Abstract

Abstract. In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP). A time lag between the development and application of the model could cause cost parameters to assume di erent 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 is to construct a perturbation set (PS) of cost coe cients which ensures the stability of an optimal solution under such uncertainties. The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added di culty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading. We propose a uni ed pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, whichmaycause cycling, and does not require any extra variables such asslack, surplus, or arti cial variables used in dual and primal simplex. The algorithm permits higherorder assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used package Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

Citations