35A00210Operations Management

Lecture 13Inventory control

Basics of inventory controlInventory models• continuous review

• periodic review• other models

Lecture 13Inventory control

Basics of inventory control

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Inventory control is boring butimportant

Operations try to meetcustomer requirements!

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Inventory management decisions

Howmuch?

When?

What?

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Sales influences inventorymanagement - ABCD -classification -

There are differences between products on howimportant they are to the company

- sales, number of customers, profit potential, invested capital, stock-out cost,criticality etc. products should be managed differently

- ABCD-classification divides products in 4 categories based on sales

A and B -products objective high turnover and goodservice levels

- strict control, continuous review (A) and periodic review (B), regularreplenishment (variable lot size) and small delivery batches

C and D -products objective to minimize economicburden

- periodic review and 2-bin system, reducing number of products, minimizingfulfillment costs, safety stocks

Classification only considers sales- no life-cycles, criticality, strategic importance etc. considered

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Not all products are equal

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improveturnover

watchstock-out

do something or drop

Objectives influence inventorymanagement

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• Low price• High discounts•Medium margin• Medium turns

• Medium price• No discounts• High margin• High turns

• High price• No discounts

• Medium margin• Low turns

Set high service levelsInvest in inventory

Improve forecasting

Minimizeextras

Maximizevolume

Minimizeinventory

costs

Swatch Citizen Rolex

Set lower service levelsInvest in “central depot”

stock locationReplenish/ transfer among

locations

Do market testing andresearch at beginning

Use also central warehousingUse early sales data to

reorder / cut back

Lecture 13Inventory control

Inventory models

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Prod

ucts

inin

vent

ory

Time

Q

Inventory control simple in theory

One product, level demand, fixed delivery timeetc.

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There are varied inventory controlmodels

Number and nature ofproducts

- one vs. many products- non-perishable vs. perishable

Type of demand- constant, random, unknown

demand- stationary- vs.- non-stationary model- back-order vs. losing orders

Inventory control model- continuous vs. periodic review

Nature of deliveries- immediate, delayed, gradual,

occasional replenishment

Time horizon- one period, several periods,

infinite time horizon

Number of warehouses- one, parallel, network of

warehouses

Nature of costs/expenses- average cost, present value of

costs etc.

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Basic inventory control models

Continuous review (Q) system- time between orders varies, lot size is fixed

- economic order quantity- volume discounts- economic production lot size

- requires continuous inventory control!- became more popular lately due to improved computerized solutions and

lower prices (e.g. bar code, point-of-sale, voice recognition)

Periodic review (P) system- time between orders is fixed, lot size varies- is based on periodic inventory control

- still the more used control method

Other systems- e.g. bin systems

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Basic models are opposites ofeach other

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Continuous review systemIn continuous review orders of fixed size are made after periodswith variable length

- central questions: order quantity, timing of the order, pursued service level, size ofsafety stock

- requires a lot especially from inventory IT systems as balances have to be correct allthe time

- instructing and motivating employees very important

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Time

Orderpoint

R

Inventory

lead time

orders

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Cos

ts

Ordering/set up costs

Economicorder quantity

Trade-off between costs- economic order quantity -

Size oforder quantity

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Order

Order

Larger order quantity meansmore products to be inventoried

Smaller order quantitymeans more orders

Shape of cost functions andcommon sense

Ordering costsC

osts

Size oforder quantity

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EOQ depends onthe size of cost components

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3 orders andhigher average inventory

5 orders andlower average inventory

averageinventory

averageinventory

vs.

Calculating EOQ

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1. Determine ordering costs (not necessarily easy)

2. Determine holding costs (not necessarily easy)

3. Calculate EOQ

Determining reorder point in EOQ-model - R = dL -

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Inventory

Time

LotsizeQ

Reorderpoint

R

Lead timeL

demand during lead time

usage rate d

order-moment

deliverymoment

Order EOQ volume wheninventory drops to reorder point

EOQ example

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Sam’s Cat Hotel needs a lot of kitty liter to operate. Hotel entrepreneur purchaseslitter at the price of $11,70/bag and average demand is 90 bags per week. Ordering

cost has been estimated to be $54 per order and annual holding cost 27% frompurchasing costs. Delivery lead time is currently 3 weeks (18 work days). Hotel usescontinuous review inventory system and is open around the year (52 weeks, 6 daysa week). Calculate economic order quantity, time between orders, reorder point and

total annual costs.

