Supplier selection and purchase problem with fixed cost and constrained order quantities under stochastic demand

This paper addresses a supplier selection and purchase problem under stochastic demand. In particular, a buyer firm (manufacturer or retailer) wants to procure a product from a group of potential suppliers, which may quote different prices and have restriction on minimum and maximum order sizes, to satisfy the uncertain demand. In addition to holding and shortage costs, a fixed cost is incurred for the buyer when a potential supplier is selected. The objective is to select suppliers and to allocate the ordering quantity properly among the selected suppliers to minimize the total cost, including selection, purchase, holding and shortage costs. The problem is modeled as a Mixed Integer Programming (MIP). Properties of the problem are explored and a branch-bound algorithm is proposed for it. Also, a simple algorithm for the subproblem is proposed based on its special structure. Numerical experiments are conducted to evaluate the performance of the algorithm and some managerial insights are obtained.