A Multi Objective Geometric Programming Model for Optimal Production and Marketing Planning

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Abstract

This paper presents a multi objective geometric programming model which determines the product`s selling price in two markets. We assume demand is a function of price and marketing expenditure in two markets. The cost of production is also assumed to be a function of demands in both markets. Our model is a posynomial function which is solved using Geometric Programming (GP). In our GP implementation, we use a transformed dual problem to change the model into an optimization of an unconstraint problem with a single variable solved using a simple line search. In order to study the behavior of the model we analyze the solution in different cases and a numerical example is used to demonstrate the implementation for each case.

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