Procurement risk management using capacitated option contracts with fixed ordering costs

This article considers a single-period, multiple-supplier procurement problem with capacity constraints and fixed ordering costs. The buyer can procure from suppliers by signing option contracts with them to meet future uncertain demand. It can purchase from the spot market for prompt delivery at an uncertain price. The objective is to find the optimal portfolio of option contracts with minimal total expected procurement cost. Three cases are discussed. For the case with constant capacity constraints and fixed ordering cost, a dynamic programming approach is used to build a cost function that is strong CK-convex and characterize the structure of the optimal procurement policy, which is similar to the (s, S) policy. However, there is no efficient algorithm for the calculation of the critical parameters or the optimal solution. For the remaining two more restricted cases, one with only capacity constraints (yet zero ordering cost) and the other one with positive ordering cost (yet without capacity constraint), two polynomial algorithms are provided that are able to solve each of them, respectively.