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
Order (Setup) CostOrder (Setup) Cost
EOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost
Holding CostHolding Cost
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
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?
Order Quantity
To
tal C
ost
BasePrice
Disc.
Price 1Disc
Price 2
Disc.Qty. 1
Disc. Qty. 2
EOQ with Quantity Discounts
$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
EOQ with Quantity Discounts
$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
EOQEOQ Disc.Qty. 1
Disc. Qty. 2
EOQ with Quantity Discounts
$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
EOQEOQ
Outside of Outside of Price Price
BracketBracket
Disc.Qty. 1
Disc. Qty. 2
EOQ with Quantity Discounts
$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
EOQ with Quantity Discounts
$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
Outside of Outside of Price Price
BracketBracket
Outside Outside of Price of Price BracketBracket
EOQ with Quantity Discounts
$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
Outside of Outside of Price Price
BracketBracket
Outside Outside of Price of Price BracketBracket
EOQ with Quantity Discounts
$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
EOQ with Quantity Discounts
$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
Outside Outside of Price of Price BracketBracket
EOQ with Quantity Discounts
$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
Outside Outside of Price of Price BracketBracket
EOQ with Quantity Discounts
$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 with Quantity Discounts
• 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
EOQ with Quantity Discounts
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
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