Nonlinear Planning Model With a Gaussian Criterion of Optimization (Gaussian Programming Model)

We propose an Economic - Probabilistic analogy: the category of cost is analogous to the category of Probability. The proposed analogy permits construction of an informal theory of nonlinear non-convex Gaussian Utility and Cost, which describes the real economic processes more adequately than a theory based on a linear and convex models. Based on the proposed analogy, we build a nonlinear non-convex planning model with a Gaussian optimality criterion - Gaussian Programming Model. We also describe a corresponding model of Generalized Piecewise-Linear Programming that can be used to approximate a Gaussian Programming model, and vice verse. Proposed constructions are illustrated on a numerical example.

💡 Research Summary

The paper tackles a fundamental limitation of conventional linear‑and‑convex planning models: they cannot adequately capture the asymmetric, non‑monotonic nature of real‑world economic objectives, nor the probabilistic uncertainty surrounding target achievement. To bridge this gap, the authors introduce an “economic‑probabilistic analogy” that treats cost (or utility) as a probability density function. In this view, the cost associated with a production level is interpreted as the probability of attaining that level, thereby allowing a direct mapping between economic performance and statistical likelihood.

Building on this analogy, the authors propose a new class of objective functions shaped like Gaussian (normal) distributions. For a single activity (i) the utility (or negative cost) is defined as
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