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

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 650 ◽  
Author(s):  
He-Yau Kang ◽  
Amy Lee
Keyword(s):  
Computer Science ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Computational Time ◽  
Routing Problem ◽  
Mip Model ◽  
Science Theory

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.

scholarly journals Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jingling Zhang ◽  
Wanliang Wang ◽  
Yanwei Zhao ◽  
Carlo Cattani
Keyword(s):  
Customer Satisfaction ◽  
Evolutionary Algorithm ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Adaptive Grid ◽  
Solution Set ◽  
Mixed Integer ◽  
Routing Problem ◽  
Nondominated Solution

The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.

A Hybrid Approach Based on LP Metric Method and Genetic Algorithm for the Vehicle-Routing Problem with Time Windows, Driver-Specific Times, and Vehicles-Specific Capacities

2018 ◽  
Vol 9 (4) ◽  
pp. 51-67 ◽  
Author(s):  
Ebrahim Asadi-Gangraj ◽  
Sina Nayeri
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Hybrid Approach ◽  
Mixed Integer ◽  
Computational Time ◽  
Routing Problem ◽  
Lp Metric

Due to increasing population, increasing number of vehicles as well as environmental pollution, planning vehicles efficiently one of important problems nowadays. This article proposes a Multi-Objective Mixed Integer Programming (MOMIP) model for the vehicle-routing problem with time windows, driver-specific times and vehicles-specific capacities (VRPTDV), a variant of the classical VRPT that uses driver-specific travel and service times and vehicles-specific capacity to model the familiarity of the different drivers with the customers to visit. The first objective function aims to minimize traveled distance and the second objective function minimizing working duration. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, the hybrid approach based on LP metric method and genetic algorithm is proposed to solve the given problem.

Sweep Algorithm and Mixed Integer Linear Program for Vehicle Routing Problem with Time Windows

2018 ◽  
Vol 17 (04) ◽  
pp. 505-513 ◽  
Author(s):  
H. Savitri ◽  
D. A. Kurniawati
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Time Windows ◽  
Heuristic Method ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Routing Problem ◽  
Sweep Algorithm ◽  
A Company

CV. Jogja Transport is a company that distribute cakes “Sari Roti” in Yogyakarta, Indonesia. It has responsibility to distribute the cakes for every customer during the customers’ time windows. The distribution problem of CV. Jogja Transport belongs to Vehicle Routing Problem with Time Window (VRPTW). This paper tries to solve the problem of CV. Jogja Transport by proposing “cluster first route second” algorithm of simple heuristic method. Then the algorithm is combined with sweep algorithm for clustering the customers and Mixed Integer Linear Programming (MILP) to select the best route so that it can minimize the distance of each cluster. The result indicate that implementation of sweep algorithm and MILP can reduce the distances and the fuel up to 10.95% and the travel distance up to 2.60%.

scholarly journals Analysis of Mixed-Integer Linear Programming Formulations for a Fuel-Constrained Multiple Vehicle Routing Problem

2017 ◽  
Vol 05 (04) ◽  
pp. 197-207 ◽  
Author(s):  
Kaarthik Sundar ◽  
Saravanan Venkatachalam ◽  
Sivakumar Rathinam
Keyword(s):  
Linear Programming ◽  
Vehicle Routing ◽  
Integer Linear Programming ◽  
Vehicle Routing Problem ◽  
Mixed Integer Linear Programming ◽  
Optimal Solution ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Computational Results ◽  
Routing Problem

This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where [Formula: see text] vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming (MILP) formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.

scholarly journals Implementation of discrete particle swarm optimization algorithm in the capacitated vehicle routing problem

2020 ◽  
Vol 4 (2) ◽  
pp. 117-128
Author(s):  
Aisyahna Nurul Mauliddina ◽  
Faris Ahmad Saifuddin ◽  
Adesatya Lentera Nagari ◽  
Anak Agung Ngurah Perwira Redi ◽  
Adji Candra Kurniawan ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimal Solution ◽  
Computational Time ◽  
Hard Problem ◽  
Np Hard ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Np Hard Problem ◽  
Capacitated Vehicle

Capacitated Vehicle Routing Problem (CVRP) is known as an NP-hard problem. It is because CVRP problems are very hard for finding optimal solutions, especially in large instances. In general, the NP-hard problem is difficult to solve in the exact method, so the metaheuristic approach is implemented in the CVRP problem to find a near-optimal solution in reasonable computational time. This research uses the DPSO algorithm for solving CVRP with ten instances of benchmark datasets. DPSO implementation uses tuning parameters with the One Factor at Time (OFAT) method to select the best DPSO parameters. The outcome objective function will be compared with several PSO models proposed in previous studies. Statistical test using One Way Reputed Measure ANOVA is needed to compare algorithm performance. First, ANOVA uses for comparing’s results. Then, ANOVA is also used to test DPSO’s performance compared with DPSO-SA, SR-1, and SR-2 algorithm. The computational result shows that the basic DPSO algorithm not competitive enough with other methods for solving CVRP.

