Case Study on Optimal Routing in Logistics Network by Priority-based Genetic Algorithm

Abstract

The definition of logistics adopted by the Council of Logistics Management is "the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services, and related information from point of origin to point of consumption for the purpose of conforming to customer requirements". Recently, the research on logistics caught more and more attention, and numerous theoretical models have been developed.However, most of the problems are much more practically intricate than that in theory. Since logistics includes almost all of the activities involved in securing, the right type of material, in the right quantity, to the right locations, at the right time, and at the right cost, also delivered with the right tailored services required by the buyer organization. It needs the expertises and experiences in business, management science, mathematics, information science and other thchoniques for defferent industries to overcome kinds of diffculties and to succeed in logistical practices for that reason. Due to the diversity and complexity of the practical problems, the existing models are usually not very satisfying to find the solutions efficiently and convinently.In the domain of logistics, the transportation problem (TP) is a well-known basic network problem. In general it is concerned with distributing commodities from the group of sources to the group of destinations, in such a way as to minize the total distribution cost. In practices, fixed cost, independent of the amount transported, is very common in TP. Involving the fixed cost, TP converts to fixed charged transportation problem (fcTP). Hultberg and Cardoso had proved that an equivalent formulation for a special case of fcTP is NP-hard. An optimal solution may occur at an extreme point of the constraint set and, for a non-degenerate fcTP with all positive fixed costs, every extreme point of the feasible region is a local minimum. Because of the complexity involved in examining and escaping from many local minima of objective functions, it requires excessssive computational effort to solve fcTP, and the existing analytical algorithms for solving fcTPs are useful only for small problems.Earlier attempts have been made to solve this problem consisted of finding an approximate solution. Balinski observed that there exists an optimal solution to the relaxed version of fcTP formed by ignoring the integer restriction, i.e. the value of the fcTP follows closely the value of its corresponding reduced TP (rTP). Other well-known heuristic approaches are the ones by Cooper and Drebes, and Diaby, while some others have offered techniques based on ranking the extreme points. Sun et al. proposed a Tabu search method. Gray has attempted to provide an exact solution to this problem by decomposing it into a master integer program and a series of transportation sub-programs. Whereas Palekar et al. attempted to provide exact algorithms based on the branch-and-bound method for the solutions of small, fxed-charge problems.Genetic algorithm (GA)...