Order quantity:

Time betweenorders:

Reorder point:

aver. inventory200 units

11,7 orders per year

Total costs:

Notice:EOQ -formula’s unitsmust be remembered!

EOQ example

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EOQ’s sensitivity analysis

Close to EOQ volume the total costs function israther flat

- impact of wrongly estimating the cost variables rather small- especially to the right from EOQ (larger lot size) the total costs

increase only slowly

Impact of different cost variables’ change tototal costs can be seen from the formula

- increase in demand increases lot size- increase in ordering costs increases lot size- increase in holding costs decreases lot size

- increase in interest rate decreases lot size- increase in unit price decreases lot size

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EOQ -models main assumptions

Demand is constant and known- demand is fulfilled from inventory; no stock-outs, no back

orders and no uncertainty what so ever

Lead time is constant and knownProducts’ unit price is fixed

- no volume discounts

Deliveries are complete lots- single delivery, no constraints on size of each lot

Limited cost functions- only cost are ordering and holding; ordering assumed to

be fixed and holding is based on average inventory

Products independent from each other

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Howrealistic

arethese?

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Demand is seldom stable and stock-out costcan be the highest cost variable

- service level thinking eases optimization- higher service level means higher safety stock

S

Demand

Service level (z L )

P(Stockout)

Prob

abili

ty

BA CTime

Inventory

A

B

Cordermoment

deliverymomentlead time

orderpoint

R

Safety stock (S)

Lot size

Manager’sdecision

EOQ -models extensions- variability in demand -

Lower order quantity often leads tolarger safety stock!

Distribution of demandduring lead time

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Standard deviation ofdelivery lead time’s demand

t = 15

+90 units

Week 1demand

t = 15

90 units

Week 2demand

t = 15

90 units

Week 3demand

+

=

270 units

Weeks 1-3demand

t = 26

delivery leadtime

lead time’sst. deviation

one “periods"st. deviation

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Safety stock example

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Use of kitty liter in Sam’s Cat Hotel is not totally steady. Due to liter’s criticalityentrepreneur wants to be prepared also for higher consumption levels. Desired

service level has been estimated to be 80%. Standard deviation of weekly demandhas been estimated from historical data to be 15 bags per week. How do safety

stocks change key inventory management numbers?

400 units and 4,44 weeks(stays the same)

from normal distribution

delivery lead time

+69,50per year

safetystock:

22 bags

Order quantity andtime between orders:

Reorder point:

Total costs:

Safety stock example

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Unfortunately there is variability also in deliverylead times

Time

Inventory

AB

C

ordermoment

expecteddeliverymomentlead time

orderpoint

RSafety stock (S)

Lot size

EOQ -models extensions- variability in delivery lead times -

STime

Like

lyho

odA C

Distribution of lead time

B

Decreasing the variably in lead times can be moreadvantageous than cutting the lead times themselves

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Ordering cost

Purchasing price

Holding cost

Order size

Total cost:

Cos

tsEOQ -model extensions- volume discounts -

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EOQ -models extensions- volume discounts -

Order size

Tota

lcos

ts

Base price 1. discount 2. discountTotal cost.base price

Total cost1. discount

Total cost2. discount

Order sizes with which ordersare feasible

2’1’

P

1

2

Lowest cost not in the area ofminimum discount volume

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2’1’

P

Lowest costs in this case by ordering thisamount every time

Order size

Tota

lcos

ts

Base price 1. discount 2. discountTotal cost.base price

Total cost1. discount

Total cost2. discount

EOQ -models extensions- volume discounts -

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A baseball-team is trying to decide the size of an order from the manufacturer. To make ananalytical decision, team’s purchaser has been going around the organization and collectedinformation he needs to make the order quantity decision. The total demand is 208 bats peryear, the order cost is $70 per order, and the annual holding cost per bat per year is 38% of

the purchase price. The bat selling company has priced its product in the following way:order 1-11 at $54,00 per bat, order 12-143 at $51,00 per bat, and in larger orders the price is

$48,50 per bat. How many bats should purchaser order?

