Variable Profit GAP

Description

The Variable Profit GAP is a new generalization of the Generalized Assignment Problem (GAP), a very well known and widely applied NP-Hard combinatorial optimization problem. It is mainly motivated by the distribution of sugar canes to sugar cane mills in Tucumán, a province in the northwest of Argentina, in which the efficiency of the mills depends upon the amount of raw material being processed, among other factors.

The main differences with the GAP are:

- There exists a minimum capacity that must be met for every factory, below which the factory cannot continue working and must stop.

- Most sugar mills reach a peak efficiency when working at a certain percentage of the maximum capacity. Working above or below a small threshold around that point reduces efficiency in a nonlinear way. We introduced a nonlinear function which measures the efficiency curve of a factory as a function of the working regime of the factory. This efficiency function multiplies the GAP profits, such as that the maximum profit is obtained at the maximum efficiency.

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