供應鏈配送網路系統在提供一個最佳化的平台來追求供應鏈需求者的時間效率與供應者的成本效益，以期追求在成本上有效率以及在時間上可快速回應的供應鏈管理。有效率的供應鏈管理主要目的在於減少並降低作業時的成本：例如設施定址成本，庫存作業成本與運輸配送成本等。快速回應的供應鏈管理主要目的，則是為了能快速回應市場上需求的急速變化，以滿足大多數的顧客。然而，成本與顧客滿意度這兩個目的之間常常是互相抵觸的。
我們的研究主要是將一個包含設施定址、庫存控制與網路配送等三種供應鏈決策規劃的議題，並以兩種相互衝突目標：需求者時間效率與供應者成本效益為追求最佳化的標竿，設計了一個整合性的多目標規劃模式稱為多目標定址庫存問題此數學模式，簡稱為MOLIP。該數學模式同時包含了三個目標函數：分別為供應鏈總成本，顧客服務水準（或訂單達交率）與供應鏈彈性（或顧客回應水準），因此，我們所建立的模式乃是一個包含非線性混合整數規劃的最佳化的問題。此問題乃是在求解最佳的分派中心設址地點並將所有不同地區的顧客與需求，指派到最適當的分派中心，並找出最佳的柏拉圖最適解。
本研究探索以多目標遺傳演算法中稱為「菁英式非支配排序遺傳演算法」(NSGA-II) 來求解MOLIP模式的可行性。為了有效求解此問題，我們以接近實際供應鏈分銷網路問題設計了模擬的問題，包含了15間分銷中心位址與50位潛在顧客，並進行相關的數值分析以驗證求解方法的成效，結果發現，該方法所獲得的答案是令人滿意的。另外，本研究亦進行了相關的敏感性分析與情境分析，用來評估該模式所呈現的不同結果，並提出相關的管理意涵給決策者作為決策參考之用。

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

BIBLIOGRAPHY	157

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

[1] Akinc U. (1993). Selecting a set of vendors in a manufacturing environment, Journal of Operations Management, 11, pp. 107-122.
[2] Altiparmak F., Gen M., Lin L. and Paksoy T. (2006). A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers and Industrial Engineering, 51(1), pp. 196-215.
[3] Ambrosino D. and Scutella M. G. (2005). Distribution network design: new problems and related models, European Journal of Operational Research, 165(3), pp. 610–624.
[4] Averbakh I. and Berman O. (2002). Minmax p-traveling salesmen location problems on a tree, Annals of Operations Research, 110(1-4), pp. 55–68.
[5] Aviv Y. and Federgruen A. (1998). The operational benefits of information sharing and vendor-managed inventory (VMI) programs, Working Paper, Olin School of Business, Washington University in St. Louis, (1998), pp. 1-40. Also available from  http://www.olin.wustl.edu/faculty/aviv/papers/vmr.pdf
[6] Aytug H., Khouja M. and Vergara F. E. (2003). Use of genetic algorithms to solve production and operations management: a review, International Journal of Production Researches, 41(17), pp. 3955-4009.
[7] Baita F., Ukovich W., Pesenti R. and Favaretto D. (1998). Dynamic routing and inventory problems: a review, Transportation Research, 32(8), pp. 585-598.
[8] Balakrishnan A., Ward J. E. and Wong R. T. (1987). Integrated facility location and vehicle routing models: Recent work and future prospects, American Journal of Mathematical and Management Sciences, 7(1-2), pp. 35–61.
[9] Ballou R. H. and Masters J. M. (1993). Commercial software for locating warehoused and other facilities, Journal of Business Logistics, 14(2), pp. 70-107.
[10] Ballou R. H. (2001). Unresolved Issues in supply chain network design, Information Systems Frontiers, 3(4), pp. 417-426. 
[11] Banerjee A. (1986). A joint economic-lot-size model for purchaser and vendor, Decision Sciences, 17(3), pp. 292-311.
[12] Barahona, F., Jensen. D. (1998). Plant location with minimum inventory. Mathematical Programming, 83(1-3), pp. 101-111.
