The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
The DARP is characterized by multiple objectives such as the maximization of the number of costumers served, the minimization of the number of vehicles used and the maximization of the level of service provided on average to the costumer (costumer waiting time, total time spent in vehicles, difference between actual and desired drop-off times). The DARP can be formulated as multiobjective mixed integer program. Exact algorithms for the single-vehicle DARP have been developed in @cite_47 @cite_38 . Recently, a branch-and-cut algorithm has been proposed in @cite_87 . Heuristics and meta-heuristics are proposed for dealing with the dynamic problem with time-dependent network @cite_50 . For a recent overview of the DARP, see @cite_61 .
@cite_61 @cite_38 @cite_87 @cite_50 @cite_47
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The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pick-up and drop-off requests between origins and destinations. The aim is to plan a set of m minimum cost vehicle routes capable of accommodating as many users as possible, under a set of constraints. The most common example arises in door-to-door transportation for elderly or disabled people. The purpose of this article is to review the scientific literature on the DARP. The main features of the problem are described and classified and some modeling issues are discussed. A summary of the most important algorithms is provided. In the dial-a-ride problem, users formulate requests for transportation from a specific origin to a specific destination. Transportation is carried out by vehicles providing a shared service. The problem consists of designing a set of minimum-cost vehicle routes satisfying capacity, duration, time window, pairing, precedence, and ride-time constraints. This paper introduces a mixed-integer programming formulation of the problem and a branch-and-cut algorithm. The algorithm uses new valid inequalities for the dial-a-ride problem as well as known valid inequalities for the traveling salesman, the vehicle routing, and the pick-up and delivery problems. Computational experiments performed on randomly generated instances show that the proposed approach can be used to solve small to medium-size instances. Abstract In real-time fleet management, vehicle routes are built in an on-going fashion as vehicle locations, travel times and customer requests are revealed over the planning horizon. To deal with such problems, a new generation of fast on-line algorithms capable of taking into account uncertainty is required. Although several articles on this topic have been published, the literature on real-time vehicle routing is still disorganized. In this paper the research in this field is reviewed and some issues that have not received attention so far are highlighted. A particular emphasis is put on parallel computing strategies. SYNOPTIC ABSTRACTThe single-vehicle dial-a-ride problem with time window constraints for both pick-up and delivery locations, and precedence and capacity constraints, is solved using a forward dynamic programming algorithm. The total distance is minimized. The development of criteria for the elimination of infeasible states results in solution times which increase linearly with problem size.