An efficient genetic algorithm for determining the optimal price discrimination

This paper proposes a genetic algorithm (GA) to solve a price discrimination model developed to determine the product’s selling price in two markets. The model considers the production as a function of price in one market and as a function of price and marketing expenditure in other market. The cost of production is also assumed to be a function of production in both markets. The objective is to maximize the benefit under restricted prices and marketing expenditure in two markets. The considered model is a posynomial geometric programming (GP) problem with continues non-linear/non-convex objective function and linear boundary constraints. The proposed model cannot be solved optimally by a common approach such as geometric programming in a reasonable amount of time. The results show that the proposed GA can become rapidly convergent to near global optimum. Some of typical numerical examples are solved by GA and results are reported. Also, we implement a sensitivity analysis on some of model parameters in order to have a better understanding of the performance and behavior of the proposed GA.