Designing a stochastic supply chain network: An error-bound-based heuristic

Abstract

Designing a stochastic supply chain is challenging because demand is often partially observable or unknown in advance. This paper presents an alternative approach to address a three-echelon stochastic supply chain network design with insufficient demand information. We formulate a stochastic mixed-integer program with chance constraints. We identify a lower and upper bound on the value at risk to deal with chance constraints, thus inducing two mixed-integer linear approximations to the stochastic program. We develop a branch-and-price scheme to solve the approximations and a primal heuristic algorithm for initial columns. We then create a heuristic algorithm for solving the original problem by implementing sensitivity analysis and error bound on the approximations. Besides network size, computational experiments find that network design performance depends on aggregate service levels and maximum demand variations. The aggregate behavior of service levels has an inverse impact on the network design performance, while maximum coefficients of demand variations present a positive effect. Computational results reveal that our proposed algorithms perform well compared to normal distributions and a robust optimization formulation. Our models and algorithms suggest a feasible network design tool for handling uncertainties in supply chains.