[13] Beamon B. M. (1998). Supply Chain Design and Analysis: Models and Methods, International Journal of Production Economics, 55(3), pp. 281-294.
[14] Benders J. F. (1962). Partitioning procedures for solving mixed variables programming problems, Numerische Mathematik, 4, pp. 238-252.
[15] Berger R. T., Coullard C. R. and Daskin M. S. (2007). Location-routing problems with distance constraints, Transportation Science, 41(1), pp. 29-43.
[16] Berman O., Jaillet P. and Simchi-Levi D. (1995). Location-routing problems with uncertainty. In: Drezner, Z. (Ed.), Facility Location: a Survey of Applications and Methods. Springer, New York, pp. 427-452.
[17] Bernstein F., Chen F. and Federgruen A. (2006). Coordinating supply chains with simple pricing schemes: The role of vendor-managed inventories, Management Science, 52(10), pp.1483-1492.
[18] Blumenfeld D. E., Burns L. D., Diltz J. D., and Daganzo C. F. (1985). Analyzing trade-offs between transportation, inventory and production costs on freight networks, Transportation Research, 19(5), pp. 361-380.
[19] Bookbinder J. H. and Reece, K. E. (1988). Vehicle routing considerations in distribution system design, European Journal of Operational Research, 37(2), pp. 204-213.
[20] Buffa F. P. and Munn J. R. (1989). A recursive algorithm for order cycle-time that minimizes logistics cost, Journal of the Operational Research Society, 40(4), pp. 367-377.
[21] Cachon G. and Fisher M. (2000). Supply chain inventory management and the value of shared information, Management Science, 46(8), pp. 1032– 1048.
[22] Campbell A., Clarke L. and Savelsbergh M. (2002). The vehicle routing problem, In Campbell A. M. (Eds.), Inventory Routing in Practice. A. Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 309-330.
[23] Cappanera P., Gallo G. and Maffioli F. (2004). Discrete facility location and routing of obnoxious activities, Discrete Applied Mathematics, 133(1-3), pp. 3-28.
[24] Chan F. T. S. and Chung S. H. (2004). A multi-criterion genetic algorithm for order distribution in a demand driven supply chain, International Journal of Computer Integrated Manufacturing, 17(4), pp. 339-351.
[25] Chen C. L., Wang B. W. and Lee W. C. (2003). Multi-objective optimization for a multi-enterprise supply chain network, Industrial and Engineering Chemistry Research, 42(9), pp. 1879-1889.
[26] Chopra S. and Meindl P. (2006). Supply chain management, 3rd Edition, Prentice Hall.
[27] Coello Coello C. A. (2000). An updated survey of GA-based multiobjective optimization techniques, ACM Computing Surveys, 32(2), pp. 109-143.
[28] Coello Coello C. A. (2006). Recent Trends in Evolutionary Multiobjective Optimization, in Abraham A., Jain L. and Goldberg R. (Eds.), Advanced Information and Knowledge Processing, Chapter 2, pp. 7-32, Springer. 
[29] Coello Coello C. A. ,Lamont G. B. and Van Veldhuizen D. A. (2007). Evolutionary algorithms for solving multi-objective problems, Second Edition, Springer, New York
[30] Cohen M. A. and Lee H. L. (1988). Strategic Analysis of Integrated Production-Distribution Systems: Models and Methods, Operations Research, 36(2), pp. 216-228.
[31] Croxton K. L. and Zinn W. (2005). Inventory considerations in network design, Journal of Business Logistics, 26(1), pp.149-168.
[32] Daganzo C. F. (1987). The break-bulk role of terminals in many-to-many logistic networks, Operations Research, 35(4), pp. 543-555.
[33] Daganzo C. F. (1999). Logistics Systems Analysis, Springer, Berlin, Reading, Germany.
[34]Daskin M. S. (1995). Network and Discrete Location: Models, Algorithms, and applications. Wiley-Interscience, New York.
[35] Daskin M. S., Coullard C. and Shen Z. J. (2002). An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results, Annals of Operations Research, 110(1-4), pp. 83–106.
[36] Daskin M. S., Snyder L. V. and Berter R. T. (2003). Facility location in supply chain design, in logistics systems, in Design and Optimization (Eds. A. Langevin and D. Riopel), Kluwer.
