1. OMSAN LOJİSTİK

2. Economic Order Quantity ‘EOQ’
Inventory Planning and Management
Latin America Logistics Center
Logistics Management Series -

3. Economic Order Quantity
EOQ

4. Economic Order Quantity
Assumptions
Constant Demand Rate
No Constraints on Lot Size
Only relevant costs are holding and ordering/setup
Decisions for items are independent from other items
No uncertainty in lead time or supply.

5. Economic Order Quantity
Receive
Order
Inventory Depletion (demand rate) Q
On-Hand Inventory (Units)
Average
Inventory Q — 2
1 cycle
Time

6. Economic Order Quantity
3000 —
2000 —
1000 —
0 —
Total Cost = ICC + OC
Annual Cost (dollars)
Inventory Carrying
Cost Q 2 =
x C x I D Q
Ordering Cost = x (S)
| | | | | | | |
Lot Size (Q)

7. Exercise
A Company sales 18 units per week of a product that costs $60 and the Inventory Carrying Cost 25%. Ordering cost is $45. Currently lot size is 390 units.
Calculate Total Inventory Costs.

8. Exercise (cont.) D = 18 units/week x 52 weeks/year = 936 units/year
ICC = 390/2 x 60 x 0.25 = 2925 $/year
OC = 936/390 x 45 = 108 $/year
TC = = 3033 $/year

9. Economic Order Quantity
3000 —
2000 —
1000 —
0 —
3033 $
Annual Cost (dollars)
| | | | | | | |
Q=390
Lot Size (Q)

10. Optimizing Equalizing Inventory Carrying Costs with Ordering Costs
ICC = OC
Q/2 x C x I = D/Q x S
Q2 = (2 x D x S) / (C x I)

11. EOQ = 75 Units

12. Costs
ICC = 75/2 x 60 x 0.25 = $/year
OC = 936/75 x 45 = $/year
TC = = 1125 $/year
Savings = 3033 – 1125 = 1908 $/year

13. Economic Order Quantity
3000 —
2000 —
1000 —
0 —
3033 $
Annual Cost (dollars)
1125
| | | | | | | |
Q=390
EOQ
Lot Size (Q)

14. Outcomes Parameters Initial Optimum Demand ‘D’ (Units/year) 936
Unit Cost ‘C’ ($) 60
Inventory Carrying Rate ‘I’ (%)
25%
Purchase Order Cost ‘S’ ($) 45
Lot Size (Units/order)
390 75
Number of orders/year (orders)
2.4
12.5
Time between orders (days)
150 29
Average Inventory Level ‘AIL’ (Units)
195
37.5
Ordering Cost ‘OC’ ($/year)
108
562.5
Inventory Carrying Cost ‘ICC’ ($/year)
2,925
Total Cost ‘TC’ ($/year)
3,033
1,125
Savings ($/year)
1,908

15. Variable Demand How much demand? When to order? How much?
How much Safety Stock?
What Fill Rate?
What are the Lead Times?

16. Continuous Review Model (Q)
Order
received
Orde
received
Order
received
Order
received Q Q Q
On-Hand Inventory R
Orden
colocada
Orden
Colocada
Orden
colocada L1 L2 L3
TBO1
TBO3
TBO2
Time

17. Reorder Point (R) Fill Rate = 85% Stock-out Probability
(1.0 – 0.85 = 0.15) = 15%
Average Demand during Lead Time R
zL

18. Reorder Point R = m + s Where:
R = Minimum Inventory Level to Place a New Order (Reorder Point)
m = Average Inventory during Lead Time
s = Safety Stock during Lead Time
s = z x σ
σ = Standard Deviation of Demand
z = f(Fill Rate)

19. Standard Deviation of Lead Time
225
Demand during 3 weeks Lead Time + 75
Demand week 1
st = 15 + 75
Demand week 2
st = 15 = 75
Demand week 3

20. Exercise
A supermarket sell a product with the following characteristics:
D=200 boxes/day
L=4 days (Lead Time)
σ=150 boxes/day
Fill Rate (planned) 95%
S=20 $/order
i=20%/year
C=10 $/box

21. Exercise (cont)
Calculate the Inventory Planning Parameters for a Continuous Review System “Q”

22. Periodic Review System (P)IP IP
Order
received IP
Order
received
Order
received Q3 Q1 OH OH Q2
IP1
IP3
IP2
On-Hand Inventory
Order
placed
Order
placed L
Time P
Protection Interval

23. Target Inventory T = m’ + s’ Where:
T = Target Inventory at the moment of placing the order
m’ = Service Stock for Lead Time and Review Period
s’ = Safety Stock for Lead Time and Review Period

24. Exercise
For the Previous Exercise Calculate the Inventory Planning Parameters for a Period Review System “P”

25. Comparison of P & Q Systems
Parameter
Continuous Review (Q)
Periodic Review (P)
Ordering Cost
Number of orders/year
Average Inventory Level
Safety Stock
Fill Rate
Inventory Carrying Cost