Optimal pricing, lot-sizing and marketing planning in a capacitated and imperfect production system

In the classical economic production quantity (EPQ) problem demand is considered to be known in advance. However, in the real-world, demand of a product is a function of factors such as product’s price, its quality, and marketing expenditures for promoting the product. Quality level of the product and specifications of the adopted manufacturing process also affect the unit product’s cost. Therefore, in this paper we consider a profit maximizing firm who wants to jointly determine the optimal lot-sizing, pricing, and marketing decisions along with manufacturing requirements in terms of flexibility and reliability of the process. Geometric programming (GP) technique is proposed to address the resulting nonlinear optimization problem. Using recent advances in optimization techniques we are able to optimally solve the developed, highly nonlinear, mathematical model. Finally, using numerical examples, we illustrate the solution approach and analyze the solution under different conditions.

► A profit maximizing EPQ model is proposed.
► A Geometric Program (GP) with six degrees of difficulty is solved.
► Optimal values of price, lot-size, quality, etc. are jointly determined.
► The problem is solved and analyzed through the CVX.