1. Inventory: Stable Demand
Dr. Ron Lembke

2. Economic Order Quantity
Assumptions
Demand rate is known and constant
No order lead time
Shortages are not allowed
Costs:
S - setup cost per order
H - holding cost per unit time

3. EOQ Decrease Due to Inventory Constant Demand Level Q* Instantaneous
Optimal
Order
Quantity
Instantaneous
Receipt of Optimal
Order Quantity
Average
Inventory Q/2
Time

4. Total Costs Average Inventory = Q/2 Annual Holding costs = H * Q/2
# Orders per year = D / Q
Annual Ordering Costs = S * D/Q
Annual Total Costs = Holding + Ordering

5. How Much to Order? Total Cost = Holding + Ordering Annual Cost
Ordering Cost
= S * D/Q
Holding Cost
= H * Q/2
Optimal Q
Order Quantity

6. Optimal Quantity Total Costs = Take derivative with respect to Q =
Set equal
to zero
Solve for Q:

7. EOQ
Inventory
Level Q*
Reorder
Point
(R)
Time
Lead Time

8. Adding Lead Time Use same order size Order before inventory depleted
Where:
= demand rate (per day)
L = lead time (in days)
both in same time period (wks, months, etc.)

9. A Question:
If the EOQ is based on so many horrible assumptions that are never really true, why is it the most commonly used ordering policy?
Cost curve very flat around optimal Q, so a small change in Q means small increase in Total Costs
If overestimate D by 10%, and S by 10%, and H by 20%, they pretty much cancel each other out
Have to overestimate all in the wrong direction before Q affected

10. Sensitivity Suppose we do not order optimal Q*, but order Q instead.
Percentage profit loss given by:
Should order 100, order 150 (50% over):
0.5*( ) =1.08 an 8%cost increase

11. Quantity Discounts

12. Quantity Discounts- Price Break
How does this all change if price changes depending on order size?
Holding cost as function of cost:
H = i * C
Explicitly consider price:

13. Discount Example
D = 10,000 S = $20 i = 20% Price Quantity EOQ C = 5.00 Q < Q >=
Must Include
Cost of Goods:

14. Discount Pricing X 633 X 667 X 716 Total Cost C=$5 Price 1 Price 2
,000
Order Size

15. Discount Example
Order 667 at a time: Hold 667/2 * 4.50 * 0.2= $ Order 10,000/667 * 20 = $ Mat’l 10,000*4.50 = $45, , Order 1,000 at a time: Hold 1,000/2 * 3.90 * 0.2= $ Order 10,000/1,000 * 20 = $ Mat’l 10,000*3.90 = $39, ,590.00

16. Excel graph of costs

17. Discount Model 1. Compute EOQ for next cheapest price
2. Is EOQ feasible? (is EOQ in range?)
If EOQ is too small, use lowest possible Q to get price.
3. Compute total cost for this quantity
Repeat until EOQ is feasible or too big.
Select quantity/price with lowest total cost.

18. Laundry soap prices - 2012 $9.99 129 oz. $0.077 $4.99 51 oz. $0.0978
$8.99
103 oz.
$0.087
$6.99
77 oz.
$/oz
savings
$0.091 7%
4.4%
11.5%

19. Value Pack - 2015 Regular: Value Pack
$1.88 for oz = $0.178 per ounce
Value Pack
$2.98 for oz = $0.188 per ounce
5.6% higher price!

20. Triscuits - 2015 $1.98 8 oz. $0.2475 $3.88 12 oz. $0.323 $/oz
30% higher price!

21. Goldfish - 2015 $2.97 11 oz. $0.270 $1.97 6.6 oz. $0.298 $6.48 30 oz.
$0.216
$/oz
savings
9.4%
20%

23. Summary Economic Order Quantity Discount Model
Perfectly balances ordering and holding costs
Very robust, errors in input quantities have small impact on correctness of results
Discount Model
Start with EOQ calculations, using H= iC
Compute EOQ for each price,
Determine feasible quantity
Compute Total Costs:
Holding, Ordering, and Cost of Goods.