An Extented Sensitivity Analysis in Linear Programming Problems

Inuiguchi, M. & Wessels, J. (1994). An Extented Sensitivity Analysis in Linear Programming Problems. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-105

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Abstract

When a real world problem is formulated as a linear programming model, we are often faced with difficulties in the parameter specification. We might know the plausible values or the possible ranges of parameters, but there still remains uncertainty. The parameter values could be obtained more exactly by experiments, investigations and/or inspections. However, to make such an experiment, investigation or inspection, expenses would be necessary. Because of capital limitations, we cannot invest in all possible experiments, investigations and inspections. Thus, we have a selection problem, which uncertainty reduction is the most profitable.

In this paper, we discuss an analytic approach to the problem. Because of the difficulty of the global analysis, we make a local analysis around appropriate values of parameters. We focus on giving the decision maker useful information for the selection. First, sensitivity analyses with respect to the uncertain parameters are developed. The sensitivities are available only for the marginal domain without changing the optimal basis. The domain is obtained as an interval. The difficulty of the sensitivity analysis is in the cases of degeneracy and multiplicity of the optimal solutions. A treatment of such difficult cases is proposed. Finally, a numerical example is given for illustrating the proposed approach.

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