Optimal sourcing from alternative capacitated suppliers with general cost structures

Most manufacturers or retailers must procure items or services necessary for their businesses, in an environment that typically includes a number of competing suppliers with varying cost structures, price schemes, and capacities. In this paper, we consider the sourcing problem in which the buyer determines the sources that should be utilized and to what extent, in turn, dictating the total quantity available for the buyer to sell/utilize, subject to stochastic demand/requirement. Our approach advocates not to determine the quantity to be sourced a priori. We allow for capacitated sources and any cost structure in which fixed costs and quantity discounts are special cases. Some simpler versions of this problem are shown to be NP-hard in the literature. By proving that the order of the sources is irrelevant for the optimal solution, we devise a dynamic programming model with pseudo-polynomial complexity to solve the multiple supplier sourcing problem to optimality. We propose two extensions: one limits the number of suppliers, and the other allows multi-period sourcing.