Inter-parametric Tolerance Analysis of a Multiobjective Linear Programming

In this paper, global sensitivity analysis of a Multiple Objective Linear Programming problem is performed. The analysis takes the views from the utilities of management and control and is focused on the global perturbations on the weights, the cost coefficients, and the right-hand sides. Different coefficients are determined by different factors (parameters). Because it is different from the multi-parametric programming, we call it the inter-parametric tolerance analysis to emphasize the interactions of the parameters. Besides, a geometric approach is adopted to find the critical region. As regards the effective control and management, a bi-level criterion based on two respective factors stated below is proposed to determine comparatively the sensitive parameters: The first level is taken on the smaller relative tolerance-ratio; if they are equal, the second level of analysis is based on the larger unit-contribution to the objectives. This is done by the direct measurement as well as from the concept of the marginal rate of substitution. Theoretical development is incorporated with numerical illustrations.