A Robust Pickup and Delivery Problem with Uncertain Travel Time

Abstract

This paper discusses a robust variant of the well known Pickup and Delivery Problem (PDP) which we called the Robust Selective PDP (RSPDP). In this problem, a fleet composed of several vehicles with a given capacity should satisfy a set of transportation requests while respecting various constraints in relation with the precedence between suppliers and customers, the capacity of vehicles, the opening and closing times of each site. Because of all these constraints, the honoring of all requests over a given period (for example, one day) is sometimes impossible so the selective aspect consists in choosing the sites to be served. This robust variant is characterized by the presence of different scenarios used to handle the uncertain traveling time for each arc. Subject to all scenarios and constraints, the goal is to find the best solution (with the higher profit) which validates all scenarios. This study introduces the mathematical formulation for this new variant. Then, an exact and a metaheuristic approaches will be used to solve it. Several tests have been done, on new generated instances for the considered problem, in order to show the efficiency of developed methods.