APPROXIMATIONS FOR MULTIPRODUCT CONTRACTS WITH STOCHASTIC DEMANDS ANDBUSINESS VOLUME DISCOUNTS - SINGLE SUPPLIER CASE

In this paper we analyze contracts for multiple products when the supp lier offers business volume discounts. The contract takes the form of price discounts for total minimum dollar volume commitments over the h orizon with flexibility to adjust the total purchases upwards by a fix ed percentage about this minimum commitment. The optimal policy could be complex since it involves the solution of a constrained multi-perio d multi-product dynamic program. We suggest approximations that give u s an upper bound. To develop this upper bound, we present the optimal policy for a similar contract for a single product problem. We then de velop a lower bound for the multiproduct problem and show, numerically , that the gap is small. Given the approximations standard single peri od resource allocation algorithms can be used to solve the problem. Th e resulting solution methodology is fast and permits evaluation of var ious what-if scenarios.