Setup reduction and machine availability

This paper is an extension of Billington, who used the framework of the economic production quantity (EPQ) to model setup cost reduction. In the present paper, the authors use the EPQ model as a starting point to investigate the nature of setup costs and the effect of setup time reduction on the increase in availabile capacity. Reducing setup is vital to a company’s success because a lengthy changeover of machinery is expensive: it demands long production runs to justify its cost, and these, in turn, lead to excessive inventory and to a slow response to customer needs. As in Billington, setup reduction is modeled as a function of an annual amortized investment. The paper examines the behaviour of the setup time, the inventory cost, the lot size, and the freeing up of machine time in the face of a capacity constraint. A solution algorithm is provided to find setup times that minimize the sum of setup and holding cost, subject to a constraint on machine availability. The analysis sheds light on the true nature of setup cost and on the opportunity cost of not reducing setups. In the constrained optimization, the Lagrangean multiplier gives an estimate of the marginal value of adding one time unit of machine capacity, or, alternatively, of reducing one unit of setup time.