Model and Algorithm for Vehicle Routing Problem with Time Windows and a Limited Number of Vehicles

2012 ◽  
Vol 482-484 ◽  
pp. 2322-2326 ◽  
Author(s):  
Yong Ji Jia ◽  
Chang Jun Wang
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Programming Model ◽  
Search Algorithm ◽  
Time Windows ◽  
Real Life ◽  
Mixed Integer ◽  
Routing Problem ◽  
Number Of Customers

In this paper, a useful variant of the vehicle routing problem, Vehicle Routing Problem with Time Windows and a limited number of vehicles (m-VRPTW) is given. The problem is to serve a number of customers at minimum cost by using a limited number of vehicles, without violating the time window constraint and the vehicle capacity constraint. The feasible solution of m-VRPTW may contain some unserved customers and third-party vehicles, such as taxies, are hired to serve these unserved customers. The mixed integer programming model of m-VRPTW is proposed and a two-phase algorithm based on insertion algorithm and tabu search algorithm is proposed to solve it. Experimental results show that our algorithm can yield effective and efficient solution and be capable of dealing with the m-VRPTW problems in real life conditions.

scholarly journals A hybrid FJA-ALNS algorithm for solving the multi-compartment vehicle routing problem with a heterogeneous fleet of vehicles for the fuel delivery problem

2021 ◽  
Vol 10 (4) ◽  
pp. 497-510 ◽  
Author(s):  
Wasana Chowmali ◽  
Seekharin Sukto
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Hybrid Algorithm ◽  
Optimal Solution ◽  
Computational Time ◽  
Second Phase ◽  
Routing Problem ◽  
Delivery Problem ◽  
Heterogeneous Fleet ◽  
Fuel Delivery

This paper proposes a new hybrid algorithm to solve the multi-compartment vehicle routing problem (MCVRP) with a heterogeneous fleet of vehicles for the fuel delivery problem of a previous study of twenty petrol stations in northeastern Thailand. The proposed heuristic is called the Fisher and Jaikumar Algorithm with Adaptive Large Neighborhood Search (FJA-ALNS algorithm). The objective of this case is to minimize the total distance, while using a minimum number of multi-compartment vehicles. In the first phase, we used the FJA to solve the MCVRP for the fuel delivery problem. The results from solving the FJA were utilized to be the initial solutions in the second phase. In the second phase, a hybrid algorithm, namely the FJA-ALNS algorithm, has been developed to improve the initial solutions of the individual FJA. The results from the FJA-ALNS algorithm are compared with the exact method (LINGO software), individual FJA and individual ALNS. For small-sized problems (N=5), the results of the proposed FJA-ALNS and all methods provided no different results from the global optimal solution, but the proposed FJA-ALNS algorithm required less computational time. For larger-sized problems, LINGO software could not find the optimal solution within the limited period of computational time, while the FJA-ALNS algorithm provided better results with much less computational time. In solving the four numerical examples using the FJA-ALNS algorithm, the result shows that the proposed FJA-ALNS algorithm is effective for solving the MCVRP in this case. Undoubtedly, future work can apply the proposed FJA-ALNS algorithm to other practical cases and other variants of the VRP in real-world situations.

scholarly journals On Modelling and Solving Heterogeneous Vehicle Routing Problem with Multi-Trips and Multi-Products

2019 ◽  
Vol 21 (2) ◽  
pp. 91-104
Author(s):  
Fran Setiawan ◽  
Nur Aini Masruroh ◽  
Zita Iga Pramuditha
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Research Area ◽  
Mixed Integer ◽  
Real Case ◽  
Computational Time ◽  
Routing Problem ◽  
Heterogeneous Vehicle Routing Problem ◽  
Distribution Company ◽  
Number Of Customers

Vehicle routing problem (VRP) is a model to determine an optimal routing plan for a fleet of homogeneous vehicles to serve a set customer which some operational constraints are satisfied. In most practical distribution problems, customer demands are served using heterogeneous fleet of vehicles. This kind of VRP is called Heterogeneous Vehicle Routing Problem (HVRP). HVRP has evolved into a rich research area because of its practical. There were many studies of rich extensions of the standar HVRP. This research aims to enrich the extentions of HVRP which is motivated by real case in one of pharmacy distribution company in Indonesia which is delivered multi-products to its 55 customers by allowing some vehicles which has small capacity to perform multi-trips. This problem is called Heterogeneous Vehicle Routing Problem with Multi-Trips and Multi-Products (HVRPMTMP).The mixed integer linear programming is developed based on four-index vehicle flow formulation. The model can be used generally in the same context of distribution problem. HVRPMTMP is generally NP-Hard problem, so the computational time using branch and bound in LINGO 16.0 is increasing exponentially by increasing the number of customers. Genetic algorithm is proposed to solve the real case. The result of the proposed GA can reduce the total cost from Rp 352540.6,- to Rp 180555,- or 48.78% from the current company policy.

scholarly journals A hybrid ant colony algorithm based on multiple strategies for the vehicle routing problem with time windows

2021 ◽  
Author(s):  
Hongguang Wu ◽  
Yuelin Gao ◽  
Wanting Wang ◽  
Ziyu Zhang
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Time Window ◽  
Time Windows ◽  
Ant Colony ◽  
Routing Problem ◽  
Multiple Strategies ◽  
Hard Time ◽  
Mutation Operation

AbstractIn this paper, we propose a vehicle routing problem with time windows (TWVRP). In this problem, we consider a hard time constraint that the fleet can only serve customers within a specific time window. To solve this problem, a hybrid ant colony (HACO) algorithm is proposed based on ant colony algorithm and mutation operation. The HACO algorithm proposed has three innovations: the first is to update pheromones with a new method; the second is the introduction of adaptive parameters; and the third is to add the mutation operation. A famous Solomon instance is used to evaluate the performance of the proposed algorithm. Experimental results show that HACO algorithm is effective against solving the problem of vehicle routing with time windows. Besides, the proposed algorithm also has practical implications for vehicle routing problem and the results show that it is applicable and effective in practical problems.

scholarly journals The last-mile vehicle routing problem with delivery options

OR Spectrum ◽  
2021 ◽  
Author(s):  
Christian Tilk ◽  
Katharina Olkis ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Resource Constraints ◽  
Time Window ◽  
Time Windows ◽  
Service Level ◽  
Optimal Solutions ◽  
Routing Problem ◽  
Common Location ◽  
Delivery Options

AbstractThe ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

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