Multimodal distribution network design problem for returnable transport items with uncertainty

Abstract This paper investigates a stochastic Returnable Transport Items (RTI) distribution network design problem for an RTI service provider responsible for managing RTI flows under uncertain demand and returns. The objective is to determine the optimal number and location of intermediate facilities to accommodate RTI flows while making repositioning decisions across the network. A two-stage stochastic programming model is developed to minimise costs associated with network design, RTI storage, the choice of direct or indirect shipping, and the allocation of multiple transportation modes in both forward and reverse flow channels. To address this complex problem, a robust sample average approximation method is proposed, with its efficiency evaluated through statistical validation. Additionally, the stochastic model’s effectiveness is assessed by computing the expected value of perfect information and the value of stochastic solutions. Comprehensive numerical experiments, including 64 instances with varying cost and robustness coefficients, provide managerial insights. The results demonstrate that efficient RTI network design significantly impacts multi-period operational decisions and highlights the critical role of RTI depots in mitigating demand uncertainty. Furthermore, the robust stochastic optimisation approach employed delivers high-quality solutions with an optimality gap of less than 1% within reasonable computational times. This study highlights the importance of integrating robust decision-making in RTI network design, offering practical insights for managing uncertainty and optimising cost efficiency across complex RTI networks.