Lean EOQ Powers Lean Manufacturing

Economic Order QuantityEOQ = √ ã 2*P*S/CP = Production in Units/monthS = Set-up and Ordering Cost per LotC = Inventory Carrying Costs $/unit/month

In the late 1940's, Toyota started in the automotive business with the goal of making 50 to 100 cars per month. The process of stamping body panels was a barrier.

The typical car body had 300 stamped steel parts. To make these stampings, Toyota purchased three used presses in Detroit and shipped them to Japan. These presses required 24 hours to change a die. After a die change, it took less than an hour to stamp the parts Toyota needed for that month.

The manager, Taiichi Ohno, had an obvious problem. Making 300 different stampings each month required 300 set-ups, and with a 24-hour set-up, 300 days were needed. However, he had three presses, which provided, even if they were used seven days a week, only 90 days of capacity. At the time, Toyota could not afford to buy enough presses. So, Ohno was forced to focus on reducing set-up. With the mantra, " small lot sizes and quick set-ups," his people got die change set-up down to 2 1/2 hours.

By the late 1950's, he reduced the time to change dies to three minutes. In the process, he made an unexpected discovery. It cost less per part to make small batches than to run enormous lots. As the old saying goes," Necessity is the mother of invention," and this insight to minimize set-up time gave birth to the Toyota Production System.

Economic Order Quantity (EOQ) is an accepted formula that is deeply embedded in our education and used in your materials management systems. Unfortunately, traditional EOQ models are sapping your business of its economic strength. The formula for EOQ calculates optimal lot sizes based on minimizing the costs for set-up and inventory. As lot size becomes larger, set-up cost per part declines. However, the larger lot causes higher inventory and related inventory carrying costs. The EOQ formula calculates the minimum point for the sum of these two costs. Its assumptions are that set-up costs are fixed and carrying costs are current interest rates.

Appalling assumptions

A student of the Toyota Production System and Lean Manufacturing will find this appalling. Unfortunately, these academic statements are commonly used assumptions by those involved in the development and commissioning of your software applications. This traditional approach to EOQ is deeply embedded in your enterprise resource planning (ERP) and Supply Chain Management programs. In the rush of installation, these factors are chosen with expediency in mind rather than the broader business implications. The numbers for set-up and inventory carrying costs in your materials management systems need to be re-examined.

Low inventory carrying cost and fixed set-up drive excessively large lot sizes. By examining the EOQ formula, we can see why. Set-up is a variable and can be reduced through process change. Because it is the numerator, a smaller set-up lowers the EOQ. When Ohno reduced set-up from 2 1/2 hours to three minutes, the EOQ was cut by 86 percent. Recent case examples indicate that this proportion of reduction is often achieved through a set-up reduction program. Simple interest

rates are currently below 5 percent. When obsolescence, breakage, material handling, facility (heat, light and building) and other costs are included, the real cost of inventory is typically 20 percent to 36 percent. This number is in the denominator, and a smaller number increases lot size. When the higher number is used, EOQ is reduced by more than 50 percent.

EOQ drives the associated work-in-process and stockroom inventory. Cutting EOQ has a corresponding reduction in this inventory. Combining the two typical examples given above provides more than a 90 percent reduction. Broadly implemented, that will have a positive change in operational performance, the balancesheet, and stockholder value.

Ralph Rio, rrio@arcweb.com ,is Research Director at ARC Advisor

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