[37] Deb K., Agrawal S., Pratab A. and Meyarivan T. (2000). A fast elitist multi-objective genetic algorithm for multi-objective optimization: NSGAII. In Proceedings of the Parallel Problem Solving from Nature Conference VI, pp. 849-858.
[38] Deb K. (2001). Multi-objective optimization using evolutionary algorithms, John Wiley and Sons.
[39]Deb K., Pratap A., Agarwal S. and Meyarivan T. (2002). A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Transactions on Evolutionary Computation Evolutionary Computation, 6(2), pp.182-197.
[40] Dimopoulos C. and Zalzala A. M. (2000). Recent developments in evolutionary computation for manufacturing optimization: problems, solutions and comparisons, IEEE Transactions on Evolutionary Computation, 4(2), pp. 93-113.
[41] Disney S. M. and Towill D. R. (2002). A procedure for the optimization of the dynamic response for a Vendor Managed Inventory supply chain, Computers and Industrial Engineering: An International Journal, 43(1-2), pp. 27-58.
[42] Dong Y. and Xu K. (2002). A supply chain model of vendor managed inventory, Transportation Research Part E, 38(2), pp. 75-95.
[43] Dror M., Ball M. and Golden B. (1985). A computational comparison of algorithms for the inventory routing problem, Annals of Operations Research, 4(1), pp. 1-23.
[44] Elhedhli S. and Goffin J. L. (2005). Efficient production-distribution system design, Management Science, 51(7), pp. 1151-1164.
[45] Eppen G. (1979). Effects of centralization on expected costs in a multi-location newsboy problem, Management Science, 25(5), pp. 498–501. 
[46] Erenguc S., Simpson N. C. and Vakharia A. J. (1999). Integrated production/distribution planning in supply chains: An invited review, European Journal of Operational Research, 115(2), pp. 219-236.
[47] Erlebacher S. J. and Meller R. D. (2000). The interaction of location and inventory in designing distribution systems, IIE Transactions, 32(2), pp. 155-166.
[48] Ernst R. and Pyke, D. F. (1993). Optimal base stock policies and truck capacity in a two-echelon system, Naval Research Logistics, 40(7), pp. 879-903.
[49] Erol I. and Ferrell W. G. Jr. (2004). A methodology to support decision making across the supply chain of an industrial distributor, International Journal of Production Economics, 89(2), pp. 119-129.
[50] Eskigun E., Uzsoy R., Preckel P. V., Beaujon G., Krishnan S. and Tew J. D. (2005) Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers- production, manufacturing and logistics, European Journal of Operational Research, 165(1), pp. 182-206.
[51] Federgruen A. and Zipkin P. (1984). Combined vehicle routing and inventory allocation problem, Operations Research, 32(5), pp. 1019-1037.
[52] Fonseca C. M. and Fleming P. J. (1993). Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization, in Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, CA, pp. 416-423.
[53] Fonseca C. M. and Fleming P. J. (1995). An overview of evolutionary algorithms in multiobjective optimization, Evolutionary Computation, 3(1), pp. 1-16.
[54] Fourman M. (1985). Compaction of symbolic layout using genetic algorithms, in Proceedings of the 1st International Conference Genetic Algorithms, pp. 141-153.
[55] Ganeshan R. (1999). Managing supply chain inventories: A multiple retailer, one warehouse, multiple supplier model, International Journal of Production Economics, 59(1-3), pp. 341-354
[56] Gaur S. and Ravindran A. R. (2006). A bi-criteria model for the inventory aggregation problem under risk pooling, Computers & Industrial Engineering, 51(3), pp. 482-501.
[57] Gen M. and Cheng R. (2000). Genetic algorithms and engineering optimization. New York: Wiley.
[58] Gen M. and Syarif A. (2005). Hybrid genetic algorithm for multi-time period production /distribution planning, Computers and Industrial Engineering, 48(4), pp. 799-809.
[59] Geoffrion A. M. and Graves G. W. (1974), Multi-commodity distribution system design by benders decomposition, Management Science, 20(5), pp. 822-844.
