A Geometric Programming Approach for a Nonlinear Joint Production-Marketing Problem

This paper presents a nonlinear model of a joint production - marketing problem intending at determining the unit selling price, unit marketing expenditure and economic production quantity per production cycle simultaneously. The proposed model involves some cost functions such as market share loss cost which is not regarded in similar models in the related literature. The model is a signomial geometric programming model with 4 degrees of difficulty which will be transformed to a standard posynomial geometric one, using the concepts behind the relations between geometric and arithmetic means. This transformed model is solved by an iterative algorithmic procedure. Eventually the presented procedure is illustrated by numerical examples.