A Multistage Stochastic Mixed-Integer Model for Perishable Capacity Expansion Problem

Abstract

We study a multi-stage capacity expansion problem under demand uncertainty. We consider the problem where there are multiple resources to be expanded at each stage. Moreover, the resources have limited life time after acquisition. Our goal is to determine the time and size of each resource to be expanded so that the expected expansion cost of capacities is minimized. Therefore, we formulate the problem as a multi-stage stochastic mixed-integer program. Capacity shortage and excess are allowed subject to a joint chance constraint. We apply the multi-stage stochastic mixed-integer model to formulate vaccine vial opening decisions in the health clinics. This formulation enables us to find the optimal combination of vial sizes to be opened. Additionally, a trade off between vaccine wastage and shortage can be addressed using the chance constraint. We provide a branch and price algorithm based on a nodal decomposition to solve the model. In addition, a heuristic algorithm is proposed to solve the subproblems where the life time of the resources is limited to one period. We implement the branch and price algorithm assuming continuous capacity expansion decisions. Computational results are presented for the vaccine vial opening problem with three vial sizes; 1-, 5-, and 10-doses. The primary results indicate the strength of the proposed algorithm in solving problems with large dimensions. Moreover we report results that indicate the usage of 10-dose vials and the portion of 10-dose vials in the total vaccine usage increases with the arrival rate. Although the total usage of 1- and 5- dose vials increase with the arrival rate, their portion in the total vaccine usage decreases. This implies that vaccination wastage or shortage can be managed by keeping moderate amount of smaller size vials while supplying most of the demand using larger vial sizes to benefit from the economies of scale.