Capacity Configuration and Allocation Under Capacity Risk: Trade-Offs Between Fill Rates and Costs

Capacity configuration and allocation problems in production networks under demand uncertainty have been extensively studied in the literature. In addition to demand uncertainty, capacity risk is also prevalent in practice. This article considers a bipartite production system consisting of multiple plants and a set of customers located in different areas. In particular, these plants will use their configured capacities, facing capacity risk, to serve those customers who have differentiated fill-rate requirements with uncertain demands. Our objective is to optimize capacity configuration and allocation decisions by formulating the problem as a two-stage stochastic program that explicitly incorporates capacity risks and budget constraints. First, we develop a novel “randomized edge-weighted max-flow” priority rule that integrates capacity risk, penalty costs of unmet demands, and allocation costs to allocate the realized capacities to satisfy fill-rate targets, with a tunable parameter introduced to balance service levels and costs. In particular, we derive necessary and sufficient conditions for identifying plants with zero capacities and obtain some practical insights, which can help reduce the potential redundancy of the network system. When partial information and correlation of distributions are known, we implement robust optimization techniques to obtain the ranges of robust capacities under various scenarios. Some practical managerial implications are derived by theoretically discussing the impacts of capacity risk and demand correlations on these ranges. From numerical experiments, we found that the long-chain configuration no longer has the “almost-as-good-as-the-fully-flexible-network” advantage when the capacities are random. In addition, we also investigate the impacts of correlations among realized capacities or demands on the associated flexibility. Finally, some interesting and useful insights for practitioners can be obtained by analyzing the impacts of costs, fill rates, and uncertainty on the total optimal capacity and total configuration cost.