OMSAN LOJİSTİK. Optimum Quantities for Procurement (Replenishment Methods) Procurement and Supplier Relationship Management Latin America Logistics Center

OMSAN LOJİSTİK

Optimum Quantities for Procurement(Replenishment Methods)

Procurement and Supplier Relationship Management

Latin America Logistics Center

Logistics Management Series

EOQ: Efficient Order Quantity

• Is the Analytical Calculation of Optimum Quantities to Replenish in any point within the Network

• Suppliers

• Production Facilities

• Replenishment to Customers

• Delivery Quantities

Supuestos Basicos del Modelo EOQ

· 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

Partial Period Balance

• Is Ordering in a manner so that Costs of Ordering and Inventory Carrying Costs are kept Equal

Y-A

xis

Order/run Quantity

Total Cost =Ordering Cost +

Inventory Carrying Cost

Inventory CarryingCost

Ordering Cost

Economic OrderQuantities

EOQ CalculationFlat Curve Around Optimum

Economic Production Quantity

0

20

40

60

80

100

120

Dollars

1 2 3 4 5 6 Rolls per run

Carrying costSet-up costTotal Cost

EOQ Trade-off

Order QuantityOrder Quantity

Annual CostAnnual Cost

Holding CostHolding Cost

EOQ Model




Order (Setup) CostOrder (Setup) Cost

EOQ Model




Total Cost CurveTotal Cost Curve

Order (Setup) CostOrder (Setup) Cost

Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)

EOQ Model

EOQ Formula Derivation

D = Annual Demand (units)C = Unit Cost ($)Q = Quantity per Order (units)S = Cost per Order ($)I = Inventory Carrying Rate (%)H = Carrying Cost ($) = I x C

Number of Orders = D / QOrdering Cost = S x (D / Q)

Average Inventory Units = Q / 2 $ = (Q / 2) x C

Average Inventory Carrying Cost= (Q / 2) x I x C

= (Q /2) x H

Total Cost = (Q/2) x I x C + S x (D/Q) carrying cost + ordering cost

Take the 1st derivative:

d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q²

To Optimise: set d(TC)/d(Q) = 0

DS/ Q² = IC / 2

Q²/DS = 2 / IC

Q²= (DS x 2 )/ IC

Q = sqrt (2DS / IC)

Efficient Order Quantity

• EOQ = [(2*S*D)/(I*C)] 1/2

• EOQ = Economic Order• S = Cost to place one order ($/order)• D = Annual Demand (units/yr)• I = Inventory Carrying Rate (%/yr)• C = Unit Cost ($/unit)

EOQ: Equations of the Model

Optimum Quantity

Number of Orders N*

Time Between Orders

/

QD SH

DQ

TN

dD

ROP d L

*

*

2

D = Annual Demand

S = Setup Cost (order)

H = Inv. Carrying Cost

d = Demand per Day

L = Lead Time (days)

Working Days Year

/Working Days Year

EOQ Example

You are the buyer of SaveMart Stores. SaveMart needs 1000 coffee makers per year. The cost of each coffee maker is $78. The cost to place one order is $100. Inventory carrying rate is 40%. The Lead Time is 5 days. SaveMart opnes 365 days/yr. What is the Economic Order Quantity (EOQ) and the Reorder Point (ROP)?

×

Solution EOQ*

( )( )( )( )( )

( )( )

QD SH

dD

ROP d L

*.

.

. .

=× ×

= =

= = =

= = =

2 2 100010040 78

80

1000365

274

274 5 137

unidades

unidades/day

unidades

/Dias Laborales Año

Cost to Place one Purchase Order

• Stationery• Deliver the PO• Communications• Authority• Entering the PO• Processing the PO

• Inspecting the PO• Tracking the PO• Staff Procurement Dept. • Office Space• Materials

Supply Costs

Automatic Calculation of EOQ

Ordering Cost Reduction

• Blanket Orders (Fixed Quantity Order)• Joint Replenishment Cycles• Procurement Cards• Vendor Managed Inventory (VMI)• Delivery Programs• Anticipated Supply Notice (ASN)• JIT II Supplier puts the order from the

