Closure efficiency index: a new method for inventory management.

The increasing pressure on companies to manage inventories efficiently demands significant changes and improvements to traditional inventory management methods. This need is magnified when considering that material purchasing and inventory management have been areas traditionally governed by intuition

The use of objective measurement is necessary to improve procurement performance. In this article, a method that measures the efficiency of inventory replenishment decisions is presented. We propose that this method, coupled with the more traditional weeks of supply, or, equivalently, days of supply inventory measure, can guide procurement personnel to effective inventory replenishment decisions. In addition, we propose that these two methods should be utilized as the cornerstones of a "management by exception" inventory analysis tool, that material planners can use to identify and isolate critical items.

Background

As we researched extensive literature in the area of inventory control, we noticed that different methods are used in the context of production control or job shop scheduling policies. We did not uncover much research that directly supports the ability to make procurement decisions.

Previous work is primarily centered on production-oriented policies or decisions. Starvation avoidance is a popular policy that incorporates inventory level as a factor into scheduling or dispatching decisions. One common way to use starvation avoidance considers the bottleneck as the key station. This station is monitored, possibly using input/output analysis and performance charts, to ensure that X hours of work are available in the associated buffer. Extra work hours, B, can be used as a safety buffer, thus X+B hours of work is coined virtual inventory. This measure of virtual inventory assists in decision making associated with job release rules. In general, the use of a starvation avoidance policy has a twofold purpose: (1) to determine the job release or material dispatching rules, and (2) to assist in setting a reorder point policy.

The difficulty in determining efficient or economical reorder points can be attributed primarily to the randomness of demand and lead time occurring together. Because of this combined randomness, there have been many proposed methodologies for characterizing this combined, or compound distribution, called the lead time demand distribution (LTDD). Most researchers have used the process of deriving a compound distribution from the specific individual lead time and demand distributions. Tyworth's approach deals with the two specific distributions individually, eliminating both the necessity for and confusion of representing a compound. Other approaches have been to assume normality for the LTDD, with justification in the central limit theorem. According to Eppen and Martin, this assumption is often unwarranted and has many potential errors. Data tracking, retrieval, and manipulation can be tedious processes, making demand and lead time distributions difficult or impossible to characterize in modern supply chain systems.

Lead time has a strong effect on the reorder point of a certain material or part. Therefore, many inventory control managers go to great lengths to determine effective, efficient reorder points and quantities, with lead time as a significant factor, but do nothing to measure the efficiency or effectiveness of their inventory control system alone. Many logistics engineers recognize this lack of an inventory control method and are calling for more finite measures. Krupp proposes a maximum operating inventory policy, where the maximum operating inventory is the safety stock plus some multiple of the lot size. Similarly, Lee and Billington call this lack of a measurement method the number one pitfall in managing the supply chain.

The concepts we present in this article directly address the need for supply chain measurement methods. In doing this, we incorporate consideration of lead time, demand, and their respective variabilities in developing a method that can meaningfully guide procurement decisions to greater efficiency of inventory control.

Proposed method of measurement

Traditional inventory measurement: weeks of suppIy - Weeks of supply (WOS), or equivalently, days of supply, is a standard inventory measurement used throughout industry, especially in the electronics industry. The measurement provides an indication of the expected time to exhaust a part's current on-hand inventory. The following formula is used for a part's WOS calculation:

Weeks of supply = on-hand inventory / weekly requirements rate

Table 1. Traditional use of WOS - Scenario 1

Part #                  XYZ                  ABC

WOS                  8 Weeks              3.5 Weeks
Table 2. TRaditional use of WOS - Scenario 2

Part #                 XYZ                   ABC

WOS                  8 Weeks              3.5 Weeks
Lead Time           16 Weeks               4 Weeks
Table 3. Traditional use of WOS - Scenario 3

Part #                 XYZ                   ABC

WOS                  8 Weeks              3.5 Weeks

Lead Time           16 Weeks               4 Weeks

Scheduled               0                 5000 Units
Receipts                             (Approximately 3 WOS)

Order Due Date                             Next Week

Status             Big Problem!           No Problem

The weekly requirement rate can be calculated by utilizing a part's past usage information or by using the part's future requirement data. In this article, we adopt a forward looking convention.

Proposed inventory measurement: closure efficiency index - WOS is easy to calculate and its meaning is intuitive. However, its scope is limited in that it represents a short term measure of inventory management performance. Its major flaw is that it only considers a part's current on-hand inventory, without incorporating future part deliveries or taking the part's lead time into account. Consequently, relying solely on the traditional use of WOS is insufficient in assessing inventory management performance as shown in the following example.

