Global Sensitivity Analysis

TLDR

Decision makers in operations research must assess sensitivity of outputs to imprecise parameter values, and existing analytic approaches rely on duality, parametric programming, or stochastic programming. The paper accommodates extensive simultaneous variations in any model parameter and outlines future research to extend its applicability. Relative sensitivity is assessed by allocating output variation to each imprecise parameter through optimization, Monte Carlo sampling, and statistical analyses, and the approach is demonstrated on a broad set of test models using off‑the‑shelf software on microcomputers. The results are easily applied by practitioners.

Abstract

In applications of operations research models, decision makers must assess the sensitivity of outputs to imprecise values for some of the model's parameters. Existing analytic approaches for classic optimization models rely heavily on duality properties for assessing the impact of local parameter variations, parametric programming for examining systematic variations in model coefficients, or stochastic programming for ascertaining a robust solution. This paper accommodates extensive simultaneous variations in any of an operations research model's parameters. For constrained optimization models, the paper demonstrates practical approaches for determining relative parameter sensitivity with respect to a model's optimal objective function value, decision variables, and other analytic functions of a solution. Relative sensitivity is assessed by assigning a portion of variation in an output value to each parameter that is imprecisely specified. The computing steps encompass optimization, Monte Carlo sampling, and statistical analyses, in addition to model specification. The required computations can be achieved with commercially available off-the-shelf software available for microcomputers and other platforms. The paper uses a broad set of test models to demonstrate the merit of the approaches. The results are easily put to use by a practitioner. The paper also outlines further research developments to extend the applicability of the approaches.