Robust bi-objective optimization of uncapacitated single allocation p-hub median problem using a hybrid heuristic algorithm

The p-hub median problem aims at locating p-hub facilities in a network and allocating non-hub nodes to the hubs such that the overall transportation cost is minimized. One issue of major importance in this problem remarks the requirement to deal with uncertain factors such as weather conditions and traffic volume. These lead to uncertainty in travel time between origin and destination points. In today’s competitive markets in which customers look for robust delivery services, it is important to minimize the upper bound of uncertainty in the network routes. In this paper, a robust bi-objective uncapacitated single allocation p-hub median problem (RBUSApHMP) is introduced in which travel time has non-deterministic nature. The problem aims to select location of the hubs and allocation of the other nodes to them so that overall transportation cost and maximum uncertainty in network are minimized. To do this, a desirability function-based approach is suggested that ensures both interested objectives to fall within their specification limits. Due to the complexity of the model, a heuristic based on scatter search and variable neighborhood descent is developed. To evaluate the performance of the proposed method a computational analysis on Civil Aeronautics Board and Australian Post data sets was performed. The obtained results using the proposed hybrid metaheuristic are compared to those of the optimum solutions obtained using GAMS. The results indicate excellent performance of the suggested solution procedure to optimize RBUSApHMP.