• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.1
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• pp.61-67
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• 2008

This paper introduces the multi-vehicle routing problem(MRP) which is different from the traveling sales problem(TSP), and presents the ant system(AS) applied to the MRP. The proposed MRP is a distributive model of TSP since many vehicles are used, not just one salesman in TSP and even some constraints exist. In the AS, a set of cooperating agents called vehicles cooperate to find good solutions to the MRP. To make the proposed MRP extended more, Tokyo city model(TCM) is proposed. The goal in TCM is to find a set of routes that minimizes the total traveling time such that each vehicle can reach its destination as soon as possible. The results show that the AS can effectively find a set of routes minimizing the total traveling time even though the TCM has some constraints.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.3
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• pp.303-311
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• 2007

This study deals with a type of vehicle routing problem faced by manager of some department stores during peak sales periods. The problem is to find a set of traveling paths of vehicles that leave a department store and arrive at a destination specified for each vehicle after visiting customers without violating time and capacity constraints. The mathematical model is formulated with the objective of maximizing the sum of the rewards collected by each vehicle. Since the problem is known to be NP-hard, a heuristic algorithm is developed to find the solution. The performance of the algorithm is compared with the optimum solutions obtained from CPLEX for small size problems and a priority-based Genetic Algorithm for large size problems.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.69-83
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• 1994

This paper deals with a capacitated ring-star network design problem (CRSNDP) with node capacity constraints. The CRSNDP is formulated as a mixed 0-1 integer problem, and a 2-phase heuristic solution procedure, ADD & VAM and RING, is developed, in which the CRSNDP is decomposed into two subproblems : the capacitated facility location problem (CFLP) and the traveling sales man problem (TSP). To solve the CFLP in phase I the ADD & VAM procedure selects hub nodes and their appropriate capacity from a candidate set and then assigns them user nodes under node capacity constraints. In phase II the RING procedure solves the TSP to interconnect the selected hubs to form a ring. Finally a solution of the CRSNDP can be achieved through combining two solution of phase I & II, thus a final design of the capacitated ring-star network is determined. The analysis of computational results on various random problems has shown that the 2-phase heuristic procedure produces a solution very fast even with large-scale problems.