Optimal production and marketing planning with geometric programming approach

One of the primary assumptions in most optimal pricing methods is that the production cost is a non-increasing function of lot-size. This assumption does not hold for many real-world applications since the cost of unit production may have non-increasing trend up to a certain level and then it starts to increase for many reasons such as an increase in wages, depreciation, etc. Moreover, the production cost will eventually have a declining trend. This trend curve can be demonstrated in terms of cubic function and the resulted optimal pricing model can be modeled in Geometric Programming (GP). In this paper, we present a new optimal pricing model where the cost of production has different trends depending on the production size. The resulted problem is formulated as a parametric GP with five degrees of difficulty and it is solved using the recent advances of optimization techniques. The paper is supported with various numerical examples and the results are analyzed under different scenarios.