Post on 15-Apr-2017
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THE EOQ MODELHASNAIN BABERASSISTANT PROFESSOR
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2SOME BASIC DEFINITIONS
An INVENTORY is an accumulation of a commodity that will be used to satisfy some future demand.
Inventories may be of the following form:- Raw material- Components (subassemblies)- Work-in-process- Finished goods- Spare parts
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3EOQ History• Introduced in 1913 by Ford W. Harris, “How Many Parts to Make at
Once”
• Interest on capital tied up in wages, material and overhead sets a maximum limit to the quantity of parts which can be profitably manufactured at one time; “set-up” costs on the job fix the minimum. Experience has shown one manager a way to determine the economical size of lots.
• Early application of mathematical modeling to Scientific Management
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4EOQ MODELING ASSUMPTIONS
1. Production is instantaneous – there is no capacity constraint and the entire lot is produced simultaneously.
2. Delivery is immediate – there is no time lag between production and availability to satisfy demand.
3. Demand is deterministic – there is no uncertainty about the quantity or timing of demand.
4. Demand is constant over time – in fact, it can be represented as a straight line, so that if annual demand is 365 units this translates into a daily demand of one unit.
5. A production run incurs a fixed setup cost – regardless of the size of the lot or the status of the factory, the setup cost is constant.
6. Products can be analyzed singly – either there is only a single product or conditions exist that ensure separability of products.
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T
Q
Time
InventoryMAX
Reorder
MINBuffer stock
Safety stock
EOQ Model
Order Quantity
Annual Cost
Order Quantity
Annual Cost
Holding Cost
EOQ Model
Why Order Cost Decreases
Cost is spread over more units
Example: You need 1000 microwave ovens
Purchase OrderDescription Qty.Microwave 1000
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
1 Order (Postage $ 0.35) 1000 Orders (Postage $350)
Order quantity
Order Quantity
Annual Cost
Holding CostOrder (Setup) Cost
EOQ Model
Order Quantity
Annual Cost
Holding Cost
Total Cost Curve
Order (Setup) Cost
EOQ Model
Order Quantity
Annual Cost
Holding Cost
Total Cost Curve
Order (Setup) Cost
Optimal Order Quantity (Q*)
EOQ Model
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• Holding cost per unit time =
2
levelinventory Average Qhh
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Industrial Managem
ent - THE EOQ MODEL
16THE AVERAGE ANNUAL COST CURVE
unit timecost
Q
2hQG(Q)
QDS *
Q*
Annual fixed ordering and holding cost
The minimum
EOQ Formula DerivationD = Annual demand (units)C = Cost per unit ($)Q = Order quantity (units)S = Cost per order ($)I = Holding cost (%)H = Holding cost ($) = I x C
Number of Orders = D / QOrdering costs = S x (D / Q)
Average inventory units = Q / 2 $ = (Q / 2) x C
Cost to carry average inventory = (Q / 2) x I x C = (Q /2) x H
Total cost = (Q/2) x I x C + S x (D/Q) inv carry cost order cost
Take the 1st derivative:
d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q²
To optimize: set d(TC)/d(Q) = 0
DS/ Q² = IC / 2
Q²/DS = 2 / IC
Q²= (DS x 2 )/ IC
Q = sqrt (2DS / IC)
D = Annual demand (units)S = Cost per order ($) C = Cost per unit ($) I = Holding cost (%)H = Holding cost ($) = I x C
Economic Order Quantity
HSDEOQ
2
EOQ Model Equations
Optimal Order Quantity
Expected Number Orders
Expected Time Between Orders Working Days / Year
Working Days / Year
Q D SH
N DQ
TN
d D
ROP d L
*
*
2
D = Demand per yearS = Setup (order) cost per orderH = Holding (carrying) cost d = Demand per dayL = Lead time in days
EOQ Example
You’re a buyer for SaveMart. SaveMart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is 40% of per unit cost. Lead time is 5 days. SaveMart is open 365 days/yr.
What is the optimal order quantity & ROP?
SaveMart EOQ
HSDEOQ
2
20.31$100$10002
EOQD = 1000S = $100C = $ 78 I = 40%H = C x IH = $31.20
EOQ = 80 coffeemakers
SaveMart ROPROP = demand over lead time = daily demand x lead time (days) = d x l
D = annual demand = 1000Days / year = 365Daily demand = 1000 / 365 = 2.74Lead time = 5 days
ROP = 2.74 x 5 = 13.7 => 14
Avg. CS = OQ / 2 = 80 / 2 = 40 coffeemakers = 40 x $78 = $3,120
Inv. CC = $3,120 x 40% = $1,248
Note: unrelated to reorder point
SaveMart Average (Cycle Stock) Inventory