×

A coordinated location-inventory model. (English) Zbl 1244.90012

Summary: We consider a coordinated location-inventory model where distribution centers (DCs) follow a periodic-review \((R, S)\) inventory policy and system coordination is achieved by choosing review intervals at the DCs from a menu of permissible choices. We introduce two types of coordination: partial coordination where each DC may choose its own review interval from the menu, and full coordination where all the DCs have an identical review interval. While full coordination increases the location and inventory costs, it likely reduces the overall costs of running the system (when the operational costs such as delivery scheduling are taken into account). The problem is to determine the location of the DCs to be opened, the assignment of retailers to DCs, and the inventory policy parameters at the DCs such that the total system-wide cost is minimized. The model is formulated as a nonlinear integer-programming problem and a Lagrangian relaxation algorithm is proposed to solve it. Computational results show that the proposed algorithm is very efficient. The results of our computational experiments and case study suggest that the location and inventory cost increase due to full coordination, when compared to partial coordination, is not significant. Thus, full coordination, while enhancing the practicality of the model, is economically justifiable.

MSC:

90B05 Inventory, storage, reservoirs
90B06 Transportation, logistics and supply chain management
90C11 Mixed integer programming
90B80 Discrete location and assignment
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Berman, O.; Krass, D.; Menezes, M.B.C., Facility reliability issues in network p-Median problems: strategic centralization and co-location effects, Operations research, 55, 332-350, (2007) · Zbl 1167.90466
[2] Berman, O.; Krass, D.; Tajbakhsh, M.M., On the benefits of risk pooling in inventory management, Production and operations management, 20, 57-71, (2011)
[3] Daskin, M.S.; Coullard, C.R.; Shen, Z.-J.M., An inventory-location model: formulation, solution algorithm and computational results, Annals of operations research, 110, 83-106, (2002) · Zbl 1013.90001
[4] Eppen, G.D., Effects of centralization on expected costs in a multi-location newsboy problem, Management science, 25, 498-501, (1979) · Zbl 0419.90049
[5] Erlebacher, S.J.; Meller, R.D., The interaction of location and inventory in designing distribution systems, IIE transactions, 32, 155-166, (2000)
[6] Fisher, M.L., The Lagrangian relaxation method for solving integer programming problems, Management science, 27, 1-18, (1981) · Zbl 0466.90054
[7] Hadley, G.; Whitin, T.M., Analysis of inventory systems, (1963), Prentice-Hall, Inc. Englewood Cliffs, N.J · Zbl 0133.42901
[8] Montgomery, D.C.; Bazaraa, M.S.; Keswani, A.K., Inventory models with a mixture of backorders and lost sales, Naval research logistics quarterly, 20, 255-263, (1973) · Zbl 0262.90020
[9] Ozsen, L.; Coullard, C.R.; Daskin, M.S., Capacitated warehouse location model with risk pooling, Naval research logistics, 55, 295-312, (2008) · Zbl 1153.90484
[10] Shen, Z.-J.M.; Daskin, M.S., Trade-offs between customer service and cost in integrated supply chain design, Manufacturing and service operations management, 7, 188-207, (2005)
[11] Shen, Z.-J.M.; Coullard, C.R.; Daskin, M.S., A joint inventory-location model, Transportation science, 37, 40-55, (2003)
[12] Shen, Z.-J.M., A multi-commodity supply chain design problem, IIE transactions, 37, 753-762, (2005)
[13] Shu, J.; Teo, C.-P.; Shen, Z.-J.M., Stochastic transportation-inventory network design problem, Operations research, 53, 48-60, (2005) · Zbl 1165.90367
[14] Silver, E.A.; Pyke, D.F.; Peterson, R., Inventory management and production planning and scheduling, (1998), John Wiley & Sons New York
[15] Snyder, L.V.; Daskin, M.S.; Teo, C.-P., The stochastic location model with risk pooling, European journal of operational research, 179, 1221-1238, (2007) · Zbl 1127.90039
[16] Talley, K., 2011. Target is entering Canada, selling card receivables. Wall Street Journal.
[17] Teo, C.P.; Ou, J.; Goh, M., Impact on inventory costs with consolidation of distribution centers, IIE transactions, 33, 99-110, (2001)
[18] Vidyarthi, N.; Çelebi, E.; Elhedhli, S.; Jewkes, E., Integrated production-inventory-distribution system design with risk pooling: model formulation and heuristic solution, Transportation science, 41, 392-408, (2007)
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.