||A Multi-Objective Evolutionary Approach for an Integrated Location-Inventory Distribution Network System
||Graduate Institute of Management Science
Supply Chain Management
Integrated Location-Inventory Distribution Network Problem
Multiobjective Evolutionary Algorithm
||Supply chain distribution network system provides an optimal platform for efficient and effective supply chain management. There are trade-offs between demand time efficiency and supply cost effectiveness. In this dissertation, an integrated two-echelon distribution network system consisting of one supplier, multiple distribution centers, and multiple customer zones is formulated under a vendor managed inventory (VMI) setup which simply assumes the vendor (supplier) manages the inventory of the customers and stores them at different distribution centers. The system also integrates the effects of facility location, distribution, and inventory issues and includes conflicting objectives such as cost (for effectiveness), volume fill rate and responsiveness level (for efficiency). With these considerations, we present a Multi-Objective Location-Inventory Problem (MOLIP) which results in a Mixed-Integer Non-Linear Programming (MINLP) formulation.
The MOLIP model consists of two steps. The first step makes the strategic decisions to determine the optimal number, sites and capacity of opening distribution centers (DCs) to be used, as well as the establishment of distribution channels and the amount of products to distribute from the supplier to assigned buyers via DCs. In the second step, the model in turn determines the inventory levels and safety stocks, economic order quantities of different facilities in the tactical level. However, the model is difficult to solve with existing optimization algorithms due to the considerable number of decision variables and constraints resulting from the integration. To obtain feasible and satisfactory solutions to the integrated MOLIP model, a hybrid multi-objective evolutionary approach is presented which is preliminarily based on a well-known NSGA-II evolutionary algorithm with a non-dominated sorting mechanism and an elitism strategy. To facilitate the genetic search and improve the search results, a heuristic method is designed to generate a well-adapted initial population.
To investigate the possibility of the proposed evolutionary approach for MOLIP model, we implemented on three experiments. First, an experimental study using practical data was then illustrated for the efficacy of the proposed approach. The hybrid approach has been successfully applied for providing promising solutions on a base-case problem with 50 buyers and 15 potential DCs. Computational analyses has presented a promise solution in solving such a practical-size problem.
Second, we implemented several scenario analyses to understand the model performance and to illustrate how parameter changes influences its output. The scenario analysis illustrates that excess capacity in the supply chain network design is beneficial for volume fill rate and responsiveness level and has only little expense of total costs. In additions, the results of the scenario analyses implied that the distribution network flexibility and competitiveness level sought by the supply chain managers is warranted. The model proposed in this research is helpful in adjusting the distribution network to these changes.
Finally, we tested and compared our NSGAII-based algorithm with the one based on the improved Strength Pareto Evolutionary Algorithm (SPEA2) by developing a test set of random problem instances of the MOLIP model to understand the efficiency between two approaches. In these test instances, two algorithms obtained similar approximations of their Pareto frontiers but NSGAII algorithm outperformed in terms of the diversity quality of the approximation to the Pareto frontier. However, the SPEA2-based algorithm was more efficient in terms of execution time in small or tight capacity instances. This suggested that the propose hybrid algorithm can be an efficient approach for providing feasible and satisfactory solutions to large-scale difficult-to-solve problems.
