S-Shaped Response Functions: Implications for Decision Models

This paper discusses the implications for analysis and parameter estimation of optimization using S-shaped (convex-concave) response functions. For both unconstrained and constrained optimization and for integer and continuous variables, the portion of the curve below the inflection point often does not have a significant influence on the optimal solution. Consequently, when defining and estimating S-shaped functions, most effort should be devoted to determination of the inflection point and the function’s behavior above the inflection point.