The eoq model

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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





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

Business

The eoq model