An integrated pricing and lot sizing model with reliability consideration

This paper addresses a production-marketing problem where the reliability of the production process can be imperfect and the inventory and the setup costs per production cycle are not known in advance. The proposed model of this paper simultaneously determines lot size, marketing expenditure, setup cost, inventory holding cost, and reliability of the production process. The demand is a function of price and marketing expenditure and the production unit cost is considered to be a function of lot size. The resulted problem is modeled in a form of nonlinear posynomial geometric programming and a closed form solution is derived. The implementation of the proposed method is illustrated using a numerical example.