• Journal of Korean Institute of Industrial Engineers
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• v.35 no.2
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• pp.150-159
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• 2009

The heterogeneous fleet vehicle routing problem(HVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles with various capacities, fixed costs and variable costs. We propose a new conceptual HVRPCR(HVRP with customer restriction) model including additional customer restrictions in HVRP. In this paper, we develop hybrid particle swarm optimization(HPSO) algorithm with 2-opt and node exchange technique for HVRP. The solution representation is a n-dimensional particle for HVRP with N customers. The decoding method for this representation starts with the transformation of particle into a priority list of customer to enter route and limit of vehicle to serve each customer. The vehicle routes are then constructed based on the customer priority list and limit of vehicle to serve. The proposed algorithm is tested using 8 benchmark problems and it consistently produces high-quality solutions, including new best solutions. The numerical results show that the proposed algorithm is robust and efficient.

• 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 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.

• 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 the Korean Operations Research and Management Science Society
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• v.36 no.1
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• pp.27-38
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• 2011

In this paper, we deal with the periodic heterogeneous fleet vehicle routing problem (PHVRP). PHVRP is a problem of designing vehicle routes in each day of given period to minimize the sum of fixed cost and variable cost over the planning horizon. Each customer can be visited once or more times over the planning horizon according to the service combinations of that customer. Due to the complexity of the problem, we suggest a heuristic algorithm in which an initial solution is obtained by assigning the customer-day and the customer-car simultaneously and then it is improved. A performance of the proposed algorithm was compared to both well-known results and new test problems.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1999.04a
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• pp.15-16
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• 1999

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.2
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• pp.8-17
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• 2005

This paper dealt with a kind of heterogeneous vehicle routing problem with known demand and time deadline of customers. The customers are supposed to have one of tight deadline and loose deadline. The demand of customers with tight deadline must be fulfilled in the deadline. However, the late delivery is allowed to customers with loose deadline. That is, the paper suggests a model to minimize total acquisition cost, total travel distance and total violation time for a fleet size and mix vehicle routing problem with time deadline, and proposes a heuristic algorithm for the model. The proposed algorithm consists of two phases, i.e. generation of an initial solution and improvement of the current solution. An initial solution is generated based on a modified insertion heuristic and iterative Improvement procedure is accomplished using neighborhood generation methods such as swap and reallocation. The proposed algorithm is evaluated using a well known numerical example.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.327-331
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• 2006

This paper considers an integrated inventory-distribution system with a fleet of heterogeneous vehicles employed where a single warehouse distributes a single type of products to many spatially distributed retailers to satisfy their dynamic demands and the product is provided to the warehouse via procurement ordering from any manufacturing plant or market The Problem is formulated as an Mixed Integer Programming with the objective function of minimizing the sum of inventory holding cost (at the warehouse and retailers), and transportation cost and procurement ordering cost at the warehouse, subject to inventory-balancing constraints, ordering constraints, vehicle capacity constraints and transportation time constraints. The problem is Proven to be NP-hard. Accordingly, a Lagrangean heuristic procedure is derived and tested for its effectiveness through computational experiments with some numerical instances.