The pickup and delivery problem with time windows (PDPTW) is a generalization of the vehicle routing problem with time windows. In the PDPTW, a set of identical vehicles located at a central depot must be optimally routed to service a set of transportation requests subject to capacity, time window, pairing, and precedence constraints. In this paper, we present a new exact algorithm for the PDPTW based on a set-partitioning–like integer formulation, and we describe a bounding procedure that finds a near-optimal dual solution of the LP-relaxation of the formulation by combining two dual ascent heuristics and a cut-and-column generation procedure. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between a known upper bound and the lower bound achieved. If the resulting problem has moderate size, it is solved by an integer programming solver; otherwise, a branch-and-cut-and-price algorithm is used to close the integrality gap. Extensive computational results over the main instances from the literature show the effectiveness of the proposed exact method.
An Exact Algorithm for the Pickup and Delivery Problem with Time Windows
BALDACCI, ROBERTO;BARTOLINI, ENRICO;MINGOZZI, ARISTIDE
2011
Abstract
The pickup and delivery problem with time windows (PDPTW) is a generalization of the vehicle routing problem with time windows. In the PDPTW, a set of identical vehicles located at a central depot must be optimally routed to service a set of transportation requests subject to capacity, time window, pairing, and precedence constraints. In this paper, we present a new exact algorithm for the PDPTW based on a set-partitioning–like integer formulation, and we describe a bounding procedure that finds a near-optimal dual solution of the LP-relaxation of the formulation by combining two dual ascent heuristics and a cut-and-column generation procedure. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between a known upper bound and the lower bound achieved. If the resulting problem has moderate size, it is solved by an integer programming solver; otherwise, a branch-and-cut-and-price algorithm is used to close the integrality gap. Extensive computational results over the main instances from the literature show the effectiveness of the proposed exact method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