Volume discount example

Price 54,00: EOQ= (2*208*70)/(54,00*38%)= 37,7 order EOQ - 38

Price 51,00: EOQ= (2*208*70)/(51,00*38%)= 38,7 order EOQ - 39

Price 48,50: EOQ= (2*208*70)/(48,50*38%)= 39,7 must order at least 144

cheapest

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Volume discount example

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EOQ -model extensions- noninstantaneous replenishment -

Inventory can also be replenished gradually duringsome period (not everything at the same time)

- very practical in production environments- e.g. consecutive steps in the production process or vertical integrated company

with it’s own sales outlets (so both producer and reseller)- practical also in some other situations

- e.g. order is sent in portions immediately at the rate fulfillment (Amazon)

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Time

build up rate= (p-d)

demand rate = d

Inventory

Productionperiod

Productionperiod

Imax

production quantity

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Economic Lot Sizing (ELS)exampleVertically integrated carpet company produces popular Super Shag model.

Management accounting shows that SS models holding costs are about0,75 pounds per meter per year and ordering costs are 150 pounds (=setup cost). SS’s demand has been forecasted to be 10 kilometers per year.

Production factory is operating six days a week (just as stores) (311 days ayear), deliveries are daily and SS’s production speed is 150 meters per day.

Calculate Super Shag carpet’s economic lot size, number of orders peryear, how long it takes to produce each batch, maximum inventory level,

and total inventory costs.

Lot size:

10,000/311

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ELS example

Number of orders per year:

Production time: Maximum inventory:

Total costs:

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ELS exampleIf inventory would be refilled

with instantaneous replenishment

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EOQ -model extensions- noninstantaneous replenishment -

Few notes on ELS and EOQ models...- if p is much larger than d, ELS and EOQ are almost equal

- due to slow usage rate the inventory filling resembles EOQ- if p and d are nearly equal, production is less like batch production

and more like a production line- product usage rate is same as production rate, and production is almost

continuous- lowering set up costs lowers the optimal production lot size

- reduced holding costs will also lead to savings- cooperation between companies and standardization of ordering

costs can dramatically decrease the order size ( JIT-production)

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Periodic review system

Periodic review is used because continuousreview is not always economically feasible andtakes too long time

- part of the orders can be done only with fixed intervals- e.g. in grocery stores fixed schedules and routes

- method is also used when several orders to one supplier arecombined

Periodic review increases stock-out risk- requires higher safety stock to guarantee same service level

Demand influences on how much is ordered- e.g. season has to be taken into account

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Periodic review system

In periodic review models orders of variablesize are made after regular time intervals

- central questions are the length of review interval, order quantity,pursued service level and size of safety stock

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Time

Inventory

Order-up-to-level

T

Lead time

Periodic review systems formulas

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Target inventory level:

Order quantity:

safetystock

inventory position(inventory + scheduledreceipts - backorders)

Total costs:

Review interval /time between orders:

Standard deviation of demandduring the protection interval:

demand*(rev.interval+lead time)

(rev.interval+lead time)

Be accurateabout time

units!

stable demandassumed

Periodic review example

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Due to constant hurry Sam’s Cat Hotel is moving to periodic review system.Calculate the inventory review interval, target inventory level, amount to be ordered

if there are 330 bags in the inventory right now, and annual total inventory costs

Target inventory level:

Order quantity:

Total costs:

Review interval / time between orders:

deviationper day

(=15/SQRT(6))

demandper day(=90/6)

lead time(=3w*6 day)

norm.distribution

(80%)

Periodic review example

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Other inventory models- bin systems -

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Two bin system

Full Empty

Order one boxto inventory

One bin system

Order enough to fill upthe box again

e.g. reminder if checkbook,”notify salespeople” in hardwarestore, bottom of label in a bar,

line in the wall