35A00210Operations Management
Lecture 13Inventory control
Basics of inventory controlInventory models• continuous review
• periodic review• other models
Lecture 13Inventory control
Basics of inventory control
OM2013 - 13
Inventory control is boring butimportant
Operations try to meetcustomer requirements!
3 OM2013 - 13
Inventory management decisions
Howmuch?
When?
What?
5
OM2013 - 13
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
6 OM2013 - 13
Not all products are equal
7
OM2013 - 13
improveturnover
watchstock-out
do something or drop
Objectives influence inventorymanagement
OM2013 - 13 9
• 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
OM2013 - 13
Prod
ucts
inin
vent
ory
Time
Q
Inventory control simple in theory
One product, level demand, fixed delivery timeetc.
11
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.
OM2013 - 13 12
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
OM2013 - 13 13
Basic models are opposites ofeach other
OM2013 - 13 14
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
OM2013 - 13 15
Time
Orderpoint
R
Inventory
lead time
orders
OM2013 - 13
Cos
ts
Ordering/set up costs
Economicorder quantity
Trade-off between costs- economic order quantity -
Size oforder quantity
16 OM2013 - 13
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
17
EOQ depends onthe size of cost components
OM2013 - 13 18
3 orders andhigher average inventory
5 orders andlower average inventory
averageinventory
averageinventory
vs.
Calculating EOQ
OM2013 - 13 19
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 -
OM2013 - 13 20
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
OM2013 - 13 21
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
22
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
OM2013 - 13 23
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
OM2013 - 13 24
Howrealistic
arethese?
OM2013 - 13
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
25
OM2013 - 13
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
26
Safety stock example
OM2013 - 13 27
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
28 OM2013 - 13
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
29
OM2013 - 13
Ordering cost
Purchasing price
Holding cost
Order size
Total cost:
Cos
tsEOQ -model extensions- volume discounts -
30 OM2013 - 13
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
31
OM2013 - 13
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 -
32 OM2013 - 13
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
33
OM2013 - 13
Volume discount example
34
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)
OM2013 - 13 35
Time
build up rate= (p-d)
demand rate = d
Inventory
Productionperiod
Productionperiod
Imax
production quantity
OM2013 - 13
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
36 OM2013 - 13
ELS example
Number of orders per year:
Production time: Maximum inventory:
Total costs:
37
OM2013 - 13
ELS exampleIf inventory would be refilled
with instantaneous replenishment
38
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)
OM2013 - 13 39
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
OM2013 - 13 40
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
OM2013 - 13 41orders
Time
Inventory
Order-up-to-level
T
Lead time
Periodic review systems formulas
OM2013 - 13 42
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
OM2013 - 13 43
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
44
Other inventory models- bin systems -
OM2013 - 13 45
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