In transportation via containers, unbalanced movement of loaded containers forces shipping companies to reposition empty containers. This study addresses the problem of empty container repositioning (ECR) in the distribution network of a European logistics company, where some restrictions impose decision making in an uncertain environment. The problem involves dispatching empty containers of multiple types and various conditions (dirty and clean) to meet the on-time delivery requirements and repositioning the other containers to terminals, depots, and cleaning stations. A multi-period optimization model is developed to help make tactical decisions under uncertainty and data shortage for flow management of empty containers over a predetermined planning horizon. Employing the operational law of uncertainty programming, a new auxiliary chance-constrained programming is established for the ECR problem, and we prove the existence of an equivalence relation between the ECR plans in the uncertain network and those in an auxiliary deterministic network. Exploiting this new problem, we give the uncertainty distribution of the overall optimal ECR operational cost. The computational experiments show that the model generates good-quality repositioning plans and demonstrate that cost and modality improvement can be achieved in the network.

Ground-based mechanized forestry requires the traversal of terrain by heavy machines. The routes that they take are often called “machine trails” and are created by removing trees from the trail and placing the logs outside it. Designing an optimal machine trail network is a complex locational problem that requires understanding how forestry machines can operate on the terrain, as well as the trade-offs between various economic and ecological aspects. Machine trail designs are currently created manually based on intuitive decisions about the importance, correlations, and effects of many potentially conflicting aspects. Badly designed machine trail networks could result in costly operations and adverse environmental impacts. Therefore, this study was conducted to develop a holistic optimization framework for machine trail network design. Key economic and ecological objectives involved in designing machine trail networks for mechanized cut-to-length operations are presented, along with strategies for simultaneously addressing multiple objectives while accounting for the physical capabilities of forestry machines, the impact of slope, and the operating costs. Ways of quantitatively formulating and combining these different aspects are demonstrated, together with examples showing how the optimal network design changes in response to various inputs.