Abstract
A wholesale company with warehouses and retail stores has its own transportation department, which is considered in this dissertation. A long-term shipping plan from warehouses to retail stores can be obtained by the transportation problem. Since the parameters of the transportation usually are estimators, a sensitivity analysis is usually adopted to realize the perturbations of parameters to the shipping plan. In addition, if decision maker has a budget to improve the shipping plan in short-term, sensitivity analysis can address the problem that how to reallocate the resources. Many papers in the literatures point out the influences of degenerate optimal solutions to the traditional sensitivity analysis, then propose advanced sensitivity analysis. However, most papers mention about advanced sensitivity analysis of a linear programming problem, but a few papers mention about advanced sensitivity analysis of the transportation problem. In addition, papers in the literature propose the auxiliary reduced model to obtain the perturbation ranges of advanced sensitivity analysis. Once the number of warehouses and retail stores increase, the computational time would increase dramatically. In this dissertation, three major issues are addressed: (1) Type II sensitivity analysis of cost coefficients of the degenerate transportation problem; (2) Optimal-routes invariant sensitivity analysis for supplies and demands when dual optimal solutions are degenerate; (3) Type III sensitivity analysis for right-hand-side parameters in the transportation problem with dual degenerate optimal solutions. We propose the auxiliary reduced models and observe some properties of each auxiliary reduced model, then develop the algorithms with labeling procedure to address the above issues, and consider the observed properties in the procedures of the algorithms. The computational results show that the proposed algorithms can provide more complete perturbation ranges to decision makers. The computational time of the algorithms with labeling procedure are more efficient than the computational time of auxiliary reduce models.