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(7.75 * 25) + (645 * .30) = 193.75 + 193.5.
Notice that the two sides are equal. (See the following graphic)
72
Lesson Two - EOQ, Process, Systems and Agency Theories
Combined
Costs $
Costs
Carrying
Cost
Order
Costs
Quantity
EOQ
This graph shows that at the EOQ the two cost lines (annual carrying cost and order
cost) cross, showing they are equal. Take a look at the same problem but with a
different set of costs associated with each component:
Annual demand is 10,000; order cost is $5 and IC is 35% of cost; cost is $2:
2*10,000*5
EOQ= = 378
.35*2
At 378 we will have 10,000/378 purchases or 26.45 purchases of 378 widgets per year.
The average inventory is 189. The annual cost will be (26.45 * 5) + (189 * .70) = 132.25 +
132.30.
Companies are beginning to realize that their carrying costs for inventory are greater
than they previously thought. Carrying costs were once considered to include rent,
capital cost (interest on holding money), and spoilage. Carrying costs are now seen to
be rent plus an allowance for what that space could yield if it was converted to
production space (known as opportunity cost), capital, spoilage, utilities for light and
heat, and some miscellaneous. Of interest is the fact that we include the cost for people
who move items within the warehouse, but we do not include a portion of the
accounting and staff people who work because of the inventory, or a portion of
supervisors and managers that work because of the warehouse people.
Large lots allow greater waste allowance on the production floor. Scrap piles are
larger in companies with large lot production and purchases. Contrast this to smaller
lots that allow the capture of defects before internal and external failure. Smaller lots
73
Total Quality Management
allow more flexibility to customer demand. There should be a cost consideration
added to the carrying cost in the EOQ formula for this as well. I referred to this in the
miscellaneous reference above.
Many production managers and purchasing agents rely on the EOQ model to
determine quantities. TQM can use the EOQ formula to explain the advantage of
small orders. I suggest that if you include all the real costs of carrying inventory and
producing in large lots, the EOQ formula does support smaller lots and a Just-In-Time
(JIT) production philosophy. More on JIT later.
Safety Stock
The old philosophy stated that all vendors take time to deliver an order once it is
placed. Thus, it was important to order more (or order earlier) to avoid running out.
Another impact on the quantity ordered and carried is safety stock. The old
philosophy said that if we run out of an item, the cost to production was greater than
the cost of carrying extra inventory.
The premise of the "new" philosophy is that lead time can in fact be reduced to zero.
Imagine a condition where the correct amount of any item is delivered at precisely the
same time as the storage bin is empty. Imagine too that there is a guarantee of
delivery, and therefore no safety stock is necessary. Although we may not achieve
utopia, we can move closer to it.
Quantity discounts can play havoc with EOQ as well. You can run several EOQ
calculations based on quantity pricing and compare the difference. You can also use
more complex mathematical expressions. The Wagner-Whiting algorithm provides a
lower inventory allotment if all mathematical inputs are correct. The drawback is that
it requires the company to accurately predict future demand. The farther into the
future you project, the less accurate your calculations. The intent is still to forecast the
next unit demand and provide for it. This text uses the EOQ formulas presented and,
for the sake of simplicity, does not use the more complex algorithims that you might
find in advanced production or inventory management texts.
Economic Manufacturing Quantity
EOQ, with a modification, can also handle manufacturing your own components. We
must allow for the rate of manufacture and the rate of use to establish an inventory
level. There is a presumption that you can manufacture the component at a rate
greater than you can use it. If the production rate is less than the use rate, then the
company would still have to buy components from an outside supplier and we would
use the EOQ equation for the purchased amount.
The model changes to the Economic Manufacturing Quantity (EMQ), such as:
2DS
EMQ =
ëø demand rate öø
interest
ìø ÷ø
íø production rateøø
74
Lesson Two - EOQ, Process, Systems and Agency Theories
for a given time period. Let s look at the last example of widgets.
Monthly demand is 1,000, monthly production rate is 1,500, order cost is $25 and IC is
15% of cost, cost is $2:
2*12,000*25
EOQ= =1738
1000
.15*2*
1500
This means that we will produce 1738 at a time. Since we produce 1500 a month, we
will run for approximately five weeks at a time. The excess production over the 1000
used in a month will go into inventory. When we are near finishing off the inventory,
we start manufacturing again.
We can use similar figures as we did for the comparison EOQ model and show that if
true carrying costs and improved set up costs were used, the lot size would change.
Manufacturing and the EOQ formula rests in large part on the setup cost. The old
philosophy says to produce more to spread out the impact of the set up costs. This is
the concept of economies of scale.
Example: if 10,000 items have variable costs of 1.00 and set up costs of 3000, then the
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