Robust Geometric Programming Approach to Profit Maximization with Interval Uncertainty

Abstract

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. In this paper, we consider the profit-maximization problem with the known Cobb-Douglas production function. Its equivalent geometric programming form is given. Then due to the presence of uncertainties in real world modeling, we have assumed interval uncertainties on the model parameters. The robust counterpart is not known to be considered as a geometric program and efficiently solvable using interior point algorithms. Thus using piecewise convex linear approximations, an approximate equivalent of the robust counterpart is given, which is in the form of a geometric programming problem. Finally an example is presented showing the impact of uncertainties.

Keywords

• Economic Profit
• Geometric Program
• Robust Optimization