||Table of Contents
LIST OF TABLES III
LIST OF FIGURES IV
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 RESEARCH SCOPE 7
1.3 RESEARCH OBJECTIVES 11
1.4 RESEARCH METHODOLOGY 12
1.5 OUTLINE OF THE DISSERTATION 15
CHAPTER 2 LITERATURE REVIEW 18
2.1 REVIEW OF INTEGRATED DECISION MODELS 18
2.1.1 Location-Routing (LR) Models 19
2.1.2 Inventory-Routing (IR) models 21
2.1.3 Location-Inventory (LI) models 22
2.2 RESEARCH PROBLEM 24
2.2.1 The Evolution of Integrated Location-Inventory Models 24
2.2.2 Key Aspects of Location-Inventory Models 29
2.2.3 Summary and Comments of Previous Optimization Models 38
2.3 EVOLUTIONARY ALGORITHMS IN MULTIOBJECTIVE OPTIMIZATION 40
2.3.1 Introduction of MOEAs 40
2.3.2 Summary of MOEAs 46
2.4 SUMMARY AND IMPLICATIONS 48
CHAPTER 3 DESIGNING AN INTEGRATED LOCATION-INVENTORY SUPPLY CHAIN DISTRIBUTION NETWORK MODELS 49
3.1 PROBLEM DESCRIPTIONS 50
3.1.1 Overview of Our Research Problem 50
3.1.2 Sourcing Strategies for Distribution Network Design 53
3.1.3 Coordination Mechanism for Distribution Network Design 55
3.2 ANALYTICAL COMPARISONS OF SPECIFIC SUPPLY CHAIN SYSTEMS 60
3.2.1 Buyer-Supplier Channel Structure 60
3.2.2 Cost Structures 61
3.3 MATHEMATICAL FORMULATION OF DISTRIBUTION NETWORK MODELS 68
3.3.1 Problem Statement and Model Assumptions 68
3.3.2 Bi-Objective Facility Location Problem (BOFLP) 71
3.3.3 Mathematical Models 73
3.5 SUMMARY 81
CHAPTER 4 METHODOLOGY OF SOLVING THE INTEGRATED LOCATION-INVENTORY DISTRIBUTION MODEL 82
4.1 BASIC CONCEPTS 83
4.1.1 Multiobjective optimization problem 83
4.1.2 Multiobjective optimization Evolutionary Algorithms 84
4.2 OVERVIEW OF NSGAII 85
4.2.1 Background 86
4.2.2 NSGAII-based Genetic Algorithm 88
4.3 SOLVING MOLIP MODEL WITH NSGAII-BASED GENETIC ALGORITHM 91
4.3.1 Solution Encoding 91
4.3.2 A Hybrid Genetic Approach for MOLIP 94
4.4 SUMMARY 97
CHAPTER 5 NUMERICAL EXAMPLES AND COMPUTATIONAL EXPERIENCE 98
5.1 TEST PROBLEM 1 AND SENSITIVITY ANALYSIS 98
5.1.1 Model Parameters of Test 1 Problem 99
5.1.2 Computational Results of Test 1 Problem 101
5.1.3 Performance Evaluation of the Genetic Algorithm 105
5.1.4 Model experiments with sensitivity analysis 107
5.2 TEST 2 PROBLEMS AND SCENARIO ANALYSIS 113
5.2.1 Base Case Scenario of Test 2 Problems 113
5.2.2 Scenario Analysis of Test 2 Problem 119
5.3 SUMMARY 138
CHAPTER 6 COMPARATIVE ANALYSIS OF EXPERIMENTAL RESULTS 140
6.1 PERFORMANCE METRICS 140
6.1.1 Evaluation metrics 140
6.1.2 Dominated-Space metric 141
6.2 COMPUTATIONAL EXPERIMENTS 145
6.3 COMPUTATIONAL RESULTS 146
6.4 SUMMARY 149
CHAPTER 7 CONCLUSION AND FUTURE RESEARCH 150
7.1 CONCLUSION 150
7.2 FUTURE RESEARCH 154
List of Tables
Table 2.2 Classification of Typical MOEA Approaches 47
Table 3.1 Model Notations for Analytical Cost Comparison 61
Table 5.1 Model Parameters for Test Problem 1 100
Table 5.2 Test 1 Problem Computational Results 102
Table 5.3 A Sensitivity Analysis with Varying Coverage Distances of DCs 107
Table 5.4 Cost Structure with Varying Coverage Distances 109
Table 5.5 Sensitivity Analysis with Varying Inventory Holding Cost 110
Table 5.6 Sensitivity Analysis with Varying Capacity Tightness of DCs 112
Table 5.7 Basic Model Parameters for Test 2 Problems 113
Table 5.8 Performance Results for Test 2 Problems (Base-Case Scenario) 116
Table 5.9 Pearson Correlations and P Values among CL and Objective Measurements 117
Table 5.10 Pearson Correlations and P Values among CL and Cost Components 119
Table 5.11 Parameter Values for Scenarios 120
Table 5.12 Comparative Results of Tight Capacity Scenario (Scenario 2) 122
