Allocation issues in network delivery systems

Abstract

Network problems arise in many real-world areas. There has been a great deal of research on the network problems, however, those researches could not cover all the complex network problems. Therefore, more diverse and profound research activities are required. This thesis is concerned with three classes of problems in network delivery systems which are the travelling salesman problem (TSP) with time considerations, the dynamic uncapacitated facility location problem (DUFLP), and the processor selection and task assignment problem. First, we present a formulation of the TSP with time windows (TSPTW), which is based on the dynamic concept of the TSP and thus has no additional constraints for the time window conditions. In our formulation, TSP is regarded as the minimum cost (one) flow problem with the specified constraints or the constrained shortest path problem. To solve the TSPTW, we use the dual-based procedure. We develop the valid inequalities for the TSPTW that can cut some fractional points of the LP relaxation problem and can be used to reduce the duality gap. The solution procedure is coded, and then computational experiments are carried out. In addition, we present two variants of TSP: the vehicle travel problem (VTP) and the maximum-benefit time-dependent traveling salesman problem (MBTDTSP). The criterion of the VTP is to maximize the sum of the time dependent benefits associated with the travels between two cities in the given time period. In the MBTDTSP, the salesman can visit candidate customers in order to maximize time dependent benefits in the given period, where travel times between two customers are time dependent. Secondly, we consider the DUFLP in which the facilities can freely enter and leave the system, that is, the facilities can be opened and closed several times. We linearize the quadratic term of the objective function of the DUFLP and present a dual-based solution procedure. A special facet for our DUFLP is presented which is not co...