Abstract
This paper studies an extension of the well-known one-to-one pickup-and-delivery problem with time windows. In the latter problem, requests to transport goods from pickup to delivery locations must be fulfilled by a set of vehicles with limited capacity subject to time window constraints. Goods are not interchangeable: what is picked up at one particular location must be delivered to one particular other location. The discussed extension consists in the consideration of a heterogeneous vehicle fleet comprising lorries with detachable trailers. Trailers are advantageous as they increase the overall vehicle capacity. However, some locations may be accessible only by lorries. Therefore, special locations are available where trailers can be parked while lorries visit accessibility-constrained locations. This induces a nontrivial tradeoff between an enlarged vehicle capacity and the necessity of scheduling detours for parking and reattaching trailers. The contribution of the paper is threefold: (i) it studies a practically relevant generalization of the one-to-one pickup-and-delivery problem with time windows. (ii) It develops an exact amortized constant-time procedure for testing the feasibility of an insertion of a transport task into a given route with regard to time windows and lorry and trailer capacities. (iii) It provides a comprehensive set of new benchmark instances on which the runtime of the constant-time test is compared with a naïve one that requires linear time by embedding both tests in an adaptive large neighbourhood search algorithm. Computational experiments show that the constant-time test outperforms its linear-time counterpart by one order of magnitude on average.
Highlights
The one-to-one pickup-and-delivery problem with time windows and trailers (PDPTWT) can be described as follows
I.e., all pickup or delivery locations, can be visited by any lorry, all locations designated as reachable by trailer can be visited by any trailer, and parking and transshipment locations (PTLs) can be visited by all lorry–trailer combinations (LTCs) lorries and trailers
In lieu of the noise mechanism used by Ropke and Pisinger (2006), insertion preference strategies are used. This means that, in each iteration of a reinsertion heuristic, one of the following five strategies is randomly selected with equal probability and applied before deciding which task to insert into which route: (i) make the insertion of tasks where the pickup location can be visited with a trailer more attractive; (ii) similar for tasks where this is not the case; (iii) make the insertion into single lorry routes more attractive; (iv) similar for LTC routes; (v) make it more attractive to insert tasks where the pickup location can be visited with a trailer into LTC routes
Summary
The one-to-one pickup-and-delivery problem with time windows and trailers (PDPTWT) can be described as follows. A route is feasible if and only if it starts at the start depot of the vehicle that performs the route, fulfils zero or more tasks, and ends at the vehicle’s end depot, while maintaining all time windows, accessibility constraints, and lorry and trailer capacities. The contribution of this paper is threefold: (i) it studies a practically relevant extension of the one-to-one pickup-and-delivery problem with time windows Put differently, it generalizes vehicle routing problems (VRPs, i.e., problems where either all pickups or all deliveries take place at a central depot) with trailers to pickup-anddelivery problems. (ii) It develops an exact amortized constant-time procedure for testing the feasibility of an insertion of a task into a given PDPTWT route concerning time windows and lorry and trailer capacities.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
