Mathematical modeling of a competitive transportation-location arc routing problem

Abstract

Depots are the centers where a supply chain can receive products, prepare them, and transfer them. Meeting the demands of depots located between suppliers and customers is essential. Here, the issue of transportation is dealt with in this research. Integrating these problems with vehicle routing can be very important in a distribution system, mainly when demand is defined on arcs. This paper addresses a competitive transportation-location-arc routing problem with a leader and a follower by developing mixed-integer linear programming models. The competition is formed with the objective of profit maximization. We propose a competition logic and apply it by considering a step-function profit sharing mechanism. A two-phase heuristic algorithm is developed for the competitive problem to solve these models. Then, two meta-heuristics (i.e., hill-climbing and late acceptance hill-climbing) are used to improve their results. The numerical results prove that the models perform well, and the heuristics provide acceptable answers. Also, a numerical example is generated inspired by actual conditions, solved, and examined. It helps the decision makers (both leaders and followers) to have a suitable view of their environments. Finally, the work is summarized along with suggestions for future research.