The information in Table 1 was presented to a group of buyers with the following question: "Which of the two parts represents the greatest risk of running out of material?" The overwhelming majority of buyers quickly indicated that part number ABC possessed the greatest risk. After all, its WOS value was less than half of XYZ's value. Buyers were then presented with the information in Table 2 and asked the same question.

Under this scenario, the answer was not clear. The same buyers who quickly indicated ABC when only presented with Table 1 were now uncertain. Questions such as: "What is on order?" and "When is the next shipment going to arrive?" were asked. Table 3 provides the answers to these questions.

The answer to the initial question, unclear when simply provided with a WOS value, was now clear. XYZ not only represents the greatest risk, but it also requires expediting, since a stockout situation is expected after the eight WOS are used. Part ABC, although operating with approximately one-half the WOS of XYZ, is managed more effectively.

This example, although fairly simplistic, illustrates the drawbacks of relying solely on WOS as the key inventory measure. A more descriptive inventory measurement must incorporate a part's lead time and its open orders. This is precisely what we propose under a method we call closure efficiency index (CEI). This method is used to answer the following question: "How efficient are replenishment and order policy decisions in 'closing' or satisfying a part's requirements during its current lead time period?"

The following formula defines the calculation of the CEI:

CEI = (OH + [SR.sub.LT])/[MRP.sub.LT] where:

* On hand (OH) - current inventory on hand available for use. This value includes a part's safety stock.

* Scheduled receipts ([SR.sub.LT]) - sum of all open order quantities scheduled to be received within a part's lead time period, excluding past due orders.

* Lead time (LT) - time that elapses between placement of order and receipt of material.

* Material requirements planning ([MRP.sub.LT]) - sum of all material requirements during a part's lead time period.

Figure 1 illustrates the key terms associated with CEI and WOS calculations, and their interrelationships, for a particular part number. The part's WOS value can be calculated by making the assumption that the part's requirements over the next five weeks (500 units/week) are indicative of its requirements over some appropriate future time horizon. Under this assumption, the WOS value can be easily determined to be seven weeks (3500/500). The part's CEI value is 2.2, which can be easily calculated with the formula outlined above ([3500 + 2000]/2500). These calculations prompt the following question: "What CEI values would indicate that the part's inventory is managed efficiently?"

Determining an efficient CEI value is not a trivial proposition. Clearly, the CEI value should be greater than 1 at all times. Any value less than 1 indicates that a part's current inventory and scheduled receipts within lead time will not cover, or "close" requirements, and that expediting will be required. For example, a CEI value of 0.5 indicates that only half of the part's requirements during lead time will be fulfilled with inventory and quantities on order. In a perfect world with no uncertainty in a part's requirements, supplier delivery lead times, and internal manufacturing processes, the goal would be to maintain a CEI value equal to 1. However, when incorporating these sources of uncertainty, experience with this method reveals that efficient material replenishment policies will usually yield a CEI value between 1 and 1.5. CEI values between 1.5 and 2 are seldom efficient and should send a signal to the buyer that corrective action may be necessary. CEI values greater than 2 are probably inefficient, as rarely will it be justified to supply twice of what is needed during a part's lead time. Exceptions to these guidelines might be for parts with high variability or relatively low cost. These rules of thumb are based on experience in the procurement of high cost, direct raw materials for the electronics industry.

CEI and WOS should not be used independently. CEI provides a long-term look at a part's inventory status over its replenishment lead time. WOS provides a short-term snapshot based solely on a part's current on-hand inventory. Even if a part possesses a satisfactory CEI value, a stockout situation may still occur. This can happen if a part's current inventory is very low and its replenishment orders, although sufficient to cover requirements during lead time, aren't scheduled to arrive until late in the lead time period. In this case, a low WOS value would be used as the trigger to the buyer indicating that the part needs attention. When used together, WOS, as a short term measure, and CEI, as a long term measure, provide full prescriptive power for managing procurement decisions.

Using CEI/WOS

CEI and WOS are currently being utilized as the key methods of an inventory analysis tool for direct raw materials inventory management. CEI/WOS was developed to satisfy the growing need for improved decision making via quantitative inventory analysis methods to gain control of raw material inventories. (It is implemented in Excel and has electronic linkages to the site material management systems.) One of the CEI/WOS's key features is that it provides procurement controllers or buyers the capability of viewing material inventory data while using CEI and WOS values as selection criteria.

