Volume 4 Issue 1 pp. 93-110 Winter, 2013


A location-inventory model for distribution centers in a three-level supply chain under uncertainty


Sara Gharegozloo Hamedani, M. Saeed Jabalameli and Ali Bozorgi-Amiri




We study a location-inventory problem in a three level supply chain network under uncertainty, which leads to risk. The (r,Q) inventory control policy is applied for this problem. Besides, uncertainty exists in different parameters such as procurement, transportation costs, supply, demand and the capacity of different facilities (due to disaster, man-made events and etc). We present a robust optimization model, which concurrently specifies: locations of distribution centers to be opened, inventory control parameters (r,Q), and allocation of supply chain components. The model is formulated as a multi-objective mixed-integer nonlinear programming in order to minimize the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. Moreover, we develop an effective solution approach on the basis of multi-objective particle swarm optimization for solving the proposed model. Eventually, computational results of different examples of the problem and sensitivity analysis are exhibited to show the model and algorithm's feasibility and efficiency.




DOI: 10.5267/j.ijiec.2012.10.004

Keywords: Location-inventory, Facility location, Uncertainty, Supply chain network design, Multi-objective particle swarm Optimization

References

References Axsater, S. (2006). inventory control, Second edition, Springer, New York.

Alvarez-Benitez, J. E., Everson, R. M., Fieldsend, J.E.. (2005). A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts. Springer-Verlag Berlin Heidelberg, 459-473.

Azaron, A., Brown, K. N., Tarim, S.A., & Modarres, M. (2008). A multi-objective stochastic programming approach for supply chain design considering risk. international Journal of Production Economics, 116, 129-138.

Berman, O., Krass, D., & Tajbakhshm, M. M. (2012). A coordinated location-inventory model. European Journal of Operational Research, 217, 500-508.

Bérubé, J. F., Gendreau, M., & Potvin, J.Y. (2009). An exact ε-constraint method for bi-objective combinatorial optimization problems: Application to the traveling salesman problem with profits. European Journal of Operational Research, 194, 39-50.

Bozorgi-Amiri, A., Jabalameli, M. S., Alinaghian, M., & Heydari, M. (2012). A modified particle swarm optimization for disaster relief logistics under uncertain environment. International Journal of Advance Manufacturing Technology, 60, 357-371.

Chen, Q., Li, X., & Ouyang, Y. (2011). Joint inventory-location problem under the risk of probabilistic facility disruptions. Transportation Research Part B, 45, 991–1003.

Daskin, M. S., Coullard, C. R. , & Shen, Z.-J.M. (2002). An inventory-location model: Formulation, solution algorithm and computational results. Annals of Operations Research, 110, 83-106.

Eckart, Z., Kalyanmoy, D., & Lothar, T. et al. (2000). Comparison of Multi objective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2), 173–195.

Ehrgott, M., & Gandibleux, X. (2002). Multi objective combinatorial optimization theory, methodology and applications. Kluwer Academic.

Eppen, G. D. (1979). Effects of centralization on expected costs in a multi-location newsboy problem. Management Science, 25, 498-501.

Erlebacher, S., & Meller, R. (2000). The interaction of location and inventory in designing distribution systems. international industrial engineering Transactions, 32, 155-166.

Kennedy, J., & Eberhart, R. C. (2001). Swarm Intelligence. San Francisco, California, Morgan Kaufmann Publishers.

Megiddo, N., & K. Supowit (1984). On the complexity of some common geometric location problems. society for industrial and applied mathematics journal on computing, 13, 182–196.

Melo, M., Nickel, S., & Saldanha-da-Gama, F. (2009). Facility location and supply chain management – a review. European Journal of Operational Research, 196(2), 401-412.

Min, H., & Zhou, G. (2002). Supply chain modeling: past, present and future. Computer and Industrial Engineering, 43, 231–249.

Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large scale systems. operational Research, 43(2), 264-281.

Nozick, L., & Turnquist, M. (1998). Integrating inventory impacts into a fixed-charge model for locating distribution centers. Transportation Research Part E, 34(3), 173-186.

Park, S., Lee, T., & Sung, C. (2010). A three-level supply chain network design model with risk-pooling and lead times. Transportation Research Part E, 46, 563–581.

Qi, L., Shen, Z. J., & Snyder, L.V. (2010). The effect of supply disruptions on supply chain design decisions. Transportation Science, 44(2), 274-289.

Rezaei Ehsan, E., Makui, A., & Shahanaghi, K. (2012). Emergency response network design for hazardous materials transportation with uncertain demand. international Journal of industrial engineering computations, 3, 893–906.

Roghanian, E., & Kamandanipour, K. (2012). A fuzzy-random programming for integrated closed-loop logistics network design by using priority-based genetic algorithm. International Journal of industrial engineering computations,4(1).

Romeijn, H. E., Shu, J., & Teo, C. (2007). Designing two-echelon supply networks. European Journal of Operational Research, 178, 449–462.

shen, Z. J., Coullard, C., & Daskin, M.S. (2003). A joint location-inventory model. transportation science, 37, 40-55.

Shen, Z. J., & Qi, L. (2007). Incorporating inventory and routing costs in strategic location models. European Journal of Operational Research, 179, 372-389.

Snyder, L. V. (2006). Facility location under uncertainty: A review. international Industrial Engineering Transactions, 38(7), 547–564.

Snyder, L. V., Daskin, M. S., & Teo, C. ( 2007). The stochastic location model with risk pooling. European Journal of Operational Research, 179(3), 1221-1238.

Sourirajan, K., Oszen, L., & Uzsoy, R. (2007). A single product network design with leadtime and safety stock consideration. HE Transaction,39(5), 411-424.

Tancrez , J.-S., Lange , J.-C. ,& Semal, P. (2012). A location-inventory model for large three-level supply chains. Transportation Research Part E, 48, 485-502.

Teo, C., & Shu, J. (2004). Warehouse-retailer network design problem. Operations Research, 52, 396–408.

Tsao, Y.-C., Mangotra, D., Lu, J.C., & Dong, M. (2012). A continuous approximation approach for the integrated facility-inventory allocation problem. European Journal of Operational Research. 222,(216-226).

YU, C., & Li, H. (2000). a robust optimization model for stochastic logistic problems. international Journal of Production Economics, 64(1-3), 385-397.

Üster, H., Keskin, B. , & Çetinkaya, S. (2008). Integrated warehouse location and inventory decisions in a three-tier distribution system. International Industrial Engineering, 40, 718-732.

Yazdian, S. A., & Shahanaghi, K. (2010). A multi-objective possibilistic programming approach for locating distribution centers and allocating customers demands in supply chains. International Journal of Industrial Engineering Computations, 2, 193-202.

Zipkin, P. H. (2000). Foundation of inventory management. McGraw-hill, Boston,Massachusetts.