A harmony search approach for the selective pick-up and delivery problem with delayed drop-off

In the last years freight transportation has undergone a sharp increase in the scales of its underlying processes and protocols mainly due to the ever-growing community of users and the increasing number of on-line shopping stores. Furthermore, when dealing with the last stage of the shipping chain an additional component of complexity enters the picture as a result of the fixed availability of the destination of the good to be delivered. As such, business opening hours and daily work schedules often clash with the delivery times programmed by couriers along their routes. In case of conflict, the courier must come to an arrangement with the destination of the package to be delivered or, alternatively, drop it off at a local depot to let the destination pick it up at his/her time convenience. In this context this paper will formulate a variant of the so-called courier problem under economic profitability criteria including the cost penalty derived from the delayed drop-off. In this context, if the courier delivers the package to its intended destination before its associated deadline, he is paid a reward. However, if he misses to deliver in time, the courier may still deliver it at the destination depending on its availability or, alternatively, drop it off at the local depot assuming a certain cost. The manuscript will formulate the mathematical optimization problem that models this logistics process and solve it efficiently by means of the Harmony Search algorithm. A simulation benchmark will be discussed to validate the solutions provided by this meta-heuristic solver and to compare its performance to other algorithmic counterparts.