Multi-sourcing under supply uncertainty and Buyer's risk aversion

Abstract

We address the combined problem of supplier (or vendor) selection and ordering decision when a buyer can choose to procure from multiple suppliers whose yields are uncertain and potentially correlated. We model this problem as a stochastic program with recourse in which the buyer purchases from the suppliers in the first period and, if needed, chooses to purchase from the spot market or from the suppliers with excess supply, whichever is beneficial, in the second period in order to meet the target procurement quantity. We solve the above problem using sample average approximation (SAA) technique that enables us to solve the problem easily in practice. We compare the performance of our solution with the certainty equivalent problem, which is practiced widely and which we use as the benchmark, to evaluate the efficacy of our approach. Next, we extend our model to incorporate buyer’s risk aversion with respect to the quantity procured. We reformulate the multi-sourcing problem as a mixed integer linear program (MILP) and adopt a statistical approach to account for buyer’s risk aversion. Thus, we design a simple computational technique that provides an optimal sourcing policy from a set of suppliers when each supplier’s yield is uncertain with a generic probability distribution.