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