Customer’s Warehouse• Orders via Internet

Set-Up Cost Reduction

• Parallel Process (Indy Cars)• Just in Time (Toyota)• Internal Separation / Interruption for External

Requirements• Minimise Internal Interruption Requirements• Sequential work to reduce change cycles• Set-Up cost elimitation with Dedicated Lines• Dedicated Factories• Practice and Experience• Minimise Equipment Brands vs the Lower Bid Cost

Adjusting the EOQ

• Space Available in Warehouse

• Number of Orders that Can be Processed

• Budget Constraints

• Quantity Discounts

EOQ with Quantity Discounts Example

You are the Buyer of SaveMart Stores. You typically buy a Soft drink in cases of 24 bottles. Demand is 10 cases per week. The supplier charges $60/case but offers a discount of 1% for orders greater than 100 cases and an additional discount of 1% for orders greater than 150 cases ($60/case in orders smaller than 100 cases, $58.81 in orders greater than 150 cases and $59.40 in orders between 100 y 150 cases).

The cost to place one order is $100. The inventory carrying rate is 40%. What is the Optimal Order Quantity?

To

tal C

ost

Order Quantity

EOQ with Quantity Discounts

Order Quantity

To

tal C

ost

Disc.Qty. 1

BasePrice

Disc.

Price 1


Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc.Qty. 1

Disc. Qty. 2


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Total Cost Total Cost @ Base Price@ Base Price

Disc.Qty. 1

Disc. Qty. 2


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2


EOQEOQ Disc.Qty. 1

Disc. Qty. 2


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2


EOQEOQ

Outside of Outside of Price Price

BracketBracket

Disc.Qty. 1

Disc. Qty. 2


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2

Total Cost Total Cost @ Disc Price@ Disc Price

EOQEOQ Disc.Qty. 1


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2


EOQEOQ Disc.Qty. 1


BracketBracket

Outside Outside of Price of Price BracketBracket


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2


EOQEOQ Disc.Qty. 1


BracketBracket



$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2

Total Cost @ Total Cost @ Disc Price 2Disc Price 2

EOQEOQ Disc.Qty. 1


$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2


EOQEOQ Disc.Qty. 1



$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2


EOQEOQ Disc.Qty. 1



$32,000

$32,250

$32,500

$32,750

$33,000

$33,250

$33,500

$33,750

$34,000

0 20 40 60 80 100 120 140 160 180 200

Order Quantity

To

tal C

ost

BasePrice

Disc.

Price 1Disc

Price 2

Disc. Qty. 2

Disc.Qty. 1

Lowest CostLowest Cost



• EOQ =

[(2 x S x D) / (I x (1-d ) x C)]

• d = discount rate

?

• Calculate EOQ for Each Discount Level

• If the Result is not within the offered range?

– If not, buy the quantity at the lower discount limit

• Calculate the Total Cost (order & hold) for each EOQ or the minimum quantity within the discount range

• Select the minimum quantity with the minium Total Cost


Periodic Order Quantity (POQ)• Periodic Order Quantity derives from the

Economic Order Quantity and the Annual Cost

• POQ denotes the optimal time between orders

• POQ = EOQ/AD = Optimal Time Between Orders

Economic Time of Supply (ETS)

ETS = [(2*S)/(D*C*I)]1/2

• Denotes the Optimal time between orders to Suppliers

• Is a Direct function of the Cost to Place a Purchase Order

• Indirect Function of Annual Demand, Inventory cost and its carrying rate

Economic Logistics Quantity (ELQ)

• ELQ = EOQ +/-– Considerations of Warehousing Capacity– Transportation Capacity– Quantity and Capacity of Pallets– Agreed Quantities– Packing Quantities– etc.

Coordinated and Consolidated Deliveries

• Savings in Purchasing Costs

• Savings in Transportation Costs

• Savings in Ordering Costs

• Easy to Schedule

Optimising EOQ by SKU

Documents

OMSAN LOJİSTİK. Optimum Quantities for Procurement (Replenishment Methods) Procurement and Supplier Relationship Management Latin America Logistics Center