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This article describes a tabu search heuristic for the dial-a-ride problem with the following characteristics. Users specify transportation requests between origins and destinations. They may provide a time window on their desired departure or arrival time. Transportation is supplied by a fleet of vehicles based at a common depot. The aim is to design a set of least cost vehicle routes capable of accommodating all requests. Side constraints relate to vehicle capacity, route duration and the maximum ride time of any user. Extensive computational results are reported on randomly generated and real-life data sets.

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The purpose of this paper is to describe TABUROUTE, a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route. This is done by means of a generalized insertion procedure previously developed by the authors. During the course of the algorithm, infeasible solutions are allowed. Numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics, and TABUROUTE often produces the best known solutions.vehicle routing problem, tabu search, generalized insertion

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The Vehicle Routing Problem (VRP) was introduced 50 years ago by Dantzig and Ramser under the title “The Truck Dispatching Problem.” The study of the VRP has given rise to major developments in the fields of exact algorithms and heuristics. In particular, highly sophisticated exact mathematical programming decomposition algorithms and powerful metaheuristics for the VRP have been put forward in recent years. The purpose of this article is to provide a brief account of this development.

The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pickup and delivery 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 a summary of the most important models and algorithms is provided.