Abstract
In pickup and delivery problems, all the demands should be transported from pickup points (suppliers) to delivery points (customers) by vehicles while respecting a set of constraints. Honoring all demands is sometimes impossible when taking all the constraints into account. Therefore, the selective aspect is added to relax the constraint that all the demands should be satisfied. This paper studies a variant called the selective pickup and delivery problem with transfers (SPDPT). The transfers mean that some demands can be transferred from one vehicle to another one, which gives a chance to find more solutions. A mixed integer linear program is firstly proposed to describe the studied problem. Two objectives have been considered in the paper, maximizing the profit and minimizing the distance. The model is then validated on new generated instances. Due to the complexity of the problem, large instances could not be solved to optimality in a reasonable time. As an alternative, a new metaheuristic based on a hybrid particle swarm optimization is developed to tackle this bi-objective problem. The results show that this proposed method is efficient and competitive.
Highlights
The general pickup and delivery problem (PDP) (Savelsbergh and Sol, 1995) is an extension of the vehicle routing problem (VRP) (Dantzig and Ramser, 1959), and can be described as a problem in which a fleet of vehicles collects goods from pickup points, and transports them to delivery points
One of the most studied variants is the pickup and delivery problem with time windows and paired demands (PDPTWPD) (Li and Lim, 2003) in which each site should be visited during a specified time window, and the vehicle should visit a supplier before its associated customer
This problem is called the selective PDPTWPD (SPDPTWPD) (Al Chami et al, 2016). Another extension of the PDPTWPD is the introducing of intermediate facility called transfer points, at which goods can be transferred from one vehicle to another one
Summary
The general pickup and delivery problem (PDP) (Savelsbergh and Sol, 1995) is an extension of the vehicle routing problem (VRP) (Dantzig and Ramser, 1959), and can be described as a problem in which a fleet of vehicles collects goods from pickup points (suppliers), and transports them to delivery points (customers). One possible extension of the PDPTWPD is the adaptation of selective aspect, which relaxes the constraint that all demands should be satisfied This problem is called the selective PDPTWPD (SPDPTWPD) (Al Chami et al, 2016). The studied problem is a combination of the SPDPTWPD and the PDPT, called the selective pickup and delivery problem with transfers (SPDPT) which considers all the constraints previously introduced. For the second objective, clustered demands could be loaded into the same vehicle at transfer point, which would largely save the traveling distance. In this context, the contributions of this paper are the following ones: The proposal of a mixed integer linear program for a new problem: the SPDPT (Section 3.2). The development of a metaheuristic approach to efficiently solve the SPDPT and its related problem, SPDPTWPD (Section 6)
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