Managing cost uncertainties in transportation and assignment problems

[摘要] In a fast changing global market, a manager is concerned with cost uncertaintiesof the cost matrix in transportation problems (TP) and assignment problems (AP).A time lagbetween the development and application of the model could cause cost parameters to assumedifferent values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool isto construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimalsolution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and theHungarian method, respectively. Both methods fail to provide direct information to construct theneeded PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might bemisleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposedalgorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationallypractical, being easy to understand,and providing useful information for managers. The resultsempower the manager to assess and monitor various types of cost uncertainties encountered inreal-life situations. Some illustrative numerical examples are also presented.

[学科分类] 自然科学（综合）