A mathematical model and a solving procedure for multi-depot vehicle routing problem with fuzzy time window and heterogeneous vehicle

Adelzadeh, Mehdi; Asl, Vahid Mahdavi; Koosha, Mehdi

doi:10.1007/s00170-014-6141-8

Cited by 46 publications

(19 citation statements)

References 28 publications

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“…A deterministic dynamic program (DP) was proposed first, and an exact algorithm based on the shortest path search was formulated next, for simple and easy implementation. Adelzadeh et al [3] proposed a mathematical model, and devised a heuristic solving procedure for multi-depot VRP with a fuzzy time window and heterogeneous vehicles that have different capacities, velocities, and costs. The fuzzy concept was applied to the service levels of the time windows, and a multi-objective model was developed.…”

Section: Literature Reviewmentioning

confidence: 99%

“…It is often related to production and inventory decisions, and the delivery cost usually accounts for a major part of the total logistic costs [1,2]. The vehicle routing problem (VRP) is a core issue in logistics, and it refers to a class of combinatorial optimization problems in which customers are to be served by a number of vehicles [3]. VRP was first introduced by Dantzig and Ramser [4], and the main objectives of the problem are to minimize the total travelling cost, time, or distance with a fleet of vehicles, starting and ending their routes at the depot while satisfying the various demands of customers [4].…”

Section: Introductionmentioning

confidence: 99%

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An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

Kang

Lee

2018

Symmetry

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The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied.Unit of measure: min.Symmetry 2018, 10, 650 9 of 20 Table 6 lists the problem configurations for the three cases, including the number of periods, number of suppliers, number of vehicles, size of the transportation network, number of variables for the MIP, and number of constraints for the MIP. In the first case, there are five periods, the number of suppliers is five, the number of vehicles is three, the transportation network is 6 × 6, and the numbers of variables and constraints for the MIP model are 931 and 1171, respectively. In the second case, there are seven periods, the number of suppliers is nine, the number of vehicles is four, the transportation network is 10 × 10, and the numbers of variables and constraints for the MIP model are 3903 and 3977, respectively. In the third case, there are nine periods, the number of suppliers is 12, the number of vehicles is five, the transportation network is 13 × 13, and the numbers of variables and constraints for the MIP model are 9758 and 9919, respectively.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

Kang

Lee

2018

Symmetry

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“…A certain demand is de ned for each customer. Its purpose is to minimize the transport cost of all routes [8]. Relief routing models can be onedepot (i.e., relief commodities are distributed through vehicles that start and end their route on only one depot), multi-depot (i.e., vehicles start from several depots and end their routes at the same depots), or no-depot (i.e., vehicles do not return to the depot).…”

Section: Introduction 1motivationmentioning

confidence: 99%

A cluster-based emergency vehicle routing problem in disaster with reliability

et al. 2017

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Abstract. In the event of natural disasters, relief distribution is the most challenging problem in emergency transportation. What is important in response to disaster is victims' relief in disaster areas with the quick distribution of vital commodity. In this regard, damage to infrastructure (e.g., roads) can make trouble in designing a distribution network. Therefore, this paper considers a problem using a three-stage approach. In the rst stage, pre-processing of model inputs is done through an Arti cial Neural Fuzzy Inference System (ANFIS) followed by investigating the safest route for each cluster using decision-making techniques and graph theory. In the second stage, a heterogeneous multi-depot multimode vehicle routing problem is formulated for minimizing the transportation time and maximizing the reliability. Finally, since the routing problem is NP-hard, 2 multi-objective meta-heuristic algorithms, namely, Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Fire y Algorithm (MOFA), are proposed to obtain the optimal solution and their performances are compared through a set of randomly generated test problems. The results show that for this routing problem, the MOFF gives better solutions than NSGA-II does, and it performs well in terms of accuracy and solution time.

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“…Recent years, new trends have been seen in the studies of fuzzy vehicle routing. Some researchers proposed mathematical models and solution methods to consider multi-depot vehicle routing problem with time windows [13], [14]. These studies supposed that depots must serve customers between their fuzzy time windows with vehicles having different capacities, velocities, and costs.…”

Section: Introductionmentioning

confidence: 99%

<b>An Ant Colony Optimization Method for Fuzzy Vehicle Routing Problem </b>

Dong

Hao

Sato

2015

iscm

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This paper deals with the vehicle routing problem involved with fuzzy/imprecise vehicle travel times and customer service times, these fuzzy/imprecise times are represented as fuzzy numbers and interpreted as possibility distributions. According to the same consideration as the stochastic programming with recourse, we treate the influence of the fuzziness of travel times and service times as recourse cost. and solve the fuzzy vehicle routing problem through twostage decisions. As the result, a two-stage possibilistic programming model is formulated. By choosing an appropriate definition of fuzzy mean, we can show that the proposed model is equivalent to an ordinary crisp programming problem. Furthermore, We propose a solution method based on Ant Colony System (ACS) to obttain the best solution of the problem. Finally, some examples are given to illustrate the two-stage model and the solution algorithm.

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A mathematical model and a solving procedure for multi-depot vehicle routing problem with fuzzy time window and heterogeneous vehicle

Cited by 46 publications

References 28 publications

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

A cluster-based emergency vehicle routing problem in disaster with reliability

<b>An Ant Colony Optimization Method for Fuzzy Vehicle Routing Problem </b>

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