Decision rule-based method for flexible multi-facility capacity expansion problem

Strategic capacity planning for multiple-facility systems with flexible designs is an important topic in the area of capacity expansion problems with random demands. The difficulties of this problem lie in the multidimensional nature of its random variables and action space. For a single-facility problem, the decision rule method has been shown to be efficient in deriving desirable solutions, but for a Multiple-facility Capacity Expansion Problem (MCEP), it has not been well studied. This article designs a novel decision rule–based method for the solution of an MCEP with multiple options, discrete capacity, and a concave capacity expansion cost. An if–then decision rule is designed and the original multi-stage problem is thus transformed into a master problem and a multi-period sub-problem. As the sub-problem contains non-binding constraints, we combine a stochastic approximation algorithm with a branch-and-cut technique so that the sub-problem can be further decomposed across scenarios and be solved efficiently. The proposed decision rule–based method is also extended to solving the MCEP with fixed costs. Numerical studies in this article illustrate that the proposed method affords not only improved performance relative to an inflexible design taken as benchmark but also time savings relative to approximate dynamic programming analysis.