[60] Ghiani G. and Laporte G. (1999). Eulerian location problems, Networks, 34(4), pp. 291-302.
[61] Giannikos I. (1998). A multiobjective programming model for locating treatment sites and routing hazardous wastes, European Journal of Operational Research, 104(2), pp. 333-342.
[62] Golden B., Assad A. and Dahl R. (1984). Analysis of a large scale vehicle routing problem with an inventory component, Large Scale Systems, 7(2-3), pp. 181-190.
[63] Goldberg D. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading.
[64] Guillen G., Mele F. D., Bagajewicz M. J., Espuna A. and Puigjaner L. (2005). Multiobjective supply chain design under uncertainty, Chemical Engineering Science, 60(6), pp. 1535-1553.
[65] Hall R. W. (1985). Determining vehicle dispatch frequency when shipping frequency differs among suppliers, Transportation Research B, 19(5), pp. 421-431.
[66] Heikkila J. (2002). From supply to demand chain management: efficiency and customer satisfaction. Journal of Operations Management, 20(6), pp. 747–767.
[67] Hinojosa Y., Kalcsics J., Nickel S., Puerto J. and Velten S. (2008). Dynamic supply chain design with inventory, Computers and Operations Research, 35(2), pp. 373-391.
[68] Holland J. H. (1975). Adaptation in Natural and Artificial Systems, Ann Arbor, MI: University of Michigan Press
[69] Hopp W. and Spearman M. L. (1996). Factory Physics: Foundations of Manufacturing Management, Irwin, Chicago.
[70] Horn J., Nafpliotis N. and Goldberg D. E. (1994). A niched Pareto genetic algorithm for multiobjective optimization, In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, volume 1, pp. 82–87, Piscataway, New Jersey, IEEE Service Center.
[71] Ishibuchi H., Yoshida T. and Murata T. (2003). Balance between genetic search and local search in memetic algorithms for multiobjective permutation flow-shop scheduling, IEEE Transactions on Evolutionary Computation, 7(2), 204-222.
[72] Jayaraman V. (1998). Transportation, facility location and inventory issues in distribution network design: An investigation, International, Journal of Operations and Production Management, 18(5), pp. 471-494.
[73] Jayaraman V. and Ross A. (2003). A simulated annealing methodology to distribution network design and management, European Journal of Operational Research, 144(3), pp. 629-645.
[74] Jozefowiez N., Semet F. and Talbi E. G. (2006). Enhancements of NSGA II and its application to the vehicle routing problem with route balancing, Lecture Notes in Computer Science, 3871, pp. 131-142,
[75] Juttner U., Christopher M. and Baker S. (2007). Demand chain management: integrating marketing and supply chain management, Industrial Marketing Management, 36(3), pp. 377-392.
[76] Kleywegt A., Nori V. S. and Savelsbergh M. (2002). The stochastic inventory routing problem with direct deliveries, Transportation Science, 36(1), pp. 94-118.
[77] Knowles J. D. and Corne D. W. (2000). Approximating the non-dominated front using the Pareto-archived evolution strategy, Evolutionary Computation, 8(2), pp. 149–172.
[78] Kohli R. and Park H. (1994). Coordinating buyer-seller transactions across multiple products, Management Science, 40(9), pp. 45-50.
[79] Labbe M., Martın I. R. and Gonzalez J. S. (2004). A branch-and-cut algorithm for the plant-cycle location problem, Journal of the Operational Research Society, 55(5), pp. 513–520.
[80] Laporte, G., Nobert Y. and Pelletier P. (1983). Hamiltonian location problems, European Journal of Operational Research, 12(1), pp. 82–89.
[81] Laporte G. and Nobert Y. (1987). Exact algorithms for the vehicle routing problem, In: S. Martello et al. (eds.), Surveys in Combinatorial Optimization, North-Holland, Amsterdam.
[82] Laporte G. (1988). Location-routing problems. In: Golden, B.L., Assad, A.A. (eds.), Vehicle Routing: Methods and Studies. North-Holland, Amsterdam, pp. 163-198.
[83]	Laporte G., Louveaux F. and Mercure H. (1989). Models and exact solutions for a class of stochastic location-routing problems, European Journal of Operational Research, 39(1), pp. 71-78.
