A supply chain design problem with facility location and bi-objective transportation choices. (English) Zbl 1262.90005

Summary: A supply chain design problem based on a two-echelon single-product system is addressed. The product is distributed from plants to distribution centers and then to customers. There are several transportation channels available for each pair of facilities between echelons. These transportation channels introduce a cost-time tradeoff in the problem that allows us to formulate it as a bi-objective mixed-integer program. The decisions to be taken are the location of the distribution centers, the selection of the transportation channels, and the flow between facilities. Three variations of the classic \(\varepsilon\)-constraint method for generating optimal Pareto fronts are studied in this paper. The procedures are tested over six different classes of instance sets. The three sets of smallest size were solved completely obtaining their efficient solution set. It was observed that one of the three proposed algorithms consistently outperformed the other two in terms of their execution time. Additionally, four schemes for obtaining lower bound sets are studied. These schemes are based on linear programming relaxations of the model. The contribution of this work is the introduction of a new bi-objective optimization problem, and a computational study of the \(\varepsilon\)-constraint methods for obtaining optimal efficient fronts and the lower bounding schemes.


90-08 Computational methods for problems pertaining to operations research and mathematical programming
90B06 Transportation, logistics and supply chain management
90B10 Deterministic network models in operations research
90B80 Discrete location and assignment
90C11 Mixed integer programming
90C29 Multi-objective and goal programming


Full Text: DOI


[1] Aikens CH (1985) Facility location models for distribution planning. Eur J Oper Res 22(3):263–279 · Zbl 0583.90022
[2] Altiparmak F, Gen M, Lin L, Paksoy T (2006) A genetic algorithm approach for multi-objective optimization of supply chain networks. Comput Indust Eng 51(1):197–216
[3] Arntzen BC, Brown GC, Harrison TP, Trafton LL (1995) Global supply chain management at Digital Equipment Corporation. Interfaces 25(1):69–93
[4] Ballou RH (1999) Business logistics management. Prentice Hall, New York
[5] Baumol WJ, Wolfe P (1958) A warehouse–location problem. Oper Res 6(2):252–263
[6] Benjamin J (1990) An analysis of mode choice for shippers in a constrained network with applications to just-in-time inventory. Transp Res Part B 24(3):229–245
[7] Chan FTS, Chung SH, Choy KL (2006) Optimization of order fulfillment in distribution network problems. J Intell Manuf 17(3):307–319
[8] Chopra S, Meindl P (2004) Supply chain management: strategy, planning, and operation. Prentice Hall, New York
[9] Cordeau JF, Pasin F, Solomon MM (2006) An integrated model for logistics network design. Ann Oper Res 144(1):59–82 · Zbl 1142.90322
[10] Cornuejols G, Nemhauser GL, Wolsey LA (1990) The uncapacitated facility location problem. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New York, pp 119–171, Chap 3 · Zbl 0727.90043
[11] Current J, Min H, Schilling D (1990) Multiobjective analysis of facility location decisions. Eur J Oper Res 49(3):295–307 · Zbl 0717.90042
[12] Ehrgott M (2005) Multicriteria optimization. Springer, Berlin · Zbl 1132.90001
[13] Ehrgott M, Gandibleux X (2007) Bound sets for biobjective combinatorial optimization problems. Comput Oper Res 34(9):2674–2694 · Zbl 1141.90509
[14] Ehrgott M, Ruzika S (2008) Improved {\(\epsilon\)}-constraint method for multiobjective programming. J Optim Theory Appl 138(3):375–396 · Zbl 1191.90054
[15] ElMaraghy HA, Majety R (2008) Integrated supply chain design using multi-criteria optimization. Int J Adv Manuf Technol 37(3):371–399
[16] Eskigun E, Uzsoy R, Preckel PV, Beaujon G, Krishnan S, Tew JD (2005) Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers. Eur J Oper Res 165(1):182–206 · Zbl 1112.90361
[17] Farahani RZ, SteadieSeifi M, Asgari N (2009) Multiple criteria facility location problems: a survey. Appl Math Modell 34(7):1689–1709 · Zbl 1193.90143
[18] Graves SC, Willems SP (2005) Optimizing the supply chain configuration for new products. Manag Sci 51(8):1165–1180 · Zbl 1232.90055
[19] ILOG SA (2008) ILOG CPLEX Callable Library C API 11.1 Reference Manual. ILOG, France
[20] Klose A, Drexl A (2005) Facility location models for distribution system design. Eur J Oper Res 162(1):4–29 · Zbl 1132.90345
[21] Kuehn AA, Hamburger MJ (1963) A heuristic program for locating warehouses. Manag Sci 9(4):643–666
[22] Melo MT, Nickel S, Saldanha-da-Gama F (2009) Facility location and supply chain management–a review. Eur J Oper Res 196(2):401–412 · Zbl 1163.90341
[23] Sahin G, Sural H (2007) A review of hierarchical facility location models. Comput Oper Res 34(8):2310–2331 · Zbl 1144.90440
[24] Simchi-Levi D, Kaminski P, Simchi-Levi E (2000) Designing and managing the supply chain: concepts, strategies and case studies. McGraw Hill, New York
[25] Steuer RE (1989) Multiple criteria optimization: theory, computation and application. Krieger, Melbourne · Zbl 0742.90068
[26] Thomas DJ, Griffin PM (1996) Coordinated supply chain management. Eur J Oper Res 94(1):1–15 · Zbl 0929.90004
[27] Truong TH, Azadivar F (2005) Optimal design methodologies for configuration of supply chains. Int J Prod Res 43(11):2217–2236
[28] Vidal CJ, Goetschalckx M (1997) Strategic production–distribution models: a critical review with emphasis on global supply chain models. Eur J Oper Res 98(1):1–18 · Zbl 0922.90062
[29] Vidyarthi N, Elhedhli S, Jewkes E (2009) Response time reduction in make-to-order and assemble-to-order supply chain design. IIE Trans 41(5):448–466
[30] Wilhelm W, Liang D, Rao B, Warrier D, Zhu X, Bulusu S (2005) Design of international assembly systems and their supply chains under NAFTA. Transp Res Part E 41(6):467–493
[31] Zeng DD (1998) Multi-issue decision making in supply chain management and electronic commerce. PhD dissertation, Graduate School of Industrial Administration and Robotics Institute, Carnegie Mellon University, Pittsburgh, USA
[32] Zhou G, Min H, Gen M (2003) A genetic algorithm approach to the bi-criteria allocation of customers to warehouses. Int J Prod Econ 86(1):35–45
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.