By Steven A. Melnyk and R.T. "Chris" Christensen

Last month we looked at one specific component of capacity utilization -- setup times. We saw that there was a strong relationship between capacity utilization and setup times and that this relationship strongly depended on the degree to which the setup times consisted of internal activities. As discussed in last month's column, internal activities are any activity which must be done while the machine (or work center) is sitting idle. We also noted that setup times could act as a major source of variability. This month we focus our attention on the role of setup times in lot sizing. For most practitioners this is a major source of confusion and misperceptions.


Lot sizing: a review
Before we look at the role of setups in lot sizing, we must first understand what is meant by lot sizing. Lot sizing is the amount or quantity that we order or make whenever we need to fill an order or replenish inventory (and the existing amount on hand and on order is insufficient to cover the demand). This amount can range from making just enough to meet the immediate demand, to making enough to cover a number of periods of demand. This amount can be determined in various ways. On one hand we can base this amount on factors such as the size of the storage bin (or the number of storage bins) or experience-based rules of thumb (whenever we place an order, we order 125 units because that was the largest demand that we had encountered in the past). Alternatively, we can use a more analytical method to determine this amount. Most of these more analytical procedures are built around the relationship between the holding costs and the setup costs. Understanding this relationship is necessary in understanding the role of setups.

If we don't have any inventory on hand when a demand occurs, then we incur a cost in the form of setups. For every order that occurs under these conditions, we must have a setup. Under many conditions, this can be a very expensive and time-consuming situation. For example, if we have very large setup costs (e.g., $1,000 every time we prepare the equipment or place an order with our supplier), then such an approach does not make a great deal of sense when we are building only a couple of units costing $5 each. One way of avoiding this situation is to hold enough inventory to meet demand (and avoid the setup costs). However, the larger the amount of inventory, the greater the costs of holding inventory. Under these conditions, we are faced with the problem of determining what order quantity best manages the total holding costs and the total setup costs.

This problem is not a new one. It was first addressed by Harris in 1913. At this time, Harris, who was working at General Electric, developed a formula now referred to as the economic order quantity (EOQ). What he determined was that the most economical order quantity was the one that balanced the total holding costs with the total costs of setups.


Setup costs
As pointed out last month, setup is the amount of time that it takes to change a machine or work center or to place an order (in the case of purchasing) to go from the last part of a production lot to the first consistently good part of the next production lot. This definition has to be modified slightly when it is applied to lot sizing. In this case, setup costs are the variable relevant costs associated in going from the last part of a production lot to the first consistently good part of the next production lot. Setup costs are limited only to the actual costs that are incurred. Every time a setup takes place, these costs are generated. To understand this notion in practice, consider the following example.

A young production supervisor was interested in determining the setup costs so that he could calculate the order quantity for a specific part that ran through a certain machine. He called a colleague in accounting and asked if he could look into the matter and call him back with an answer. About a week later, he got a call from his friend in accounting who told him that the setup costs were $510. This number shocked the young supervisor. The supervisor asked the accountant to explain this number.

The $510 was based on the following costs: 1) $150 came from two setup men who had to work two hours each on the job (at $37.50 per hour -- including all benefits. These men were paid by the hour and not by the number of setups that were performed); 2) $10 came from the machine operator who had to help on part of the setup; 3) $150 came from tooling expenses, of which $50 was directly consumed by the setup and $100 was a prep charge (this number was determined by taking the total overhead expenses for the tool room and dividing by the number of orders processed); 4) $100 came from the budgeted scrap of four units which were expected to be discarded as a result of the setup (each unit had a variable cost of $25); and 5) $100 was budgeted allocations.

There is a basic problem with this setup cost -- it is overstated. It is overstated by the presence of fixed costs and allocated costs. These costs should not be considered when determining the setup cost for lot sizing. For example, the first $150 should not be considered because the setup men represent fixed costs. We would pay them for eight hours irrespective of whether they do setups or not. The tooling expense represents a mixture of allocated and variable costs. The $100 is an allocated cost and should be discarded. Consider its behavior for a moment. If we had experienced one more order in the tool room and if this was really a variable cost, then the costs should have gone up by $100. But this is not what happened. We arrived at this number by taking the total overhead for the tool room and dividing it by the total number of orders. The arrival of the additional order would have reduced the prep charge [total expenses/(orders+1) < total expenses/(orders)]. Similarly, the last $100 should also be dropped because it is a budgeted allocation. The true setup cost should have been $10 (for the operator) + $50 for consumed tooling + $100 for scrapped parts, or $160.

What this little exercise shows is that determining the actual setup costs is really a more difficult exercise than simply taking numbers given by accounting.


The impact of relevant costs
Before leaving this discussion, we should understand the notion of relevant costs. To this point, we have focused our attention on variable costs alone. Relevant costs have been traditionally defined as those that change as a direct result of a decision. Often these costs are identical to variable costs. However, we should recognize that relevant costs (especially as applied to setup costs) are also sensitive to the level of capacity utilization. A setup cost may be relevant under one level of capacity utilization and irrelevant under another level. To understand this notion, consider this next example.

The production supervisor that we introduced in the preceding example knows that his utilization of equipment experiences significant movements. At times, the entire shop can be severely underutilized (running between 30 to 50 percent utilization). Yet, at other times, it can be very busy (running between 80 to 95 percent). Setups are relevant only under the high utilization situations; they are not relevant when capacity utilization is low. The reason lies in the opportunity cost of a setup. When capacity utilization is low, the opportunity cost is low. The hour of capacity utilization that we spend for setup would have been idle otherwise. Alternatively, when capacity utilization is high, there is a real significant opportunity cost associated with setup. The hour that we spend on setup we get by taking it away from production. Production generates value. Please note that this discussion pertains to the capacity impact of a setup. We must still consider the parts scrapped during the setup as well as the tooling consumed.

Before we leave this discussion, we should briefly touch on holding costs. Holding costs represent the costs of having inventory. In a broader sense, it represents the costs of investing in inventory as compared to the best possible alternative investment. As a result, holding costs include the costs of having inventory (storage expenses, taxes associated with the inventory, obsolescence, etc.) and the opportunity costs of investing in inventory. For example, if we can borrow money from the bank at 8 percent, and if we can invest that money in another area in the firm and earn 20 percent, then we should be charging ourselves at least 20 percent (the best alternative return for money) whenever we invest in inventory.

One final point to consider about holding costs and interest rates. These are very much management controls. They are used to tell the rest of the firm whether we, as management, want inventory or not. If we don't want to have inventory, then we set the rates high so that inventory becomes very expensive. People will respond appropriately.

Finally, it is important to remember that with setup costs the key challenge is not that of measuring them. Rather, the challenge is to reduce the actual changeover time. That is the challenge of Just-in-Time manufacturing.

Next month, we continue our exploration of capacity.

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