Investing in Reduced Setups in the EOQ Model

This paper is 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 available to use to think about such efforts. The object of this paper is to begin to provide such a framework. The framework developed identifies only one aspect of the advantages of reducing setups, namely reduced inventory related operating costs. The other advantages, such as improved quality control, flexibility, and increased effective capacity, are not accounted for in this paper. Nevertheless, substantial reductions in setups may be warranted based solely on the benefits identified in this paper. The approach taken here introduces an investment cost associated with changing the (current) setup level and adds a per unit time amortization of this cost to the other costs identified in the standard EOQ model. The general problem becomes that of minimizing the sum of a convex and a concave function. In two special cases, the minimization can be carried out explicitly. In one of these cases, numerous interpretations of the results are made, including comparisons of Japanese and American practices. For example, holding other parameters constant, there is a critical sales level such that investment is made in reducing setups if and only if the sales rate is above that level. When such investment is made, the optimal lot size is independent of the sales rate. The paper also addresses the joint selection of the setup cost and the sales rate. Selection of the sales rate is seen as incorporating explicit production and holding costs into the classical monopolist’s pricing problem. An explicit solution is obtained for the model postulated.