Moment-based distributionally robust joint chance constrained optimization for service network design under demand uncertainty

Abstract

This paper proposes a distributionally robust joint chance constrained (DRJCC) programming approach to optimize the service network design (SND) problem under demand uncertainty. The distributionally robust method does not need complete distribution information and utilizes restricted historical data knowledge, which is significant in scarce data situations. The joint consideration of chance constraints enables more effective control of event probability, by which network managers can realize the purpose of controlling the overall service level of multi-commodities in a service network. DRJCC optimization can also help decision-makers adjust the network’s conservativeness, robustness, and service rates by setting the probability parameters of the chance constraints. We reformulate the DRJCC model by addressing the corresponding distributionally robust joint chance constraints with the worst-case Conditional Value-at-Risk method and Lagrange duality theory. The model is approximately reformulated as a mixed-integer linear program, which is easier to solve than the mixed-integer semi-definite programming model in existing literature. We also develop two benchmark approaches for comparison: Bonferroni inequality approximation and scenario-based stochastic program. Comparative numerical studies demonstrate the robustness and the validation of the proposed formulations. A case study is conducted to demonstrate the industrial performance of the uncertain SND under the DRJCC formulation. We explore the impact of the confidence level parameter on operational cost and real service level, reveal the general correlation between them. We also extract several risk-averse managerial insights for logistics fleet managers.