Chapter 10Order Quantities
IM417 Manufacturing Resources Analysis
Southeast Missouri State University
Compiled by Bart Weihl
Spring 2001
1
Order Quantities
Inventory Management
How much should be ordered at one time?
When should an order be placed?
Stock-Keeping Unit (SKU)
http://www.inventoryops.com
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Order Quantities
Decision Rules
Lot-size Decision Rules
Lot-for-lot
Order what is needed - no more - no less
Fixed order quantity
Specifies the number to order each time
Easily understood, but does not minimize costs
Order “n” periods supply
Order enough to satisfy future demand for a given period
of time.
3
Order Quantities
Economic Order Quantity (EOQ)
The EOQ is based on assumptions:
Demand is relatively constant and known
The item is produced or purchased in lots or batches
Order preparation costs and inventory carrying costs are
constant and known
Replacement occurs at once
Assumptions usually valid for finished goods
whose demand is independent and uniform.
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Order Quantities
A Model of Inventory
200
100
Q = Lot Size
1
2
3
4
Time (weeks)
5
Example: Average Inventory
and Number of Orders
Q: The annual demand for an SKU is 6,750 units, and it is ordered in
quantities of 450 units. Calculate the average inventory and the number of
orders placed per year.
A:
Average inventory = order quantity / 2
= 450 / 2
= 225 units
Number of orders per year = annual demand / order quantity
= 6,750 / 450
= 15
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Order Quantities
EOQ Costs
Annual cost of placing orders
Annual cost of carrying orders
Total Cost
Ordering Costs
Carrying Cost
Lot Size
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Order Quantities
EOQ Formula
Carrying costs = Ordering costs
Qic / 2 = AS / Q
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Order Quantities
EOQ Formula
Q2 =
2AS
ic
or
Q
=
2AS
ic
where Q = Economic Order Quantity
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Example: EOQ
Q: An item has a annual demand of $10,000, carrying costs of 15% per
order, and ordering costs of $50. What is the EOQ in dollars?
A:
A = Annual usage in dollars = $10,000
S = ordering cost in dollars = $50
i = carrying cost rate as a decimal of a percent = 15% = 0.15
Therefore -
EOQ = 2AS / i
= (2 x 10000 x 50) / 0.15
= $2,582
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Order Quantities
Costs and Lot Size
EOQ will increase as annual demand and ordering
costs increase.
EOQ will decrease as carrying costs and unit costs
increase.
The cost of ordering is either the cost of placing a
purchase order or the cost of placing a
manufacturing order.
The cost of a manufacturing order includes production
control costs and setup costs.
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Order Quantities
Quantity Discounts
A discount given by a supplier on orders over a
certain size.
When deciding whether to accept a discount the
total cost must be considered including:
Purchase costs
Ordering costs
Carrying costs
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Order Quantities
EOQ When Costs Are Not Known
Many times the costs are not known or easy to
determine
The ordering and carrying costs are generally the
same for each item in a family
Use an approach to arrive at an average of “K” to
reduce the total cost of inventory
Where K = SQRT(Ad)/N
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Order Quantities
Period Order Quantity
When demand is not uniform the EOQ may not
produce the lowest total cost
The POQ uses the EOQ to calculate an economic
time between orders
Orders are placed to satisfy requirements for the
calculated time period
POQ = EOQ/Avg. weekly usage
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Order Quantities
Miscellaneous Considerations
Lumpy Demand
The EOQ assumes that demand is fairly uniform
Determining Costs
The EOQ model is relatively robust with respect to cost
estimates
Minimum Orders
Some suppliers require a minimum order quantity
Often “C” items where plenty is ordered not EOQ
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Example # 10.4, pg. 271. . .
Q. A company wishes to establish an EOQ for an item for which the
annual demand is $800,000, the ordering cost is $32, and the cost of
carrying inventory is 20%. Calculate the following:
a. The EOQ in dollars.
A = $800,000
EOQ = 2AS/i
S = $32
i = 20%
= (2 x 800,000 x 32)/.2
EOQ = $16,000
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Example # 10.4, pg. 271. . .
b. Number of orders per year
Number of Orders = A / Q = 800,000 / 16,000 = 50
c. Cost of ordering, cost of carrying inventory, and total cost.
Cost of Ordering = AS / Q = (800,000 X 32) / 16,000 = $1600
Cost of Carrying = QiC / 2 = (16,000 X 0.2) / 2 =
$1600
Total Cost = $3200
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Next Week. . .

Work the following:
– 10.1
– 10.2
– 10.3
– 10.10
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