[84] Laumanns M., Rudolph G. and Schwefel H. P. (1999). Approximating the Pareto set: Concepts, diversity issues, and performance assessment, Technical Report CI-72/99, University of Dortmund.
[85] Liao S. H. and Hsieh C. L. (2010). Integrated location-inventory retail supply chain design: a multi-objective evolutionary approach, Lecture Notes in Computer Science, 6457, pp. 533-542.
[86] Lin C. K., Chow C. K. and Chen A. (2002). A location-routing loading problem for bill delivery services, Computers and Industrial Engineering, 43(1-2), pp. 5–25.
[87] Maister D. H. (1976). Centralization of inventories and the square root law, International Journal of Physical Distribution, 6(3), pp. 124-134.
[88] Martin J. and Grbac B. (2003). Using supply chain management to leverage a firm’s market orientation, Industrial Marketing Management, 32(1), pp. 25-38.
[89] Medaglia, A. L. and Fang S. C. (2003). A genetic-based framework for solving (Multi-criteria) weighted matching problems, European Journal of Operational Research, 149(1), 77-101.
[90] Melo M.T., Nickel S. and Saldanha-da-Gama F. S. (2006). Dynamic multi-commodity capacitated facility location: A mathematical model framework for strategic supply chain planning, Computers and Operations Research, 33(1), pp. 181-208.
[91] Melo M.T., Nickel S. and Saldanha-da-Gama F. S. (2009). Facility location and supply chain management- A review. European Journal of Operational Research, 196(2), pp. 401-412.
[92] Michalewicz Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs. Berlin, Springer-Verlag.
[93] Miettinen K. M. (1999). Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston.
[94] Min H., Jayaraman V. and Srivastava R. (1998). Combined location-routing problems: A synthesis and future research directions, European Journal of Operational Research, 108(1), pp. 1–15.
[95] Minner S. (2003). Multiple-supplier inventory models in supply chain management: a review, International Journal of Production Economics, 81-82(1), pp. 265-279.
[96] Miranda P. A. and Garrido R. A. (2004). Incorporating inventory control decisions into a strategic distribution network model with stochastic demand, Transportation Research Part E, 40(3), pp. 183-207.
[97] Miranda P. A. and Garrido R. A. (2006). A simultaneous inventory control and facility location model with stochastic capacity constraints, Networks and Spatial Economics, 6(1), pp. 39-53.
[98] Mishra B. K. and Raghunathan S. (2004). Retailer vs. vendor-managed inventory and brand competition, Management Science, 50(4), pp. 445-457.
[99] Moin N. H. and Salhi S. (2007). Inventory routing problems: a logistical overview, Journal of the Operational Research Society, 58(9), pp. 1185-1194.
[100] Morse J. N. (1980). Reducing the size of the nondominated set: pruning by clustering, Computers and Operations Research, 7(1–2), pp.55–66.
[101] Nagy G. and Salhi S. (1996). Nested heuristic methods for the location-routing problem, The Journal of the Operational Research Society, 47(9), pp. 1166-1174.
[102] Nagy G. and Salhi S. (1998). The many-to-many location-routing problem, TOP, 6(2), pp. 261-275.
[103] Nagy G. and Salhi S. (2007). Location-routing: issues, models and methods, European Journal of Operational Research, 177(2), pp. 649-672.
[104] Nahmias S. (1997). Production and Operations Management, Irwin, Chicago.
[105] Nozick L. K. and Turnquist M. A. (1998). Integrating inventory impacts into a fixed-charge model for locating DCs, Transportation Research. Part E, 34(3), pp. 173-186.
[106] Nozick L. K. (2001). The fixed charge facility location problem with coverage restrictions, Transportation Research. Part E, 37(5), pp. 281-296. 
[107] Nozick L. K. and Turnquist M. A. (2001). A two-echelon allocation and distribution center location analysis, Transportation Research. Part E, 37(5), pp. 425-441. 
[108] Owen S. H. and Daskin M. S. (1998). Strategic facility location: a review, European Journal of Operational Research, 111(3), pp. 423-447.
