Economic Order Quantity

The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding inventory (TC).

Economic Order QuantityAssumptions

Demand (D) is known and constant H is known and constant Order costs (S) are constant The order quantity arrives in a

single shipment No quantity discounts are available All demand will be met (no

shortages)

We want to minimize TC D, S, and H are constant. TC is a function of Q.

1

2 2

D Q HTC S H DS Q

Q Q

Economic Order Quantity (3)

* 2DSQ

H

*

* 2

D QTC S H

Q

Let Q* be the economic order quantity. Then

For Q*, annual order cost = annual inventory cost

*

* 2

D QS H

Q

Simple Reorder Point

Use this method when daily demand is constant.

R = reorder point d = daily demand (may have to

compute this) L = lead time (Caution: if lead time is

given in weeks, convert this to days). R = dL

Reorder Point with Safety Stock Safety stock (SS) is extra inventory that is

kept to meet unexpected demand.

Reorder point withoutsafety stock

Reorder pointwith safety stock

Reorder Point with Safety Stock (2)

How much safety stock (SS) ?

Reorder point with safety stock: Service level is the probability of having

enough inventory to meet demand during lead time

The probability of a stockout is (1 - service level)

Demand during lead time is normally distributed with mean and standard deviation dL

SSLdR demanddaily average d

Ld

Reorder Point with Safety Stock (2)

How much safety stock (SS) ?

z is the number of standard deviations required to meet the desired service level

SS = zdL

Reorder point with safety stock: R = +

zdL

Ld

Reorder Point with Safety StockExample

Given D = annual demand = 10,000 N = number of business days per year = 250 The company operates 5 days per week = average daily demand dL = standard deviation of demand during lead

time = 20 L = lead time = 1 week Service level = 96%Find: reorder point with safety stock: R = + zdL

Ld

d

Computing Reorder Point with Safety Stock

1. If average daily demand ( ) is not given, compute it.Note: = D/N and D = = 10,000/250 = 40

2. If the lead time is given in weeks or months, compute lead time in days.L = 1 week = 1(5) = 5 daysNote: 1 week is the number of days per

week that the company operates. This may be 5, 6, or 7.

d

d

d dN

Computing Reorder Point with Safety Stock (2)

3. Find the z value for the service level (96%)

Probability of a stockout =1 – servicelevel = 4%

z

50% 46%

Ld

Appendix B givesthis area.

Computing Reorder Point with Safety Stock (3)

3. Find the z value for the service level (96%) (cont.)(a) Write the service level as a decimal

96% = 0.9600(b) Subtract 0.5000 from the service level

0.9600 – 0.5000 = 0.4600(c) Use the table in Appendix B, page 652, to

find the area that is closest to 0.4600The closest area in the table is 0.4599, which occurs when z = 1.75Use z = 1.75

Computing Reorder Point with Safety Stock (4)

4. Compute R

R = L+ zdL

= 40(5) + 1.75(20) = 200 + 35 = 235

Note: If the computation gives a fractional value, round up to nearest integer.

Example: Computed R = 210.2 R = 211

d

Economic Production Quantity

Key question: How many units of a part or product should be made at one time?

The economic production quantity (EPQ) is the production quantity (lot size) that minimizes the total annual cost of setups and holding inventory.

Economic Production Quantity (2)

Notation

Q = Amount to make (lot size) D = annual demand for the item d = daily demand for the item p = daily production rate S = cost of one setup H = inventory holding cost per unit per year

(commonly called holding cost) TC = annual cost of setups

+ annual cost of holding inventory The EPQ is the quantity that minimizes TC

Economic Production Quantity (3)Assumption: Daily demand < daily production. When the item is being made, some is sold or used to make a product. The remainder goes into inventory. When production stops, the inventory is used until there is no inventory left. Then production resumes.

Ending inventory= beginning inventory+ production- sales or usage

Economic Production Quantity (4)

Length of production run = Q/p During production, d units are sold or used each day. (p

– d) units go into inventory.

p

dQdp 1)(

p

QIMAX

Maximum inventory:

Total cost:

H

2

IS

Q

DTC MAX

EPQ

Economic productionquantity (EPQ):

p

d1H

2DSEPQ

EOQ vs. EPQ When to use economic order quantity

(EOQ): Demand is independent Compute how much to order (order quantity)

When to use economic production quantity (EPQ): Parts or products will be produced: demand

is dependent Compute how much to make at one time

(production lot size)