A metaheuristic for crew scheduling in a pickup-and-delivery problem with time windows

Abstract

A simultaneous vehicle routing and crew scheduling problem (SVRCSP) consists of planning routes for a fleet of vehicles and scheduling their crews, with the particularity that the vehicle–crew correspondence is not fixed through time. This allows a greater planning flexibility and a more efficient use of the fleet, but in counterpart it requires high synchronization. In this work, an SVRCSP is presented, where long-distance pickup-and-delivery requests must be fulfilled over a multiday planning horizon, subject to several constraints such as multiple time windows, hour of services regulation, among others. Crews can be composed of one or two drivers and any of them can be relieved in a given set of locations. Also, they are allowed to travel between locations with noncompany shuttles. The objective is to minimize the cost of travel in company and noncompany vehicles, which depends on the distance, and the penalization for completing requests with delay. A two-stage sequential approach is applied: a set of truck routes is computed in the first stage and a set of driver routes consistent with the previous routes is obtained in the second stage. An algorithm based on the GRASP × ILS metaheuristic, embedded with a repair heuristic to facilitate the construction of initial solutions, is proposed and evaluated for the latter stage. High-quality solutions were found for instances generated with up to 3000 requests and a planning horizon of one to four weeks spread over 15 Argentine cities in less than an hour. Additionally, the possibility of carrying an additional driver reduced the cost of external shuttles by 2.25 times on average compared to individual crews and, in some cases, removed this cost completely.