Guidelines for setup‐cost reduction programs to achieve zero inventory

Abstract

Abstract Historically, academics and managers have approached inventory management by assuming setup cost is constant. However, recently, particularly through the experience of the Japanese, we have seen that setup time and setup cost are by no means fixed. For example, one approach to reduce setup, SMED (single minute exchange of die) suggests setups can be reduced from days to minutes. Furthermore, setup reduction is identified as one of the key facilitating factors for just‐in‐time manufacturing. In light of this development, there is an emerging stream of literature on setup reduction. This research stream generally follows the tradition of the lot‐sizing literature; the optimal amount of setup reduction is determined given a total cost model and a setup cost/reduction investment function. However, a limitation of these models is that they focus on a single item and typically include only setup and inventory costs. A key insight from the literature is the counter‐intuitive notion that setup reduction yields increasing marginal returns. Thus, we consider the issues faced by a manager trying to prioritize setup reductions for multiple items. As with the SMED philosophy, where the target is to reduce all setups to less than ten minutes, we do not seek to optimize the amount of setup reduction. Instead we are concerned with establishing an economical sequence for reductions. In general, we assume setup reductions are cost‐justified by direct or indirect benefits. This paper is organized into six sections. The first two sections introduce the problem and review the relevant literature. The third section determines for a single item operating under the EOQ assumptions, what fraction setup must be reduced to achieve a target order quantity. The target may be zero‐inventory, which is alternately defined as an EOQ of one or lot‐for‐lot production. A simple graph for use by managers is provided to show the relationship of target order quantity and fraction setup reduction required. In the fourth section, the implications of setup reduction are extended to multiple items. The principal management issue in this situation is that given two items, which item should be scheduled for setup reduction first. We provide the manager with a simple guideline in the form of the savings ratio (SR), which contrasts the potential savings of the two setups. We show that the decision between two items is dependent on the dollar volume of the items adjusted for how far each item is from a period order quantity of one. Section five develops a formula for determining the maximum allowable setup cost to achieve lot‐for‐lot (zero‐inventory) production for the case of time‐varying demand. Using a marginal cost approach, we determine that a manager need only target setup reduction to justify not batching the lowest expected single period demand over the planning horizon. We show that a setup should be reduced more when a longer planning horizon is considered because there is a greater chance for a low single period demand. In the special case where there are periods of zero demand we find that the maximum setup cost may be higher because the setup cost is compared against multiple periods of carrying charges. The final section considers the application of the savings ratio concept to multiple items with time‐varying demand. SR is defined only for the general case, because the unique interactions of item parameters and the calculation of total costs with the Wagner‐Whitin algorithm preclude a closed‐form solution. However, we did find items with greater variability and. therefore, lower expected single period demands will tend to have higher priority for setup reduction. Thus. a management objective parallel to setup reduction may be to manage the variability of demand. This research is unique in that it suggests guidelines for managers initiating setup‐reduction agendas with multiple items. Our research shows that the potential savings and preferred sequence of reductions is dependent on the interactions of several item parameters (i.e., current setup cost, unit costs, total demand, demand variability, and target lot‐size). To account for these interactions we introduce the savings ratio as a simple procedure to prioritize items for setup reduction. This paper concentrates on setup defined as setup time and assumes a “relevant range” of capacity in which the opportunity costs are constant per unit time. Thus. we assume that regardless of how much additional time is generated by setup‐time reduction, each time unit will yield the same benefit.

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