proporcionimin

Proporcionimin is a neologism used in discussions of proportions within multi-component systems. The term blends the Spanish word proporcion (proportion) with min, signaling a minimum proportion constraint. It describes a rule or metric that requires a component to occupy at least a specified share of the total across various domains, such as operations research, economics, and nutrition planning.

In its simplest form, for a system with components x1, x2, ..., xn and total X = sum xi, a proporcionimin applies to a subset S of components, requiring xi >= pi * X for each i in S, where 0 <= pi <= 1. The pi values should satisfy that the sum over i in S of pi is less than or equal to 1 to keep the constraint feasible.

In optimization models, proporcionimin constraints can be nonlinear because X depends on the decision variables. They are commonly linearized by introducing auxiliary variables or by reformulating as a set of linear constraints, depending on the modeling framework. They interact with other bounds, resource limits, and objective functions, influencing feasible portfolios or product mixes.

Applications include manufacturing and supply chain product mix, dietary planning to ensure minimum intake shares, and investment portfolios where a baseline level of diversification is desired. The term remains specialized and is not universally standardized, appearing primarily in discussions of proportion-based constraints rather than formal textbooks. See also proportional constraints, minimum quantity requirements.