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OMSAN LOJİSTİK
Economic Order Quantity ‘EOQ’
Inventory Planning and Management
Latin America Logistics Center
Logistics Management Series -
Economic Order Economic Order QuantityQuantity
Economic Order QuantityEconomic Order Quantity
1. Constant Demand Rate2. No Constraints on Lot Size3. Only relevant costs are holding and
ordering/setup4. Decisions for items are independent
from other items5. No uncertainty in lead time or
supply.
Assumptions
Economic Order QuantityEconomic Order QuantityO
n-H
and
In
ven
tory
(U
nit
s)
Time
AverageInventory
Q—2
1 cycle
ReceiveOrder
Inventory Depletion (demand rate)
Q
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total Cost = ICC + OC
Ordering Cost = x (S)DQ
An
nu
al C
ost
(d
oll
ars)
Inventory CarryingCost
Q2
= x C x I
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.
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 = 2925 + 108 = 3033 $/year
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
An
nu
al C
ost
(d
oll
ars)
3033 $
Q=390
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)
CxI
xDxSEOQ
2
• EOQ = 75 Units
25.060
459362
x
xxEOQ
Costs
• ICC = 75/2 x 60 x 0.25 = 562.50 $/year
• OC = 936/75 x 45 = 562.5 $/year
• TC = 562.50 + 532.50 = 1125 $/year
• Savings = 3033 – 1125 = 1908 $/year
Economic Order QuantityEconomic Order Quantity
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
An
nu
al C
ost
(d
oll
ars)
3033 $
Q=390EOQ
1125
Outcomes
Parameters Initial Optimum
Demand ‘D’ (Units/year) 936 936
Unit Cost ‘C’ ($) 60 60
Inventory Carrying Rate ‘I’ (%) 25% 25%
Purchase Order Cost ‘S’ ($) 45 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) 2,925 562.5
Total Cost ‘TC’ ($/year) 3,033 1,125
Savings ($/year) 1,908
Variable Demand
• How much demand?• When to order?• How much?• How much Safety Stock?• What Fill Rate?• What are the Lead Times?
Continuous Review Model (Q)
Time
On
-Han
d I
nve
nto
ry
Orderreceived
Q
Ordencolocada
OrdenColocada
Orderreceived
R
TBO1 TBO2TBO3
L1 L2 L3
Q
Ordencolocada
Q
Orderreceived
Ordereceived
Reorder Point (R)
Stock-out Probability(1.0 – 0.85 = 0.15) = 15%
Fill Rate = 85%
Average Demand
during Lead Time
zL
R
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)
Standard Deviation of Lead Time
t = 15
=
+
+75
Demand week 1
75Demand week 2
75Demand week 3
t = 26
225Demand during 3 weeks Lead Time
t = 15
t = 15
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
Exercise (cont)
• Calculate the Inventory Planning Parameters for a Continuous Review System “Q”
Periodic Review System (P)
Time
On
-Han
d I
nve
nto
ry
IP1
IP3
IP2
Orderreceived
Orderreceived
IP IP
OH OH
Orderplaced
Orderplaced
Q1Q2
Q3
L L LP P
Protection Interval
T
Orderreceived
IP
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
Exercise
• For the Previous Exercise Calculate the Inventory Planning Parameters for a Period Review System “P”
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