Buyers have responded favorably to the tool's functionality. The ability to query inventory data with CEI and WOS as the key selection criteria is a tremendous improvement over current processes which tend to be burdensome and mired in paperwork. Buyers using CEI/WOS have seen the advantages of being able to perform selective queries and manage their parts on an exception basis. One buyer is so sold on the informational value of CEI that he commences his weekly planning activities by requesting a list of all parts with a CEI value between zero and one. This gives him a snapshot of parts needing corrective action since they represent potential stockout situations.

It took a painful experience for another buyer to recognize the value of the CEI. He realized that a recent stockout of a critical part could have been prevented had he monitored the part's CEI value. The part's inventory started declining in the middle of July, and the buyer waited until the latter part of July to place new orders. If he had been using CEI's analysis tool to chart trends in the part's three month requirements, parts on order, and WOS, he would have known when to order the part to prevent a stockout. Using this analytical feature allowed the buyer to see the part's history and take corrective action, as well as track changes in material requirements by plotting the trends in the three month requirements' value on a weekly basis. Considering that this buyer manages more than 60 critical part numbers, CEI/WOS's capability represents a tremendous opportunity.

Future steps

With the acceptance of CEI by buyers has come the realization that we can improve procurement decisions by more carefully characterizing the behavior of the CEI method in the face of different system variabilities. We are currently carrying out research that will define important variabilities based on studies in current literature and our own experience. We will then conduct a simulation-based experiment to analyze the behavior of CEI and raw material inventory in the face of differing system variations to determine CEI target ranges with a foundation on analytical results. Numerous studies associated with determining safety stock levels take into account the principle factors used in the calculation of CEI. These factors include lead time, demand, quality, and associated variation. Once we understand more about the effects of these factors on the behavior of CEI, we will be better able to specify CEI target ranges for effective procurement decision making.

For further reading

Bagchi, U., J. Hayya, and C. Chu, "The Effect of Lead Time Variability: The Case of Independent Demand," Journal of Operations Management, February 1986.

Eppen, G., and K. Martin, "Determining Safety Stock in the Presence of Stochastic Lead Time and Demand," Management Science, November 1988.

Glassey, C.R., and M. Resende, "Closed-Loop Job Release Control for VLSI Circuit Manufacturing," IEEE Transactions on Semiconductor Manufacturing, February 1988.

Grotzinger, S.J., R. Srinivasan, R. Akella, and S. Bollapragada, "Component Procurement and Allocation for Products Assembled to Forecast: Risk-pooling Effects," IBM Journal of Research and Development, July 1993.

Keaton, Mark, "Determining Reorder Points when Lead Time is Random: A Spreadsheet Implementation," Production and Inventory Management Journal, First Quarter 1995.

Krupp, James, "Measuring Inventory Management Performance," Production and Inventory Management Journal, Fourth Quarter 1994.

Lee, H., and C. Billington, "Managing Supply Chain Inventory: Pitfalls and Opportunities," Sloan Management Review, Spring 1992.

Lozinski, C., and R. Glassey, "Bottleneck Starvation for Shop Floor Controls," IEEE Transactions on Semiconductor Manufacturing, November 1988.

McFadden, Fred, "On Lead Time Demand Distributions," Decision Sciences, Vol. 3, No. 2, 1972.

Tyworth, John, "Modeling Transportation-Inventory Trade-offs in a Stochastic Setting," Journal of Business Logistics, Vol. 13, No. 2, 1992.

Uzsoy, R., C. Lee, and L. Martin-Vega, "Shop Floor Control (A Review of Production Planning and Scheduling Methods, Part 2)," lie Transactions, Vol. 26, No. 5, 1994.

Zinn, W. and M. Howard, "Comparing Two Alternative Methods of Determining Safety Stock Levels: The Demand and Forecast Systems," Journal of Business Logistics, Vol. 11, No. 1, 1990.

Miguel Pena, CPIM, is a supply chain engineer in the Inkjet Business Unit for Hewlett-Packard Corp. in Corvallis, Oregon. He has also worked for IBM in Austin, Texas. Terrence Beaumariage, Ph.D., is an assistant professor in industrial and manufacturing engineering at Oregon State University. He is a senior member of IIE. Diane Nelson is a master's candidate in industrial engineering at Oregon State University.