On Solving the Multi-depot Vehicle Routing Problem (original) (raw)
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A Novel Three-Phase Approach for Solving Multi-Depot Vehicle Routing Problem with Stochastic Demand
Algorithms Research, 2012
The Mult i-Depot Veh icle Routing Problem (MDVRP), an extension of classical VRP, is a NP-hard problem for simu ltaneously determining the routes for several vehicles fro m mu ltip le depots to a set of customers with demand and then return to the same depot. Main goal of this thesis is to solve MDVRPSD in three phases. Firstly we've used nearest neighbour classification method for grouping the customers, then Su m of Subset method have been used for routing. Finally the routes are optimized using greedy method. The routes obtained using these methods are better for the vehicles considering demands of the customers. As an input we consider here some customers position, the depots position. Also the demand is in itialized randomly. Here we solve the problem for 4 depots to 10 depots. The input customer ranges fro m 20 to 50. Then by using the three-phases the problem is solved for the input combinations. Actually the main target to solve this problem is to reduce the number of vehicles needed to serve the customers. We have to serve the customers of a definite route by a vehicle. So if the routes are min imized then number of needed vehicles is also min imized. The t ime is also an impo rtant issue. So the time is also measured for solving the whole problem with three-phases. So at the last part of the paper the performance is measured according to time for solving the problem and the number of vehicle needed for each of the problem.
A Survey on the Vehicle Routing Problem and Its Variants
In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. The vehicle routing problem comes under combinatorial problem. Hence, to get solutions in determining routes which are realistic and very close to the optimal solution, we use heuristics and meta-heuristics. In this paper we discuss the various exact methods and the heuristics and meta-heuristics used to solve the VRP and its variants.
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...
2015
Vehicle Routing Problem (VRP) is one of the most challenging problems in combinatorial optimization. Objective of VRP is to find minimum length route starts and ends in a depot. There are some additional constraints such as more than one depot, service time, time window, capacity of vehicle, and many more. These are cause of VRP variants. Vehicle Routing Problem with Time Windows (VRPTW) is a variant of VRP with some additional constrains, that are number of requests may not exceed the vehicle capacity, as well as travel time and service time may not exceed the time window. Multi Depot Vehicle Routing Problem (MDVRP) has number of depots serving all customers, a number of vehicles distributing goods to customers with a minimum distance of distribution route without exceeding the capacity of the vehicle. Many researches have presented algorithms to solve VRPTW and MDVRP. This article discusses solution characteristics of VRPTW and MDVRP algorithms, and their performance. VRPTW algori...
Sustainable Development Research
A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper.
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.
International Journal of Recent Technology and Engineering
This paper introduces the multi depot vehicle routing problem (MDVRP) with location depot, a hard combinatorial optimization problem arising in several applications. The MDVRP with location depot based on two well-known NP-hard problems: the facility location problem (FLP) and the multi depot vehicle routing problem (MDVRP) with location depot. In the first phase, the problem consists of selecting on which sites to install a warehouse and assigning one and only one warehouse to each customer. In the second phase, for each depot, we search to solve a vehicle routing problem (VRP), multiple vehicles homogenous leave from a single depot and return to the same one. Each route must respect the capacity of each vehicle. The goal of this problem is to minimize the total distances to the performed routes. The MDVRP with location depots is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve this problem. In this work, we propose a method to solve it to optimality. The proposed procedure initially uses K-means algorithm to optimize the location selection and customer assignment, then planning the routes from the selected warehouses to a set of customers using Clarke and Wright saving method. The routes from the resulting multi-depot vehicle-routing problem (MDVRP) are improved using a Genetic Algorithm (GA). The proposed approach is tested and compared on a set of twelve benchmark instances from the MDVRP literature. The computational experiments confirm that our heuristic is able to find best solutions.
Vehicle routing problem: recent literature review of its variants
International Journal of Operational Research, 2018
The vehicle routing problem is the most studied combinatorial optimisation problem. The purpose of this study is to provide an overview of the research to date in vehicle routing problem variants. The literature is reviewed with a focus on research in three major variants of the vehicle routing problem, namely capacitated vehicle routing problem, mixed depot vehicle routing problem and vehicle routing problem with pickup and delivery. Journal articles from three academic databases, namely Taylor and Francis, Elsevier and Emerald, are selected and reviewed. Ample literature is available on this problem so to restrict the scope, we screened the journal articles using the above mentioned variants precisely, excluding those that are in combination with other variants. This review takes a closer look at 117 research articles selected from various journals. By presenting the past literature, we hope to motivate further research in the field.
2012
A mathematical model and heuristic method for solving multi-depot and multi-product vehicle routing problem with heterogeneous vehicle have been proposed in this paper. Customers can order several products and depots must deliver customer's orders before due date with different vehicle. Hence mathematical model of multidepot vehicle routing problem has been developed to represent these conditions. Aim of this model is to minimize total delivery distance or time spent in servicing all customers. As this problem is very complex, we have offered a heuristic method that includes four steps. Grouping, routing and vehicle selection, scheduling and packing of products and improvement are the aforementioned steps. Efficiency of heuristic has been tested by a case study and several numerical examples. Comparing the results of heuristic and optimal solving has revealed that the deviation of heuristic results from optimal answer is lower than eight perce.
A systematic review of multi-depot vehicle routing problems
Systematic Literature Review and Meta-Analysis Journal
Multi-Depot Vehicle Routing Problem (MDVRP) is a heuristic optimization problem that capture interest of several researchers' for its applicability to real-life situations. The variant of MDVRP are solved with some certain constraints such as service time, time window, vehicle capacity, travelled distance etc. these makes MDVRP to cover several situations In this, 76 studies related to MDVRP from 2012 to 2022 were systematically reviewed. The studies are review based on their constraints and an application through various fields. The goal of this research is to examine the contemporary state of MDVRP and its applications. To achieve this goal, we formed a comprehensive search process which was employed on high rated scientific journals databases. The search process resulted to numerous important research papers in the research domain which were theoretically reviewed. The research papers found are screened based on the titled, abstract, year of publication and exhaustive reading...