Minimizing the Total Cost in an Integrated Vendor—Managed Inventory System
In this paper we consider a complex production-distribution system, where a facility produces (or orders from an external supplier) several items which are distributed to a set of retailers by a fleet of vehicles. We consider Vendor-Managed Inventory (VMI) policies, in which the facility knows the inventory levels of the retailers and takes care of their replenishment policies. The production (or ordering) policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The cost includes the fixed and variable production costs at the facility, the inventory costs at the facility and at the retailers and the transportation costs, that is the fixed costs of the vehicles and the traveling costs. We study two different types of VMI policies: The order-up-to level policy, in which the order-up-to level quantity is shipped to each retailer whenever served (i.e. the quantity delivered to each retailer is such that the maximum level of the inventory at the retailer is reached) and the fill-fill-dump policy, in which the order-up-to level quantity is shipped to all but the last retailer on each delivery route, while the quantity delivered to the last retailer is the minimum between the order-up-to level quantity and the residual transportation capacity of the vehicle. We propose two different decompositions of the problem and optimal or heuristic procedures for the solution of the subproblems. We show that, for reasonable initial values of the variables, the order in which the subproblems are solved does not influence the final solution. We will first solve the distribution subproblem and then the production subproblem. The computational results show that the fill-fill-dump policy reduces the average cost with respect to the order-up-to level policy and that one of the decompositions is more effective. Moreover, we compare the VMI policies with the more traditional Retailer-Managed Inventory (RMI) policy and show that the VMI policies significantly reduce the average cost with respect to the RMI policy.
KeywordsVendor-Managed Inventory VMI transportation inventory heuristics logistics
Unable to display preview. Download preview PDF.
- Campbell, A.M., L. Clarke, A.J. Kleywegt, and M.W.P. Savelsbergh. (1998). “The Inventory Routing Problem.” In T.G. Crainic and G. Laporte (eds.), Fleet Management and Logistics, Boston: Kluwer Academic Publishers, pp. 95–113.Google Scholar
- Erengüç, Ş.S., N.C. Simpson, and A.J. Vakharia. (1999). “Integrated Production/Distribution Planning in Supply Chains: An Invited Review.” European Journal of Operational Research 115, 219–236.Google Scholar
- Fry, M.J., R. Kapuscinski, and T.L. Olsen. (2001). “Coordinating Production and Delivery under a (z,Z)-Type Vendor-Managed Inventory Contract.” Manufacturing & Service Operations Management 3, 151–173.Google Scholar
- Hu, T.C. (1982). Combinatorial Algorithms, Reading, MA: Addison Wesley.Google Scholar
- Lee, H.L. and S. Nahmias. (1993). “Single-Product, Single-Location Models.” In Handbooks in Operations Research & Management Science, vol. 4, North-Holland: Elsevier Science Publishers, pp. 3–55.Google Scholar
- Rabah, M.Y. and H.S. Mahmassani. (2002). “Impact of Electronic Commerce on Logistics Operations: A Focus on Vendor Managed Inventory (VMI) Strategies.” Technical Report N. SWUTC/02/167227-1, Center for Transportation Research, University of Texas at Austin.Google Scholar
- Toth, P. and D. Vigo. (2002). The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications, Philadelphia.Google Scholar
- Wagner, H.M. and T.M. Whitin. (1958). “Dynamic Version of the Economic Lot Size Model.” Management Science 5, 89–96.Google Scholar