An efficient transformation of the generalized vehicle routing problem (original) (raw)
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Constructive and Clustering Methods to Solve Capacitated Vehicle Routing Problem
Oriental journal of computer science and technology, 2017
Vehicle Routing Problem (VRP) is a real life constraint satisfaction problem to find minimal travel distances of vehicles to serve customers. Capacitated VRP (CVRP) is the simplest form of VRP considering vehicle capacity constraint. Constructive and clustering are the two popular approaches to solve CVRP. A constructive approach creates routes and attempts to minimize the cost at the same time. Clarke and Wright’s Savings algorithm is a popular constructive method based on savings heuristic. On the other hand, a clustering based method first assigns nodes into vehicle wise cluster and then generates route for each vehicle. Sweep algorithm and its variants and Fisher and Jaikumar algorithm are popular among clustering methods. Route generation is a traveling salesman problem (TSP) and any TSP optimization method is useful for this purpose. In this study, popular constructive and clustering methods are studied, implemented and compared outcomes in solving a suite of benchmark CVRPs. ...
An Exact Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem
Operations Research, 2013
In the two-echelon capacitated vehicle routing problem (2E-CVRP), the delivery to customers from a depot uses intermediate depots, called satellites. The 2E-CVRP involves two levels of routing problems. The first level requires a design of the routes for a vehicle fleet located at the depot to transport the customer demands to a subset of the satellites. The second level concerns the routing of a vehicle fleet located at the satellites to serve all customers from the satellites supplied from the depot. The objective is to minimize the sum of routing and handling costs. This paper describes a new mathematical formulation of the 2E-CVRP used to derive valid lower bounds and an exact method that decomposes the 2E-CVRP into a limited set of multidepot capacitated vehicle routing problems with side constraints. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.
Transport
This paper considers a Capacitated Location-Arc Routing Problem (CLARP) with Deadlines (CLARPD) and a fleet of capacitated heterogeneous vehicles. The proposed mixed integer programming model determines a subset of potential depots to be opened, the served roads within predefined deadlines, and the vehicles assigned to each open depot. In addition, efficient routing plans are determined to minimize total establishment and traveling costs. Since the CLARP is NP-hard, a Genetic Algorithm (GA) is presented to consider proposed operators, and a constructive heuristic to generate initial solutions. In addition, a Simulated Annealing (SA) algorithm is investigated to compare the performance of the GA. Computational experiments are carried out for several test instances. The computational results show that the proposed GA is promising. Finally, sensitivity analysis confirms that the developed model can meet arc routing timing requirements more precisely compared to the classical Capacitate...
The Vehicle Routing Problem: An overview of exact and approximate algorithms
In this paper, some of the main known results relative to the Vehicle Routing Problem are surveyed. The paper is organized as follows: (1) definition; (2) exact algorithms; (3) heuristic algorithms; (4) conclusion. The Vehicle Routing Problem (VRP) can be described as the problem of designing optimal delivery or collection routes from one or several depots to a number of geographically scattered cities or customers, subject to side constraints. The VRP plays a central role in the fields of physical distribution and logistics. There exists a wide variety of VRPs and a broad literature on this class of problems (see, for example, the surveys of Bodin et al., 1983, Christofides, 1985a, Laporte and Nobert, 1987, Laporte, 1990, as well as the recent classification scheme proposed by Desrochers, Lenstra and Savelsbergh, 1990). The purpose of this paper is to survey the main exact and approximate algorithms developed for the VRP, at a level appropriate for a first graduate course in combinatorial optimization. 1. Definition Let G = (V, A) be a graph where V = {1 .... , n} is a set of vertices representing cities with the depot located at vertex 1, and A is the set of arcs. With every arc (i, j) i 4=j is associated a non-negative distance matrix C = (cii). In some contexts, ci~ can be interpreted as a travel cost or as a travel time. When C is symmetrical, it is often convenient to replace A by a set E of undirected edges. In addition, assume there are m available vehicles based at the depot, where m L < m < m U. When m L = mrs, m is said to be fixed. When m L = 1 and m U = n-1, m is said to be free. When m is not fixed, it often makes sense to associate a fixed cost f on the use of a vehicle. For the sake of simplicity, we will ignore these costs and unless otherwise specified, we assume that all vehicles are identical and have the same capacity D. The VRP consists of designing a set of least-cost vehicle routes in such a way that (i) each city in V\{1} is visited exactly once by exactly one vehicle; (ii) all vehicle routes start and end at the depot; (iii) some side constraints are satisfied.
On the Selective Vehicle Routing Problem
Mathematics
The Generalized Vehicle Routing Problem (GVRP) is an extension of the classical Vehicle Routing Problem (VRP), in which we are looking for an optimal set of delivery or collection routes from a given depot to a number of customers divided into predefined, mutually exclusive, and exhaustive clusters, visiting exactly one customer from each cluster and fulfilling the capacity restrictions. This paper deals with a more generic version of the GVRP, introduced recently and called Selective Vehicle Routing Problem (SVRP). This problem generalizes the GVRP in the sense that the customers are divided into clusters, but they may belong to one or more clusters. The aim of this work is to describe a novel mixed integer programming based mathematical model of the SVRP. To validate the consistency of the novel mathematical model, a comparison between the proposed model and the existing models from literature is performed, on the existing benchmark instances for SVRP and on a set of additional be...