2. SOME BASIC DEFINITIONS
An INVENTORY is an accumulation of a commodity that will be used to
satisfy some future demand.
Inventories may be of the following form:
- Raw material
- Components (subassemblies)
- Work-in-process
- Finished goods
- Spare parts
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3. 3EOQ History
• Introduced in 1913 by Ford W. Harris, “How Many Parts to Make at Once”
• Interest on capital tied up in wages, material and overhead sets a maximum
limit to the quantity of parts which can be profitably manufactured at one
time; “set-up” costs on the job fix the minimum. Experience has shown one
manager a way to determine the economical size of lots.
• Early application of mathematical modeling to Scientific Management
4. EOQ MODELING ASSUMPTIONS
1. Production is instantaneous – there is no capacity constraint and the entire lot is
produced simultaneously.
2. Delivery is immediate – there is no time lag between production and availability to
satisfy demand.
3. Demand is deterministic – there is no uncertainty about the quantity or timing of
demand.
4. Demand is constant over time – in fact, it can be represented as a straight line, so that
if annual demand is 365 units this translates into a daily demand of one unit.
5. A production run incurs a fixed setup cost – regardless of the size of the lot or the
status of the factory, the setup cost is constant.
6. Products can be analyzed singly – either there is only a single product or conditions
exist that ensure separability of products.
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11. Why Order Cost Decreases
Cost is spread over more units
Example: You need 1000 microwave ovens
Purchase Order
Description Qty.
Microwave 1000
Purchase Order
Description Qty.
Microwave 1
Purchase Order
Description Qty.
Microwave 1
Purchase Order
Description Qty.
Microwave 1
Purchase Order
Description Qty.
Microwave 1
1 Order (Postage $ 0.35) 1000 Orders (Postage $350)
Order
quantity
15. 15
• Holding cost per unit time =
2
levelinventoryAverage
Q
hh
16. THE AVERAGE ANNUAL COST CURVE 16
unit time
cost
Q
2
hQ
G(Q)
Q
DS *
Q*
Annual fixed ordering
and holding cost
The minimum
17. EOQ Formula Derivation
D = Annual demand (units)
C = Cost per unit ($)
Q = Order quantity (units)
S = Cost per order ($)
I = Holding cost (%)
H = Holding cost ($) = I x C
Number of Orders = D / Q
Ordering costs = S x (D / Q)
Average inventory
units = Q / 2
$ = (Q / 2) x C
Cost to carry
average inventory = (Q / 2) x I x C
= (Q /2) x H
Total cost = (Q/2) x I x C + S x (D/Q)
inv carry cost order cost
Take the 1st derivative:
d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q²
To optimize: set d(TC)/d(Q) = 0
DS/ Q² = IC / 2
Q²/DS = 2 / IC
Q²= (DS x 2 )/ IC
Q = sqrt (2DS / IC)
18. D = Annual demand (units)
S = Cost per order ($)
C = Cost per unit ($)
I = Holding cost (%)
H = Holding cost ($) = I x C
Economic Order Quantity
H
SD
EOQ
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19. EOQ Model Equations
Optimal Order Quantity
Expected Number Orders
Expected Time Between Orders
Working Days / Year
Working Days / Year
Q
D S
H
N
D
Q
T
N
d
D
ROP d L
*
*
2
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
20. EOQ
Example
You’re a buyer for SaveMart.
SaveMart needs 1000 coffee makers per year.
The cost of each coffee maker is $78.
Ordering cost is $100 per order. Carrying cost
is 40% of per unit cost. Lead time is 5 days.
SaveMart is open 365 days/yr.
What is the optimal order quantity & ROP?
22. SaveMart ROP
ROP = demand over lead time
= daily demand x lead time (days)
= d x l
D = annual demand = 1000
Days / year = 365
Daily demand = 1000 / 365 = 2.74
Lead time = 5 days
ROP = 2.74 x 5 = 13.7 => 14
23. Avg. CS = OQ / 2
= 80 / 2 = 40 coffeemakers
= 40 x $78 = $3,120
Inv. CC = $3,120 x 40% = $1,248
Note: unrelated to reorder point
SaveMart
Average (Cycle Stock) Inventory
