Abstract
In this study, a new mathematical model is provided for the hub covering-routing problem (HCRP) through an extension of the travelling salesman problem (TSP). The objective of HCRP is to minimise the total related costs. This model assumes that if existence nodes are at a certain distance from a given node, they will be covered. The problem is a complete graph, so the seller must enter and leave once on each node. The main decision variables are to determine the tours and how to use the hubs in the way that total cost can be minimised. Since the proposed model is NP-hard, a genetic algorithm (GA) is developed for solving the model in real-world sizes. The results show that the proposed model and solution method are useful for dealing with real-world problems. The computational results show that in large-scale instances, GA solves the problem in a reasonable CPU time where GAMS is unable to find even a feasible solution. The average running time of GA is 62.69 seconds for large scale instances.
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