Multi-parametric analysis of the maximum tolerance in a linear programming problem

This study intends to propose an alternative approach to the multi-parametric sensitivity analysis of a linear programming problem by the concept of a maximum volume in the tolerance region. For the purposes of management and control, the study first proposes the necessary and sufficient conditions of the focal parameters. Then, those nonfocal parameters that have unlimited variations can be idenitfied and thus because of their low sensitivity in practice and simplicity in analysis, they will be deleted. For those focal parameters, their different levels of sensitivity are investigated and conceived by the proposed Maximum Volume Region so that they can be handled with the greatest flexibility, simultaneously and independently. This Maximum Volume Region is bounded by a symmetrically rectangular parallelepiped. It can be characterized by a maximization problem and solved by the existing technique-Dynamic Programming. Besides, an extension to the Extended Maximum Volume Region for the case of semi-bounded region is considered. Theoretical proofs are provided with numerical illustrations. The result has been compared to Wendell’s approach.