Chapter 15
Managing Service Inventory




Reasons to Hold Inventory
Inventory Models
ABC Classification
News Vendor Problem
Focus: Matching Supply with Demand

Demand can vary and is unpredictable.

Supply is inflexible and maybe costly.


Demand < Supply  Impossible to stock
service
Demand > Supply  Customers may not
want to wait
2
1
Who Cares About Inventory?
Acer reported its first-ever quarterly loss yesterday. The
Taiwanese PC maker suffered a net loss of 6.79 billion in
Taiwanese dollars ($234.3 million)
Acer has been hit hard by overestimating demand for its
PCs. It has lost $150 million to get rid of excess inventory.
3
What About a Shortage of Vaccine?
In 2006, Nintendo launched the Wii game console and could not
make enough units to keep up with the demand. Some people
would wait in long lines to purchase scarce units and resell them
online for several hundred dollars over the retail price
4
2
Physical Goods Distribution
5
Reasons to Hold Inventory






In-transit Inventory
Seasonal Inventory
Cycle Inventory
Decoupling Inventory/Buffers
Safety Inventory
Speculative Inventory
6
3
Reasons to Hold Less Inventory





Inventory might become obsolete.
Inventory might perish.
Inventory might disappear.
Inventory requires storage space
and other overhead cost.
Opportunity cost.
7
Inventory Costs

Holding or Carrying cost
Overestimate the demand
storage cost: facility, handling
risk cost: depreciation, pilferage, insurance
opportunity cost

Ordering cost
cost placing an order: preparing, negotiating, receiving and inspection

Shortage costs or Lost Sales
Underestimate the demand
costs of canceling an order or penalty
Annual cost ≈ 20% to 40% of the inventory’s worth
8
4
Review: Inventory Performance
avg. Inventory value = avg. sales × avg. flow time



Cost of Goods Sold
Inventory turn = ___________________
average inventory value
Service level = in-stock probability before the
replenishment order arrives
number of sales
Fill rate = _________________
number of demands
9
Inventory Control Models
Multiple Period Inventory Control
Ordering of general merchandise, supplies
Buyer
Supplier
When to order?
When to deliver?
How many to order?
How many to deliver?
Single Period Inventory Control
Ordering of Fashion items, Airline/Hotel Overbooking
 One-time ordering decision
 No replenishment, inventory are perishable
10
5
Fixed Order Quantity Models
11
Economic Order Quantity
D=annual demand, Q=order quantity, S=setup cost, H=unit holding cost
TC(Q) 
D
Q
S H
Q
2
Total annual cost =ordering cost + holding cost
Economic Order Quantity
Q* 
2 DS
H
d=daily demand L=lead time
Reorder point =dL
Q
dL
What about Safety stock?
L
12
6
13
Inventory Control with Planned Shortage
2
14
7
Inventory Management under Demand Uncertainty
Q model: fixed order quantity
ROP
ROP is the reorder point. Place a new order whenever the
inventory level drops to ROP.
15
Safety Stock

amount of inventory carried in addition to the expected demand,
in order to avoid shortages when demand increases
Service level=probability of no shortage
=P (demand ≤ inventory)
=P(demand ≤ E(D)+safety stock)
safety stock

depends on service level, demand variability, order lead time

service level depends on Holding cost  Shortage cost
16
8
=daily demand
=std dev. of daily demand
ROP  expected demand during L
 safety stock
   L  z  L 
Service level or probability of no shortage
=95% (99%)  z=1.64 (2.33)
17
P model: fixed time period
RP
RP
RP
RP is the review period.
TIL is the target inventory level determined by the
forecasts.
We place an order to bring the inventory level up to TIL.
18
9
Timespan = length of review period + lead time = RP+ L
Target Inventory = expected demand + safety stock
  ( RP  L)  z  RP  L  
Order Quantity = target inventory –
inventory position
19
ABC Classification
dollar usage=usage × cost
Pareto’s 80/20 principle
There are other ways to do ABC classification.
Review ABC classification periodically.
20
10
ABC Classification for Inventory Control and Storage
A  Q model
B  P model with R=1 week
C  P model with R=1 month
21
Long Tail Effects

A retailing concept describing the niche strategy of selling
small volumes of hard-to-find items to many customers
instead of only selling large volumes of popular items.

Rhapsody, a subscription-based streaming music service,
currently offers more than 735,000 tracks. Once you dig below
the top 40,000 tracks, you cannot find inventory in most realworld record stores. However, not only is every one of
Rhapsody's top 100,000 tracks streamed at least once each
month, the same is true for its top 400,000.

The market that lies outside the reach of the physical retailer is
big and getting bigger.
22
11
Single Period Model

Only one production or procurement opportunity.

Stochastic demand leads to lost sales or leftover.

There are losses of profit and goodwill for each
unsatisfied customer.

There is a salvage value for
each unit of leftover.

Forecasting helps balancing
cost of ordering too much vs.
cost of ordering too little.
23
Case : Order Management at Sport Obermeyer





Klaus Obermeyer founded Obermeyer in 1947, when he
was among the first ski instructors on Aspen Mountain.
Customer service, marketing, design & research,
accounting in Colorado Rockies.
Contract manufacturers in Hong Kong and China.
Long lead time, short sales period
Increasing product variety, more marked downs
12
Forecasting at Sport Obermeyer




Demands depend on weather, fashion trend, economy.
Forecasts based on Panel Consensus.
Dominant members have stronger influence on the
outcome of a consensus forecast.
Independent forecasts can provide an indicator of the
forecast accuracy for each style.
25
Working with Customers to Improve Forecasts


Obermeyer invites key customers to place early orders
(20% of total sales) to get market information.
Forecasts are updated based on those early orders.
26
13
Production Planning at Sport Obermeyer
Panel
forecasts
Early bird
orders
Phase 1
min. orders
Revised
forecasts
1st
shipment
Phase 2
revised orders
2nd
shipment
Summer
extra orders and
expensive styles
Selling
season
27
News Vendor Problem
D = newspapers demanded
Q = newspapers stocked
P = price of newspaper, $10
C = cost of newspaper, $4
S = salvage value of newspaper, $2
28
14
P = price of newspaper, $10
C = cost of newspaper, $4
S = salvage value of newspaper, $2
Cu = unit contribution: P-C = $6
Co = unit loss: C-S = $2
29
Finding Optimal Order Quantity

F(Q) = probability of having leftover inventory

To maximize expected profit, we order Q units so that
the expected loss on the Qth unit equals the expected
gain on the Qth unit:
Co  F (Q )  Cu  1  F Q 
Cu
C o  Cu

Rearrange the above equation -> F (Q) 

Cu / (Co+Cu) is called the critical ratio.

Choose Q such that the probability of no lost sales (i.e.,
demand < Q) equals the critical ratio.
30
15
31
Retail Discounting Model





S = current selling price
D = discount price
P = profit margin on cost (% markup as decimal)
Y = average number of years to sell entire stock of “dogs” at
current price (total years to clear stock divided by 2)
N = inventory turns (number of times stock turns in one year)
Loss per item = Gain from revenue
S – D = D(PNY)
D
S
(1  PNY )
32
16