Energy Minimizing Vehicle Routing Problem (original) (raw)
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Development of a fuel consumption optimization model for the capacitated vehicle routing problem
Computers & Operations Research
Fuel consumption accounts for a large and increasing part of transportation costs. In this paper, the Fuel Consumption Rate (FCR), a factor considered as a load dependant function, is added to the classical capacitated vehicle routing problem (CVRP) to extend traditional studies on CVRP with the objective of minimizing fuel consumption. We present a mathematical optimization model to formally characterize the FCR considered CVRP (FCVRP) as well as a string based version for calculation. A simulated annealing algorithm with a hybrid exchange rule is developed to solve FCVRP and shows good performance on both the traditional CVRP and the FCVRP in substantial computation experiments. The results of the experiments show that the FCVRP model can reduce fuel consumption by 5% on average compared to the CVRP model. Factors causing the variation in fuel consumption are also identified and discussed in this study.
Minimal load constrained vehicle routing problems
Computational Science–ICCS 2005, 2005
Abstract. In this paper, the Capacitated Vehicle Routing Problem is extended to the case where each vehicle is restricted to an additional minimal starting or returning load constraint. We refer to this extension as the Minimal Load Constrained Vehicle Routing Problem. We present integer programming formulations for single and multidepot cases. An illustrative example is also provided to show how a decision maker can use the proposed formulation as an aid in distribution planning.
Proceedings of the Institute for System Programming of the RAS, 2018
Vehicle Routing Problem (VRP) is one of the most widely known questions in a class of combinatorial optimization problems. It is concerned with the optimal design of routes to be used by a fleet of vehicles to serve a set of customers. In this study we analyze Capacitated Vehicle Routing Problem (CVRP)-a subcase of VRP, where the vehicles have a limited capacity. CVRP is mostly aimed at savings in the global transportation costs. The problem is NP-hard, therefore heuristic algorithms which provide near-optimal polynomial-time solutions will be considered instead of the exact ones. The aim of this article is to make a survey on mathematical formulations of CVRP and on methods for solving each type of this problem. The first part presents a general information about the problem and restrictions of this work. In the second part, the classical mathematical formulations of CVRP are described. In the third part, a classification of most popular subcases of CVRP is given, including description of additional constraints with their math formulations. This section also includes most perspective methods that can be applied for solving special types of CVRP. The forth part contains an important note about the most powerful algorithm LKH-3. Finally, the fourth part consists of table with solving techniques for each subproblem and of scheme with basic problems of the CVRP class and their interconnections.
Integer linear programming formulation of the generalized vehicle routing problem
2003
The Generalized Vehicle Routing Problem (GVRP) is an extension of the Vehicle Routing Problem (VRP) defined on a graph in which the nodes (customers, vertices) are grouped into a given number of mutually exclusive and exhaustive clusters (nodesets). In this paper, an integer linear programming formulation of the GVRP with O(n 2) binary variables and O(n 2) constraints is presented. It is shown that, under specific circumstances, the proposed model reduces to the well-known routing problems. The computational performance of the models solved using a commercial code on test problems are also presented.
Modified Savings Algorithm for Capacitated Vehicle Routing Problem: Development and Analysis
Lecture Notes on Multidisciplinary Industrial Engineering, 2020
Fuel consumption accounts for a larger and increasing part of transportation costs. This chapter proposes an approach to solve the Fuel Capacitated Vehicle Routing Problem (FCVRP). The aim of this research is to identify, analyze and model various factors that are involved in calculating and optimizing fuel consumption in VRPs. Through an extensive literature review, the major factors on which fuel consumption depends were identified. A formula for calculating fuel consumption is modelled to include these factors. Clarke and Wright algorithm is modified to develop a set of routes with minimum fuel consumption based on fuel savings. The algorithm is integrated with Google application programming interfaces to work with real locations. As a case study, the VRP for a gas agency in the northern region of Kerala is solved using the proposed modified savings algorithm. The results show that the fuel consumed could be reduced by 6% compared with that of the classical Clarke and Wright algorithm.
Operations Research, 2004
The capacitated vehicle routing problem (CVRP) is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. In this paper, we describe a new integer programming formulation for the CVRP based on a two-commodity network flow approach. We present a lower bound derived from the linear programming (LP) relaxation of the new formulation which is improved by adding valid inequalities in a cutting-plane fashion. Moreover, we present a comparison between the new lower bound and lower bounds derived from the LP relaxations of different CVRP formulations proposed in the literature. A new branch-and-cut algorithm for the optimal solution of the CVRP is described. Computational results are reported for a set of test problems derived from the literature and for new randomly generated problems.
A unified exact method for solving different classes of vehicle routing problems
Mathematical Programming, 2009
This paper presents a unified exact method for solving an extended model of the well-known Capacitated Vehicle Routing Problem (CVRP), called the Heterogenous Vehicle Routing Problem (HVRP), where a mixed fleet of vehicles having different capacities, routing and fixed costs is used to supply a set of customers. The HVRP model considered in this paper contains as special cases: the Single Depot CVRP, all variants of the HVRP presented in the literature, the Site-Dependent Vehicle Routing Problem (SDVRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). This paper presents an exact algorithm for the HVRP based on the set partitioning formulation. The exact algorithm uses three types of bounding procedures based on the LP-relaxation and on the Lagrangean relaxation of the mathematical formulation. The bounding procedures allow to reduce the number of variables of the formulation so that the resulting problem can be solved by an integer linear programming solver. Extensive computational results over the main instances from the literature of the different variants of HVRPs, SDVRP and MDVRP show that the proposed lower bound is superior to the ones presented in the literature and that the exact algorithm can solve, for the first time ever, several test instances of all problem types considered.
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.
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.