Establishment of military movement plans using no-wait in-process sequencing problem

Abstract

This thesis describes a no-wait in-process job shop sequencing problem(NWP). We relax the assumption that infinite intermediates storage exists which can hold all the partially processed jobs when these jobs cannot be further processed because the subsequent machines are busy. We illustrate this problem with the establishment of the military movement plans. The convoy column is regarded as a job and the junction where more than two convoy columns meet one another is thought of as a machine. The problem is to find an ordering of convoy columns which minimizes the total time to complete marching through all the junctions. The NWP is formulated as an integer linear problem with either-or constraints. Using order relations, the NWP can be transformed into the problem of finding the transitive tournament with the minimum weight. The transitive tournament is defined as a complete asymmetric digraph. We suggest a branch and bound algorithm of constructing an optimal solution. Computational results show that a good solution can almost always be obtained in a reasonable time. The military movement plans can be established successfully in terms of the NWP.