• IE interfaces
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• v.20 no.2
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• pp.103-111
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• 2007

A heterogeneous VRP which considers various capacities, fixed and variable costs was suggested in this study. The transportation cost for vehicle is composed of its fixed and variable costs incurred proportionately to the travel distance. The main objective is to minimize the total sum of transportation costs. A mathematical programming model was suggested for this purpose and it gives an optimal solution by using OPL-STUDIO (ILOG CPLEX). A genetic algorithm which considers improvement of an initial solution, new fitness function with weighted cost and distance rates, and flexible mutation rate for escaping local solution was also suggested. The suggested algorithm was compared with the results of a tabu search and sweeping method by Taillard and Lee, respectively. The suggested algorithm gives better solutions rather than existing algorithms.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.179-184
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• 2002

We consider the heterogeneous fleet vehicle routing problem (HVRP), a variant of the classical vehicle routing problem (VRP). The HVRP differs from the classical VRP in that it deals with a heterogeneous fleet of vehicles having various capacities, fixed costs, and variables costs. Therefore the HVRP is to find the fleet composition and a set of routes with minimum total cost. We give an integer programming formulation of the problem and propose an algorithm to solve it. Although the formulation has exponentially many variables, we can efficiently solve the linear programming relaxation of it by using the column generation technique. To generate profitable columns we solve a shortest path problem with capacity constraints using dynamic programming. After solving the linear programming relaxation, we apply a branch-and-bound procedure. We test the proposed algorithm on a set of benchmark instances. Test results show that the algorithm gives best-known solutions to almost all instances.

• Journal of Distribution Science
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• v.10 no.12
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• pp.19-24
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• 2012

Purpose - This paper discusses the heterogeneous fixed fleet vehicle routing problem with pick-up and delivery (HFFVRPPD), for vehicles with different capacities, fixed costs, and travel costs. Research Design, data, methodology - This paper made nine assumptions for establishing a mathematical model to describe HFFVRPPD. It established a practical mathematical model, and because of the non-deterministic polynomial-time hard (NP-hard), improved the traditional simulated annealing algorithm and tested a new algorithm using a certain scale model. Result - We calculated the minimum cost of the heterogeneous fixed fleet vehicle routing problem (HFFVRP) with a single task and, on comparing the results with the actual HFFVRP for the single task alone, observed that the total cost of HFFVRPPD reduced significantly by 46.7%. The results showed that the new algorithm provides better solutions and stability. Conclusions - This paper, by comparing the HFFVRP and HFFVRPPD results, highlights certain advantages of using HFFVRPPD in physical distribution enterprises, such as saving distribution vehicles, reducing logistics cost, and raising economic benefits.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.228-239
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• 2005

In this paper, we propose a new conceptual HVRPCR(Heterogeneous Fleet Vehicle Routing Problem with Customer Restriction) model including additional restrictions that are consisted of loadage limit and possible visit number of demand post in HVRP. We propose HVRPCR algorithm using the heuristic in order to solve speedily because VRP is NP-Hard and need many solution time. The proposed model is simulated with changing demand post location, demand weight, loading and possible visit number limitation. Results of the computational experiment are provided along with some analysis like travel cost reduction rate.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.53
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• pp.37-44
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• 1999

The problem to be studied here is the minimization of the total travel distance and the number of vehicles used for delivering goods to customers. Vehicle routes must also satisfy a variety of constraints such as fixed vehicle capacity, allowed operating time. Genetic algorithm to solve the VRPTW with heterogeneous fleet is presented. The chromosome of the proposed GA in this study has the 3-dimension. We propose GA that has the cubic-chromosome for VRPTW with heterogeneous fleet. The newly suggested ‘Cubic-GA (or 3-D GA)’ in this paper means the 2-D GA with GLS(Genetic Local Search) algorithms and is quite flexible. To evaluate the performance of the algorithm, we apply it to the Solomon's VRPTW instances. It produces a set of good routes and the reasonable number of vehicles.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.6
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• pp.554-561
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• 2013

As a special topic of the vehicle routing problems (VRP), VRPSDP extends the vehicle routing problem as considering simultaneous pickup and delivery for goods. The past studies have mainly dealt with a only weight constraint of a loading capacity for heterogeneous products. However. this study suggests VRPSDP considering separate loading area according to characteristics of loading species. The objective is to design a set of minimum distance routes for the vehicle routing assignment with independent capacity for heterogeneous species. And then we present a another HVRPSDP model which is easy to utilizes in a unique circumstance that is a guarantee of executing a task simultaneously from the various areas under restricted time and raising an application of vehicles that returns at the depot for the next mission like the military group. The optimal results of the suggested mathematical models are solved by the ILOG CPLEX software ver. 12.4 that is provided by IBM company.

• Korean Management Science Review
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• v.30 no.2
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• pp.31-42
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• 2013

The vehicle routing problem (VRP) can be described as a problem to find the optimum traveling routes from one or several depot (s) to number of geographically scattered customers. This study executes a revised Heterogeneous Vehicle Routing Problem (HVRP) to minimize the cost that needs to conduct efficiently the snow removal operations of Air Wing under available resources and limited operations time. For this HVRP, we model the algorithm of an hybrid Ant Colony System (ACS). In the initial step for finding a solution, the modeled algorithm applies various alterations of a parameter that presents an amount of pheromone coming out from ants. This improvement of the initial solution illustrates to affect to derive better result ultimately. The purpose of this study proves that the algorithm using Hybrid heuristic incorporated in tabu and ACS develops the early studies to search best solution.

• Journal of the Korea Institute of Military Science and Technology
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• v.25 no.4
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• pp.425-433
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• 2022

This paper studies the method of delivering munitions using both drones and UGVs that are developing along with the 4th Industrial Revolution. While drones are more mobile than UGVs, their loading capacity is small, and UGVs have relatively less mobility than drones, but their loading capacity is better. Therefore, by simultaneously operating these two delivery means, each other's shortcomings may be compensated. In addition, on actual battlefields, time constraints are an important factor in delivering munitions. Therefore, assuming an actual battlefield environment with a time limit, we establish delivery routes that minimize delivery time by operating both drones and UGVs with different capacities and speeds. If the delivery is not completed within the time limit, penalties are imposed. We devised the hybrid genetic algorithm to find solutions to the proposed model, and as results of the experiment, we showed the algorithm we presented solved the actual size problems in a short time.