Abstract
In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.
Similar content being viewed by others
References
Berman, O., & Krass, D. (2001). Facility location problems with stochastic demands and congestion. In A. Drezner & H. W. Hamacher (Eds.) Facility location: applications and theory (pp. 331–373). New York: Springer.
Franca, P. M., & Luna, H. P. L. (1982). Solving stochastic transportation-location problems by generalized benders decomposition. Transportation Science, 16, 113–126.
Gebennini, E., Gamberini, R., & Manzini, R. (2009). An integrated production-distribution model for the dynamic location and allocation problem with safety stock optimization. International Journal of Production Economics, 122, 286–304.
Keskin, B. B., Melouk, S. H., & Meyer, I. L. (2010). A simulation-optimization approach for integrated sourcing and inventory decisions. Computers and Operations Research, 37, 1648–1661.
Laporte, G., Louveaux, F. V., & van Hamme, L. (1994). Exact solution to a location problem with stochastic demands. Transportation Science, 28, 95–103.
Louveaux, F. V., & Peeters, D. (1992). A dual-based procedure for stochastic facility location. Operations Research, 40, 564–573.
Manzini, R., & Bindi, F. (2009). Strategic design and operational management optimization of a multi stage physical distribution system. Transportation Research, 45E, 915–936.
Mirchandani, P. B., Oudjit, A., & Wong, R. T. (1985). Multidimensional extensions and a nested dual approach for the M-median problem. European Journal of Operational Research, 21, 423–447.
Ozsen, L., Coullard, C. R., & Daskin, M. S. (2008). Capacitated warehouse location model with risk pooling. Naval Research Logistics, 55, 295–312.
Owen, S. H., & Daskin, M. S. (1998). Strategic facility location: a review. European Journal of Operational Research, 111, 423–447.
ReVelle, C., & Williams, J. C. (2001). Reserve design and facility siting. In A. Drezner & H. W. Hamacher (Eds.) Facility location: applications and theory (pp. 310–330). New York: Springer.
Roundy, R. O. (1985). 98% effective integer-ratio lot-sizing for one warehouse multi-retailer systems. Management Science, 31, 1416–1430.
Shen, Z. J. M., Coullard, C. R., & Daskin, M. S. (2003). A joint location-inventory model. Transportation Science, 37, 40–55.
Sheppard, E. S. (1974). A conceptual framework for dynamic location-allocation analysis. Environment and Planning A, 6, 547–564.
Shu, J. (2010). An efficient greedy heuristic for warehouse-retailer network design optimization. Transportation Science. doi:10.1287/trsc.1090.0302.
Shu, J., Teo, C. P., & Max Shen, Z. J. (2005). Stochastic transportation-inventory network design problem. Operations Research, 53, 48–60.
Snyder, L. V. (2006). Facility location under uncertainty: a review. IIE Transactions, 38(7), 537–554.
Snyder, L. V., Daskin, M. S., & Teo, C. P. (2007). The stochastic location model with risk pooling. European Journal of Operational Research, 179, 1221–1238.
Sourirajan, K., Ozsen, L., & Uzsoy, R. (2007). A single-product network design model with lead time and safety stock considerations. IIE Transactions, 39, 411–424.
Sourirajan, K., Ozsen, L., & Uzsoy, R. (2009). A genetic algorithm for a single product network design model with lead time and safety stock considerations. European Journal of Operational Research, 197, 599–608.
Teo, C. P., & Shu, J. (2004). Warehouse-retailer network design problem. Operations Research, 52, 396–408.
Üster, H., Keskin, B. B., & Çetinkaya, S. (2008). Integrated warehouse location and inventory decisions in a three-tier distribution system. IIE Transactions, 40, 718–732.
Vidyarthi, N., Celebi, E., Elhedhli, S., & Jewkes, E. (2007). Integrated production-inventory-distribution system design with risk pooling: model formulation and heuristic solution. Transportation Science, 41, 392–408.
Weaver, J. R., & Church, R. L. (1983). Computational procedures for location problems on stochastic networks. Transportation Science, 17, 168–180.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shu, J., Ma, Q. & Li, S. Integrated location and two-echelon inventory network design under uncertainty. Ann Oper Res 181, 233–247 (2010). https://doi.org/10.1007/s10479-010-0732-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-010-0732-z