[109] Ozsen L, Coullard C. R. and Daskin M. S. (2008). Capacitated warehouse location model with risk pooling. Naval Research Logistics, 55(4), pp. 295-312.
[110] Revelle C. and Laporte G. (1996). The plant location problem: new models and research prospects, Operations Research, 44(6), pp. 864-874.
[111] Romeijn H. E., Shu J. and Teo C. P. (2007). Designing two-echelon supply networks, European Journal of Operational Research, 178(2), pp. 449-462.
[112] Ronen D. (2002). Marine inventory routing: shipments planning, Journal of the Operational Research Society, 53(1), pp. 108-114.
[113] Sabri E. H. and Beamon B. M. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design, Omega, 28(5), pp. 581-598.
[114] Salhi S. and Fraser M. (1996). An integrated heuristic approach for the combined location vehicle fleet mix problem, Studies in Locational Analysis, 8, pp. 3-22.
[115] Schaffer J. D. (1985). Multiple objective optimization with vector evaluated genetic algorithms. In Proceedings of the First International Conference on Genetic Algorithms: Genetic Algorithms and their Applications, pp. 93-100, Hillsdale, NJ.
[116] Schwardt M. and Dethloff J. (2005). Solving a continuous location-routing problem by use of a self-organizing map, International Journal of Physical Distribution and Logistics Management, 35(6), pp. 390–408.
[117] Shen Z. J. (2000). Approximation Algorithms for Various Supply Chain Problems, PhD Thesis, Department of Industrial Engineering and Management Sciences, Northwestern University.
[118] Shen Z. J., Coullard C. R. and Daskin M. S. (2003), A joint location-inventory model, Transportation Science, 37(1), pp. 40-55.
[119] Shen Z. J. and Daskin M. S. (2005). Trade-offs between customer service and cost in integrated supply chain design, Manufacturing and Service Operations Management, 7(3), pp. 188-207.
[120] Shen Z. J. (2007). Integrated supply chain design models: a survey and future research directions, Journal of Industrial and Management Optimization, 3(1), pp. 1-27. 
[121] Shen Z. J. and Qi L. (2007). Incorporating inventory and routing costs in strategic location models, European Journal of Operational Research, 179(2), pp. 372-389. 
[122] Shu J., Teo C. P. and Shen Z. J. (2005). Stochastic transportation-inventory network design problem, Operations Research, 53(1), pp. 48-60.
[123] Simchi-Levi D., Kaminsky P. and Simchi-Levi E. (2009). Designing and managing the supply chain: concepts, strategies, and case studies (3/e). New York: McGraw-Hill.
[124] Snyder L. V., Daskin M. S. and Teo C. P. (2003). The stochastic location model with risk pooling. Working paper, Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA.
[125] Snyder L. V., Daskin M. S. and Teo C. P. (2007). The stochastic location model with risk pooling, European Journal of Operational Research, 179(3), pp. 1221-1238 
[126] Sourirajan K., Ozsen L. and Uzsoy R. (2009). A genetic algorithm for a single product network design model with lead time and safety stock considerations, European Journal of Operational Researh,197(2), pp. 599–608.
[127] Srinivas N. and Deb K. (1994). Multiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation, 2(3), pp. 221–248.
[128] Stowers C. L. and Palekar U. S. (1993). Location models with routing considerations for a single obnoxious facility, Transportation Science, 27(4), pp. 350-362.
[129] Svensson G. (2002). Supply chain management: The re-integration of marketing issues and logistics theory and practice. European Business Review, 14(6), pp. 426– 436.
[130] Taha H. A. (2003). Operations Research, 7th Edition, New Jersey: Prentice Hall.
[131] Tayur, S. R., Ganeshan R. and Magazine M. J. (eds.) (1999). Quantitative Models for Supply Chain Management, International Series in Operations Research & Management Science, vol. 17, Springer-Verlag, New York.
[132] Tempelmeier H. (2006). Inventory Management in Supply Networks - Problems, Models, Solutions. Norderstedt, Books on Demand.
[133] Teo C. P. and Shu J. (2004). Warehouse-retailer network design problem, Operations Research, 52(3), pp. 396-408.
