A two-stage stochastic mixed-integer program for reliable supply chain network design under uncertain disruptions and demand

Abstract

Having a reliable supply chain network is one of the most effective ways to plan and deal with facility failures and demand uncertainty due to very limited options available in a facility location problem. This research addresses issues bordering on capacitated supply chain problems, specifically on how reliable supply chain networks can be designed in the face of random facility disruptions and uncertain demand with a combination of hardening selected facilities and product reassignment. The proposed multi-period capacitated facility location and allocation problem is modeled as a two-stage stochastic mixed-integer formulation that minimizes the total establishing and transportation cost. The L-shaped method of stochastic linear programming is applied by integrating with two types of optimality and feasibility cuts for solving the stochastic model. This research aims to improve the proposed algorithm in two different ways: replacing the single-cut approach with a multi-cut and showing relatively complete recourse in the stochastic model by reformulating the original model. Finally, to illustrate the applicability of the model and computational effectiveness of the improved algorithm, a case study with different scenarios is presented and the results are discussed. Our computational results show that the proposed solution algorithm is not only capable of solving large-scale problems, but also avoids long run times. It is also demonstrated that substantial improvements in reliability of the system can often be possible with minimal increases in facility cost.