Sensitvity Analysis for Optimization Problems based on Quantifier Elimination Techniques

Abstract

We propose a sensitivity analysis technique for the class of mathematical programming problems. So far, there are no concrete methodologies of sensitivity analysis for the mathematical programming problems especially with integer constraints in general. Quantifier elimination is a concept of simplification used in mathematical logic and enables problems to be analyzed of their sensitivities to the objective functions. In this paper, we applied the quantifier elimination to a class of job shop scheduling problems as a case of mixed integer programming problems in order to demonstrate the evaluation of the sensitivities of the processing time to both of the makespan and the due date tardiness. In order to cope with computational complexities of quantifier elimination, we propose the problem decomposition and the sequential application of the quantifier elimination techniques based on the decomposition.