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In recent years new insights and algorithms have been obtained for the classical, deterministic, vehicle routing problem as well as for natural stochastic and dynamic variations of it. These new developments are based on theoretical analysis, combine probabilistic and combinatorial modelling and lead to (1) new algorithms that produce near optimal solutions and (2) a deeper understanding of uncertainty issues in vehicle routing. In this paper we survey these new developments with an emphasis on the insights gained and on the algorithms proposed. Research supported in part by ONR contract N00014-90-J-1649, NSF contracts DDM-8922712, DDM9014751, and by a Presidential Young Investigator award DDM-9158118 with matching funds from Draper Laboratory. y Sloan School of Management, MIT, Cambridge, MA 02139. z Dept. of Industrial Engineering and Operations Research, Columbia University, NY, NY, 10027 and Department of Operations Research and Management Sciences, Northwestern Universi...

Generically, ejection chains are methods conceived to allow solution transformations to be efficiently carried out by modifying a variable number of their components at each step of a local search algorithm. We consider a subpath ejection chain method for the vehicle routing problem (VRP) under capacity and route length restrictions. The method undertakes the identification of a substructure named the flower reference structure which besides coordinating moves during an ejection chain construction allows the creation of neighborhood structures with interesting combinatorial characteristics. Specifically, we base the method on a fundamental property of creating alternating paths and cycles during an ejection chain construction. A new algorithm based on a Tabu search framework is proposed and computational results on a set of academic and real-world problems indicate that the algorithm may be a good alternative to the best heuristic algorithms for the VRP. 1 Introduction We consider t...

We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the Capacitated Concentrator Location Problem. We apply this framework to two classical routing problems: the Capacitated Vehicle Routing Problem and Inventory-Routing Problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and in most cases outperforms all published heuristics on a set of standard test problems. 1 Introduction Vehicle routing problems have received much attention in recent years due to the increased importance of determining efficient distribution strategies to reduce operational costs in distribution systems. A typical routing problem consists of a fleet of vehicles located at a central depot or warehouse that must be scheduled to provide some type of service to customers geograp...

We develop a new local search approach based on a network flow model that is used to simultaneously evaluate several customer ejection and insertion moves. We use this approach and a direct customer swap procedure to solve the well-known Vehicle Routing Problem. The capacity constraints are relaxed using penalty terms whose parameter values are adjusted according to time and search feedback. Tabu Search is incorporated into the procedure to overcome local optimality. More advanced issues such as intensification and diversification strategies are developed to provide effective enhancements to the basic tabu search algorithm. Computational experience on standard test problems is discussed and comparisons with best-known solutions are provided.

The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

The successful application of Branch and Cut methods to the TSP has drawn attention also to the polyhedral properties of the symmetric capacitated vehicle routing problem, which is the capacitated counterpart of the TSP. We investigate three classes of valid inequalities for the CVRP, multistars, pathbin inequalities and hypotours and give computational results we obtained with a Branch and Cut implementation.

An aboundant literature on vehicle routing problems is available. However, almost all the work deals with static problems where all data are known in advance, i.e. before the optimization has started.

We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where the violated inequalities are found directly from the relaxation basis. An improvement heuristic with the same flavor is also presented. 1 Introduction The generalized assignment problem is to assign jobs to machines, where each machine has a capacity and each job has a size and a cost, each possibly dependent on the machine to which it is assigned. This problem has applications in vehicle routing ([4, 9]), distribution systems ([1]), facility location ([17]), and other fields in operations research. Supported in part by postdoctorate fellowships from the Institut fur Okonometrie und Operations Research, Bonn, West Germany and NATO, awarded by NSERC, Canada. Address: Graduate School of ...

this paper is to describe a new tabu search algorithm for the general VRP defined above. Tabu search is a metaheuristic proposed by Glover [13]. The method is generically presented in Glover [14,15] and recent developments may be found in Glover [18,19] (see Glover and de Werra [22], Glover [21] for a survey on tabu search applications and challenges). A number of algorithms based on this approach have already been applied to the VRP, each one using different types of moves leading from one solution to another (see, Pureza and Franca [33], Osman [32], Taillard [40], Gendreau, Hertz and Laporte [11], Rochat and Taillard [38], Rego [36], Xu and Kelly [41]). An important contribution of our method is the use of embedded neighborhood structures based on the idea of ejection chains. Embedded neighborhoods may be conceived as the outcome of compressing a sequence of moves into a single compound move, and ejection chain procedures give a useful way to build these neighborhoods. For a comprehensive description of ejection chain methods we refer to Glover [20,16] and Rego [34]. A number of methods based on this prespective have recently been proposed for various combinatorial problems (see Laguna et al. [28], Dorndorf and Pesch [8], Hubscher and Glover [27], Rego [35,36], Glover, Pesch and Osman [24], Cao and Glover [2]). The remainder of this paper is organized as follows. In section 2, we briefly summarize the ideas underlying ejection chains and we describe their application to the VRP. Section 3 describes the sequential version of the proposed algorithm and a parallel approach is described in section 4. Then, the computational results and a comparative analysis of the algorithms are presented in section 5. Finally, section 6 contains a summary and concluding remarks. 2 New...