Case Study I . . . . . . 16
4.2 Case Study 2 . . . . . 21
4.3 Example from Practice . . . . . 26
5 Conclusion . . . . . . . 27
References . . . . . 27
Linear Optimization . . . . 29
Franz W. Peren
1 Introduction . . . . . . 29
2 The Linear Programming Approach . . 29
3 Graphical Solution 30
4 Primal Simplex Algorithm . . 32
5 Simplex Tableau (Basic Structure) . . . 32
Queueing Theory . . . . . . . 69
Maximilian Adolphs, Sascha Feistner & Violetta Jahnke
1 Overview 69
1.1 Fundamentals of the Queueing Theory 69
1.2 Economic Relevance . . . . . . . 70
2 Queueing Model . . 71
2.1 Elements of the Queueing Model . . . . 71
2.2 Structures and Queue Disciplines . . . . 75
3 Description of Queueing Systems . . . . 76
3.1 Kendall Notation . . 76
3.2 Excursion: Markov Process . 78
3.3 Parameters . . . . . . . 78
4 Example . 80
5 Exercise . 83
6 Summary 84
References . . . . . 85
Sequencing Problems . . . 87
Thomas Neifer & Franz W. Peren
1 Introduction . . . . . . 87
2 Definition of Terms88
3 Solving Sequencing Problems . . . . . . . 89
3.1 Traveling Salesman Problem 89
3.2 Flow Shop Scheduling Problem . . . . . . 94
References . . . . . 103
Regression Analysis Using Dummy Variables 105
Thomas Neifer
1 Introduction . . . . . . 105
2 Methodology . . . . . 106
2.1 Derivation of the Simple and Multiple Regression
Function . 106
2.2 Estimation of the Regression Parameters according to
the Least Squares Method . . 107
2.3 Integration of Categorial Influences via Dummy Variables108
2.4 Quality Measures. . 110
3 Examples 119
4 Case Study . . . . . . . 121
4.1 Data Preparation . . 122
4.2 Conducting the Regression Analysis . . 124
5 Conclusion . . . . . . . 128
References . . . . . 128
Heuristic Methods . . . . . . 131
Laura Schwarzbach & Ramona Schmitt
1 Introduction . . . . . . 131
1.1 Definition and Characteristics . . . . . . . 132
1.2 Analytical vs. Heuristic Methods . . . . . 134
1.3 Heuristic Procedures . . . . . . . 135
2 Selected Heuristic Problems 136
2.1 Traveling-Salesman Problem 137
2.2 Dynamic Warehousing . . . . . 143
2.3 Knapsack Problem 148
3 Conclusion . . . . . . . 153
References . . . . . 153
Part II Simulation
Simulation Processes in Business and Economics: Fundamentals of the
Monte Carlo Simulation . 157
Alexander Wachholz & Richard Malzew
1 Fundamentals of Simulation Processes . . . . . . . 157
1.1 Definition and Purpose . . . . . 157
1.2 Workload 158
1.3 Fields of Application . . . . . . . 159
1.4 Types of Simulations. . . . . . . 159
2 Monte Carlo Simulations . . . 159
2.1 Introduction . . . . . . 159
2.2 Case Study - Project Management . . . . 161
References . . . . . 164
Markov Chain Monte Carlo Methods . . . . . . 167
Thomas Neifer
1 Introduction . . . . . . 167
2 Theoretical Foundations . . . . 168
2.1 Bayes Theorem . . . 168
2.2 Multivariate Distributions . . 169
2.3 Markov Chain . . . . 169
2.4 Monte Carlo Simulation . . . . 170
3 Markov Chain Monte Carlo Simulation . . . . . . . 171
3.1 Metropolis(-Hastings) Approximation Algorithm . . . . . . . 172
3.2 Gibbs Sampling Algorithm . 174
4 Solving Traveling Salesman Problem using Metropolis
Algorithm in Python . . . . . . . 175
References . . . . . 182
Part III Nonlinear Optimization
