This paper examines the spoke and hub location decisions in a routing problem. To minimize the total cost, the study analyzes on how to locate the spokes, hubs and the allocation of spoke nodes to hub nodes, the routing among the nodes and the number of vehicles assigned to each hub thoroughly. As there might be no facility assigned to some points, unsatisfied demands must be distributed to other nodes with available facilities. Furthermore, the realized demand is determined by considering the perceived utility of each path, using The Gravity rule. For this purpose, the proposed nonlinear model is transformed into a linear programming model, where some tightening rules and preprocessing procedures are applied, and also the sequential and integrated approaches are developed to solve the problem. In the sequential method, spokes are allocated, and hubs are selected based on the location of the spokes, after which the routing in the local tour is determined. Meanwhile, in the integrated approach, the aggregated model is solved. A heuristic is presented to address the integrated model. Numerical experiments are run on both approaches, to compare both, and obtain insights from the model.

Sustainable development in supply chain management is of great importance, as it emphasizes that the procurement process in sustainable supply chains addresses not only current needs but also future requirements. This subject, by improving processes, reducing waste and energy consumption, increasing efficiency, and establishing sustainable relationships with suppliers and customers, contributes to the sustainability and success of companies in international competition. Moreover, hub location is crucial for optimizing distribution processes and reducing costs in the supply chain, especially for perishable products with a defined and limited shelf life, which imposes various constraints on the supply chain. Additionally, to bring mathematical models closer to reality, uncertainty approaches can be employed, and strategies to deal with uncertainty can be considered. This research delves into these issues in the realm of supply chain management, focusing on sustainability and uncertainty, and provides a review of research conducted in the literature of this field.

Uncertainty plays an important role on many engineering problems and there is a growing interest in having reliable solutions especially for problems with sensitive parameters. The paper presents a robust optimization (RO) model for multi-objective operation of capacitated P-hub location problems (MCpHLP) under uncertainty set. There are, at least, two parameters in any P-hub problems, which are under uncertainty. The first one is associated with demand and the second one is the amount of time required to process commodities. We present a scenario based robust optimization technique, where these two items are considered under various scenario and a RO is implemented to find reliable solutions. The implementation of the proposed RO model is demonstrated for an example using weighting method.

Hub covering problem is one of the most popular areas of research due to wide ranges of applications in different service or manufacturing industries. This paper considers a multi-objective hub covering location problem under congestion. The proposed study of this paper considers two objectives where the first one minimizes total transportation cost and the second one minimizes total waiting time for all hobs. The resulted multi-objective decision making problem is formulated as mixed integer programming. Simulated annealing is used to solve the resulted model and the performance of the proposed model is compared against two other alternative methods, particle sward optimization and NSGA-II. The results are compared in terms of four criteria including quality metric, mean ideal distance, diversification metric and spacing metric. The results indicate that the proposed model could perform better than the other two alternative methods in terms of quality metric but the results are somehow mix in terms of other three criteria.