A joint lot-sizing and marketing model with reworks, scraps and imperfect products

In this paper, we establish an economic production quantity (EPQ) based inventory model by considering various types of non-perfect products. We classify products in four groups of perfect, imperfect, defective but reworkable and non-reworkable defective items. The demand is a power function of price and marketing expenditure and production unit cost is considered to be a function of lot size. The objective of this paper is to determine lot size, marketing expenditure, selling price, set up cost and inventory holding cost, simultaneously. The problem is modeled as a nonlinear posynomial geometric programming and an optimal solution is derived. The implementation of the proposed method is demonstrated using a numerical example and the sensitivity analysis is also performed to study the behavior of the model.