The economic production and pricing model with lot-size-dependent production cost

In this paper, the economic production quantity problem for a single-product single-machine system is extended. It is assumed that annual demand of the product is a function of price set by manufacturer. This extension considers sales revenue, inventory and setup costs as well as a variable cost of production which is a function of the lot size. Several linear and non-linear functions of demand and variable cost are considered in this paper and a global solution methodology is presented for the models developed. Newton's method is used to find local optima and asymptotic convergence of the solution algorithm to a global optimum is proved. Numerical studies followed by a discussion provide additional insights into the problem.