[134] Thomas D. J. and Griffin P. M. (1996). Coordinated supply chain management, European Journal of Operational Research, 94(11), pp. 1-15.
[135] Truong T. H. and Azadivar F. (2005). Optimal design methodologies for configuration of supply chains, International Journal of Production Researches, 43(11), pp. 2217-2236.
[136] Tuzun D. and Burke L. I. (1999). A two-phase tabu search approach to the location routing problem, European Journal of Operational Research, 116(1), pp. 87-99.
[137] Van Veldhuizen D. A. (1999). Multiobjective evolutionary algorithms: Classifications, analyses, and new innovations. PhD Thesis. Technical Report No. AFIT/DS/ENG/99-01. Air Force Institute of Technology, Dayton, Ohio.
[138] Van Veldhuizen, D. A. and Lamont G. B. (2000). On measuring multiobjective evolutionary algorithm performance, in Proceedings of the 2000 Congress on Evolutionary Computation, pp. 204-211.
[139] Vidal C. and Goetschalckx M. (1997). Strategic production-distribution models: A critical review with emphasis on global supply chain models, European Journal of Operational Research, 98(1), pp. 1-18.
[140] Viswanathan S. and Mathur K. (1997). Integrating routing and inventory decisions in one warehouse multi-retailer, multi-product distribution systems, Management Science, 43(3), pp. 294-312.
[141] Vidyarthi N., Çelebi E., Elhedhli S. and Jewkes E. (2007). Integrated production-inventory-distribution system design with risk pooling: model formulation and heuristic solution, Transportation Science, 41(3), pp. 392-408.
[142] Waller M. A., Johnson M. E. and Davis T. (1999). Vendor-managed inventory in the retail supply chain, Journal of Business Logistics, 20(1), pp.183-203.
[143] Waller M. A., Cassady C. R. and Ozment J. (2006). Impact of cross-docking on inventory in a decentralized retail supply chain, Transportation Research Part E, 42(5), pp.359-382.
[144] Warszawski A. and Peer S. (1973). Optimizing the location of facilities on a building site, Operational Research Quarterly, 24(1), pp. 35-44.
[145] Webb I. R. and Larson R. C. (1995). Period and phase customer replenishment: a new approach to strategic inventory/routing problem, European Journal of Operational Research, 85(1), pp. 132-148.
[146] Weng Z. K. (1995). Channel coordination and quantity discount, Management Science, 41(9), pp. 1509-1522.
[147] Wu T. H., Low C. and Bai J. W. (2002). Heuristic solutions to multi-depot location-routing problems, Computers and Operations Research, 29(10), pp. 1393-1415.
[148] Yan H., Yu Z. and Cheng C. E. (2003). A strategic model for supply chain design with logical constraints: formulation and solution, Computers and Operations Research, 30(14), pp. 2135-2155.
[149] Zeleny M. (1982), Multiple Criteria Decision-Making, New York: McGraw-Hill.
[150] Zinn W., Levy M., and Bowersox D. J. (1989). Measuring the effect of inventory centralization/decentralization on aggregate safety stock: the ‘Square Root Law’ revisited, Journal of Business Logistics, 10(2), pp. 1-14.
[151] Zipkin P. H. (1997). Foundations of Inventory Management, Irwin, Burr Ridge, IL.
[152]	Zitzler E. and Thiele L. (1998). Multiobjective optimization using evolutionary algorithms - a comparative study, Parallel Problem Solving from Nature V (PPSN-V), pp. 292-301.
[153]	Zitzler E. and Thiele L. (1999). Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions Evolutionary Computing, 3(4), pp. 257-271.
[154]	Zitzler E., Deb K. and Thiele L. (2000). Comparison of multi-objective evolutionary algorithms: empirical results, Evolutionary Computation, 8(2), pp. 173-195.
[155]	Zitzler E., Laumanns M., and Thiele L. (2002). SPEA2: Improving the strength Pareto evolutionary algorithm for multi-objective optimization. In K. C. Giannakoglou et al. (eds.), Evolutionary Methods for Design, Optimization and Control with Application to Industrial Problems (EUROGEN 2002), pp. 95-100.