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.

Abstract We propose a heuristic method for solving the overall risk minimization problem, specifically the infinite-horizon dynamic programming problem, which uses a coherent risk measure of the overall discounted reward as its criterion. The original problem is very complex, and its optimal policies may depend on the entire history of previous decisions. The heuristic consists in restricting attention to Markov policies—those depending only on the current state—and in consecutive local approximations of the criterion, a static coherent risk measure, by its nested dynamic counterpart: a limit nested risk measure. The approximating problems with the nested measures can be reformulated using the Bellman equation and, as such, can be solved by standard algorithms. We introduce several variants of this heuristic. Consequently, we conduct three numerical experiments, all of which demonstrate the efficiency of our heuristic in finding effective solutions. Due to its speed, the heuristic is suitable for finding “good enough” solutions, which may be further refined.

Remanufacturing-as-a-Service promises scalable, lower-cost repair of metal components by coordinating distributed capabilities through a cloud platform. This paper formulates a quantitative, supply-chain optimization of cloud-enabled remanufacturing built on a hybrid additive–subtractive (ASM) repair cost model and evaluates three delivery scenarios: (i) centralized national hubs with hybrid ASM; (ii) collaborations with tier-one local facilities that own separate AM and SM equipment; and (iii) collaborations with tier-two local facilities that provide only partial capability, requiring multi-facility routing. Using a U.S. tooling and machinery case study, this paper quantitatively fuses stepwise ASM repair economics with strategic facility location under an explicit quality–cost trade-off, closing a gap between process modeling and supply-chain design in remanufacturing. Results show that across plausible freights and capital costs, decentralized collaborations remain within 5% of the cost optimum while improving regional responsiveness; longer planning horizons shift the near-optimal set toward 5–8 hubs, rather than a single national site. Sensitivity tests confirm that (a) higher transportation costs and longer horizons favor additional hubs, while (b) tighter accuracy thresholds steer volume to hybrid hubs or vetted tier-one partners. The model provides clear trigger points—based on accuracy targets, capital expenditures, and freight conditions—for deciding when to build new hubs versus contracting with local partners. It offers managers a robust tool to navigate the critical trade-offs between cost efficiency, service reach, and quality.