Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization.

The article focuses on sensitivity analysis of the objective function cost coefficients in multiobjective integer linear programming (MOILP) problems. It defines the sensitivity region as the set of simultaneous changes to these coefficients for which the efficient set of solutions and their component-wise relations remain unchanged, ensuring that inefficient solutions remain dominated. The authors develop theoretical conditions and practical algorithms to compute this region, showing that for changes to a single coefficient, the sensitivity region is convex and can be determined by inspecting a subset of inefficient solutions linked to efficient solutions of related auxiliary problems. Computational experiments on multiobjective knapsack problems and a mean-variance capital budgeting example demonstrate the applicability of the approach, with sensitivity regions computed for problems involving hundreds of variables within reasonable CPU times. The work extends existing sensitivity analysis methods by addressing discrete variables and multiobjective settings, providing tools potentially integrable into future optimization software.