Nonlinear Optimization: The Nelder-Mead Simplex Search Procedure . . . 187
Franz W. Peren
1 Introduction . . . . . . 187
2 Basic Properties of Nonlinear Optimization . . . 188
3 Nonlinear Optimization Methods . . . . 189
3.1 Search Strategies . . 189
3.2 Deterministic Search Strategies . . . . . . 190
3.3 The Nelder-Mead Simplex Search Procedure . . . 191
4 Conclusion . . . . . . . 197
References . . . . . 198
Dynamic Programming . . 201
Thomas Neifer & Dennis Lawo
1 Introduction . . . . . . 201
2 Theoretical Foundations. . . . 204
2.1 Definition and Properties of DO Models . . . . . . 204
2.2 Solution Principle of Dynamic Optimization . . . 206
2.3 Bellman’s Functional Equation Method . . . . . . . 207
3 Applications . . . . . 208
3.1 Basic Example: Finding the Shortest Route . . . . 208
3.2 Bellman-Ford Algorithm in Python . . . 210
4 Conclusion . . . . . . . 212
References . . . . . 212
Part IV Project Management
Gantt Charts . . 217
Franz W. Peren
1 Introduction . . . . . . 217
1.1 History of the Gantt Chart . . 218
1.2 Definition of a Gantt Chart and its Appearance . 219
2 Theoretical Overview . . . . . . 220
2.1 Targets of Using a Gantt Chart. . . . . . . 220
2.2 Elements of a Gantt Chart . . 220
2.3 Creation of a Gantt Chart . . . 221
3 Computer-based Gantt Charts . . . . . . . 226
3.1 Think-cell 226
3.2 Microsoft Excel . . . 228
3.3 Microsoft Project . . 235
3.4 ProjectLibre . . . . . . 237
3.5 Gantt Project . . . . . 238
4 Summary 238
References . . . . . 239
Network Analysis Method 243
Matthias Krebs
1 Introduction . . . . . . 243
2 Theory . . 244
2.1 The Graph in the Context of Network Analysis Methods . 244
2.2 Benefits of Network Analysis Methods 245
2.3 Different Types of Illustration Facilities . . . . . . . 245
2.4 The Metra Potential Method (MPM) . . 247
3 Case Study - Moving . . . . . . 250
3.1 Step 1: Identify activities, predecessors and determine
durations . 250
3.2 Step 2: Illustrate Dependencies in a Network Diagram . . . 251
3.3 Step 3: Forward and Backward Calculation . . . . 251
3.4 Step 4: Float Calculation . . . 254
3.5 Step 5: Critical Path . . . . . . . 255
3.6 Case Study Insights 255
4 Computer-based Application with OmniPlan3 (macOS . . 256
5 Using Excel to Create a Precedence Diagram . . 259
6 Conclusion . . . . . . . 261
References . . . . . 261
The Peren-Clement Index 263
Reiner Clement & Franz W. Peren
1 Introduction . . . . . . 263
1.1 Definition of a Foreign Direct Investment . . . . . 263
1.2 Structural Features 264
2 Theory of Direct Investment 265
2.1 Justification for Foreign Direct Investment . . . . . 265
2.2 Valuation Perspectives . . . . . 269
3 Direct Investments and Site Selection. 274
3.1 Framework for Decision-Making . . . . . 275
3.2 Risk Assessment . . 280
3.3 Case Study . . . . . . . 282
4 Conclusion . . . . . . . 287
References . . . . . 288
The Peren Theorem . . . . . 291
Franz W. Peren
1 Synopsis. 291
2 The Current Human Lifestyle Cannot be Continued . . . . . 291
3 The Peren Theorem . . . . . . . 292
4 Options for Securing Human Livelihood . . . . . . 294
5 Individual Prosperity Effects 295
References . . . . . 296
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