Investing in New Parameter Values in the Discounted EOQ Model

Recently, Porteus (7) was motivated by the observation that the Japanese have devoted much time and energy to decreasing setup costs in their manufacturing processes and that there has been little in the way of a formal framework for thinking about such efforts. That paper began to provide such a framework by considering the ‘parameters’ of the classical undiscounted EOQ model to be decision variables, introducing an investment cost function that reflects the cost of changing them, and studying the ensuing optimization problem. This paper continues that effort by extending the framework to the discounted EOQ model, encompassing not only altering the setup cost, but the sales (demand) rate, unit cost, and unit holding cost as well. A parametric analysis of the discounted EOQ model is carried out in which the behavior of the optimal order quantity and minimum cost are characterized as functions of the parameters. Seeking to optimize over one of the ‘parameters’ of the model leads naturally to minimizing the sum of a convex and a concave function. Whereas explicit formulas were obtained in Porteus (7), this paper specifies an algorithmic approach for solving such generic optimization problems and uses it to solve a few numerical examples. Certain qualitative results obtained in Porteus (7) are obtained here as well. For example, in a special case of the investment cost function for changing the setup cost, there is a critical sales level, below which no reductions in the setup are made, and above which such reductions are made, with more reduction made for higher sales rates. The problems of optimally selecting the sales rate is treated as incorporating explicit production and holding costs into the classical monopolist’s pricing problem. The setting analyzed here is more general than that in Porteus (7).