Table 5.13 Comparative Results of Excess Capacity Scenario (Scenario 3) 125
Table 5.14 Comparative Results of Dominated Facility-Cost Scenario (Scenario 4) 127
Table 5.15 Comparative Results of Dominated Transportation-Cost Scenario (Scenario 5) 130
Table 5.16 Comparative Results of Dominated Inventory-cost Scenario (Scenario 6) 133
Table 5.17 Comparative Results of Dominated Lead Time Scenario (Scenario 7) 136
Table 5.18 Pearson Correlations and P Values among CL and Cost Components 137
Table 6.1 Metrics for evaluating solutions to multi-objective problems 141
Table 6.2 Comparisons between NSGAII and SPEA2-based Approaches 147
List of Figures
Figure 1.1 Four Strategic Planning Issues in Distribution Network Design 4
Figure 1.2 The Dissertation Framework 15
Figure 3.1 Overview of the Strategic Design and Tactical Planning Models 51
Figure 3.2 Two-Echelon Supply Chain Distribution Network Problem 54
Figure 3.3 System Diagram of Traditional Supply Chain System 55
Figure 3.4 System Diagram of VMI System 59
Figure 3.5 Cost Structure of Traditional Supply Chain System 62
Figure 3.6 Cost Structure of VMI System 65
Figure 3.7 Two-Echelon Distribution Network Problem 69
Figure 3.8 The VMI Diagram of our Distribution Network Problem 70
Figure 3.9 Set Coverings of an Illustrative Example 72
Figure 4.1 A Nondominated Sorting Process 87
Figure 4.2 The Crowding Distance Calculation 87
Figure 4.3 Graphical Representation of the NSGAII Algorithm 91
Figure 4.4 Solutions Encoding of the MOLIP Problem 92
Figure 4.5 The Block Diagram of MOLIP via Hybrid Genetic Approach 94
Figure 4.6 Uniform Crossover for the MOLIP Problem 96
Figure 5.1 Geographical Locations of Test Problem 1 99
Figure 5.2 Graphical Display of the Base-line Solution of Alternative 33 104
Figure 5.3 Approximate Pareto Frontier of the Test 1 Problem 105
Figure 5.4 Evolution Procedure of the Proposed Genetic Algorithm 105
Figure 5.5(a) The Approximate Pareto Frontier of TC and VFR 106
Figure 5.5(b) The Approximate Pareto Frontier of TC and RL 106
Figure 5.6 Results with Changes in GA Parameters 106
Figure 5.7 Sensitivity Analysis with Varying Dmax 108
Figure 5.8 Cost Components with Varying Dmax 109
Figure 5.9 Sensitivity Analysis with Varying hj 111
Figure 5.10 Sensitivity Analysis with Varying μj 112
Figure 5.11 Clustered Bar Chart with Cost Components118
Figure 5.12 Scatter Plot of Cost Components against Competitiveness Level118
Figure 5.13 Percentage Gaps of Objective Differences (S2 vs. S1)121
Figure 5.14 Percentage Gaps of Cost Components (S2 vs. S1)123
Figure 5.15 Percentage Gaps of Objective Differences (S3 vs. S1)124
Figure 5.16 Percentage Gaps of Cost Components (S3 vs. S1)126
Figure 5.17 Percentage Gaps of Objective Differences (S4 vs. S1)128
Figure 5.18 Percentage Gaps of Cost Components (S4 vs. S1)129
Figure 5.19 Percentage Gaps of Objective Differences (S5 vs. S1)131
Figure 5.20 Percentage Gaps of Cost Components (S5 vs. S1)132
Figure 5.21 Percentage Gaps of Objective Differences (S6 vs. S1)132
Figure 5.22 Percentage Gaps of Cost Components (S6 vs. S1)134
Figure 5.23 Percentage Gaps of Objective Differences (S7 vs. S1)135
Figure 5.24 Percentage Gaps of Cost Components (S7 vs. S1)137
Figure 6.1 Examples of the Dominated Space Metric142
Figure 6.2 Formulation of the Dominated-Space Metric (Z1 v.s. Z2)143
Figure 6.3 Formulation of the Dominated-Space Metric (Z2 v.s. Z3)144
Figure 6.4 Approximate Pareto Tradeoff Curves for Problem Instance A100_500_F3_C1149
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