Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem

The generalized vehicle routing problem with flexible fleet size (GVRP‐flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.

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“…Quite recently, Bektas et al. () designed a branch‐and‐cut procedure and a LNS for the GVRP with limited fleet.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The fourth set ( B ), adapted from the CVRP library available at http://branchandcut/VRP/data/, was used by Bektas et al. () and Moccia et al. ().…”

Section: Computational Experimentsmentioning

confidence: 99%

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

Afsar

Prins

Santos

2013

Int Trans Operational Res

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“…In most studies (see e.g, Gouveia, VoB 1995;Stadtler 1996;Sarin et al 2005;Ordóñez et al 2008;Öncan et al 2009;Özgüven et al 2010;Bektas et al 2011;Ebadi, Moslehi 2012;Bektas 2012;Wu et al , 2012 evaluation is based on some basic indicators, i.e. linear programming relaxation value (LPR), solution time, GAP value (this is defined as (U − L)/L, where U is the value of either the best or the optimal solution obtained within the time limit, and L is the value of the best lower bound after branching), and the number of optimally solved problems in a set of experiments.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Capability of Alternative Mixed Integer Programming Formulations

Keçeci

Derya

Dinler

et al. 2017

Technological and Economic Development of Economy

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Abstract. In selecting the best mixed integer linear programming (MILP) formulation the important issue is to figure out how to evaluate the performance of each candidate formulation in terms of selected criteria. The main objective of this study is to propose a systematic approach to guide the selection of the best MILP formulation among the alternatives according to the needs of the decision maker. For this reason we consider the problem of "selecting the most appropriate MILP formulation for a certain type of decision maker" as a multi-criteria decision making problem and present an integrated AHP-TOPSIS decision making methodology to select the most appropriate formulation. As an example the proposed decision making methodology is implemented on the selection of the MILP formulations of the Capacitated Vehicle Routing Problem (CVRP). A numerical example is provided for illustrative purposes. As a result, the proposed decision model can be a tool for the decision makers (here they are the scientists, engineers and practitioners) who intend to choose the appropriate mathematical model(s) among the alternatives according to their needs on their studies. The integrated AHP-TOPSIS approach can simply be incorporated into a computer-based decision support system since it has simplicity in both computation and application.

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“…There are many solutions are proposed to solve VRP but finding a globally minimum solution is computationally complex. (Zhang et al, 2010, Fisher, 1994 and branch and cut (Bektas et al, 2009), Heuristic algorithms: (Battarra, 2010) and Meta heuristic algorithm: Genetic Algorithm (GA) (Sarabian and Lee, 2010;Nazif and Lee, 2010), Ant colony optimization (ACO) (Reimann et al, 2004, Yu et al, 2008 and Particle Swarm Optimization (PSO) (Kanthavel and Prasad, 2011;Shanmugam et al, 2010;Srichandum and Rujirayanyong, 2010) are developed by many researchers for deterministic VRP. But they are not suitable for many real-time applications.…”

Section: Introductionmentioning

confidence: 99%

Meta Heuristic Algorithms for Vehicle Routing Problem with Stochastic Demands

Shanmugam¹

2011

Journal of Computer Science

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Problem statement: The shipment of goods from manufacturer to the consumer is a focal point of distribution logistics. In reality, the demand of consumers is not known a priori. This kind of distribution is dealt by Stochastic Vehicle Routing Problem (SVRP) which is a NP-hard problem. In this proposed work, VRP with stochastic demand is considered. A probability distribution is considered as a random variable for stochastic demand of a customer. Approach: In this study, VRPSD is resolved using Meta heuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Hybrid PSO (HPSO). Dynamic Programming (DP) is used to find the expected cost of each route generated by GA, PSO and HPSO. Results: The objective is to minimize the total expected cost of a priori route. The fitness value of a priori route is calculated using DP. In proposed HPSO, the initial particles are generated based Nearest Neighbor Heuristic (NNH). Elitism is used in HPSO for updating the particles. The algorithm is implemented using MATLAB7.0 and tested with problems having different number of customers. The results obtained are competitive in terms of execution time and memory usage. Conclusion: The computational time is reduced as polynomial time as O(nKQ) time and the memory required is O(nQ). The ANOVA test is performed to compare the proposed HPSO with other heuristic algorithms.

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Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem

Cited by 86 publications

References 22 publications

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

A Comparative Study of the Capability of Alternative Mixed Integer Programming Formulations

Meta Heuristic Algorithms for Vehicle Routing Problem with Stochastic Demands

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