2 inventory management
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inventory supply chain... logisitics , inn bound out boundTRANSCRIPT
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Inventory Management - Victor Araman
Inventory and (Yield) Management
Best Buy’s Lesson
In the 1990s, Eric Morley, Best Buy’s director of transportation,
remembers $15 million worth of personal computers were on the
way to stores in time for the holidays when chip maker Intel Corp.
unexpectedly announced it was going to introduce a new Pentium
processor, which wouldn’t be available until after the New Year. “We
were stuck,” Morley says. It became the Christmas without a PC. That’s
when we learned
that you don’t buy inventory just in case - you buy it just in
time”
Inventory Management – Victor Araman
2
Inventory Management – Victor Araman
A First Look at Inventory Management
– Motivation
Continuous Replenishment Model
– Economic Order Quantity (EOQ)
– EOQ variants
Periodic Review Model
– News Vendor
– LL Bean (see other slides)
Supply Chain Inventory
Agenda
Inventory Management – Victor Araman
A First Look at Inventory Management
– Motivation
Continuous Replenishment Model
– Economic Order Quantity (EOQ)
– EOQ variants
Periodic Review Model
– News Vendor
– LL Bean (see other slides)
Supply Chain Inventory
Agenda
3
Inventory is the stock or store of an item or a resource used by
an organization.
Different types of inventory
Finished Goods (FGI) | Work in Process (WIP) | Raw Material
Examples
Cash in an ATM/bank
Half assembled engines in a car manufacturing plant
Phones in a retail store
Silicon in a semiconductor manufacturing plant
Seats in a plane
Advertising slots for a TV broadcaster
What Is Inventory?
Inventory Management – Victor Araman
Inventory Management – Victor Araman
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Inventory Management – Victor Araman
Inventory Management – Victor Araman
2-Mar-12 25-Feb-11 26-Feb-10
Cash And Cash
Equivalents1,199,000 1,103,000 1,826,000
Short Term
Investments- 22,000 90,000
Net Receivables 2,288,000 2,348,000 2,020,000
Inventory 5,731,000 5,897,000 5,486,000
Other Current
Assets1,079,000 1,103,000 1,144,000
10,297,000 10,473,000 10,566,000
140,000 328,000 324,000
3,471,000 3,823,000 4,070,000
1,335,000 2,454,000 2,452,000
359,000 336,000 438,000
- - -
403,000 435,000 452,000
- - -
16,005,000 17,849,000 18,302,000
Deferred Long Term Asset Charges
Total Assets
Long Term Investments
Property Plant and Equipment
Goodwill
Intangible Assets
Accumulated Amortization
Other Assets
Period Ending
Assets
Current Assets
Total Current Assets
Inventory 5,731,000 5,897,000 5,486,000
30-36% of
Total Assets
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Inventory Management – Victor Araman
Importance of Inventory
Inventories represent a major commitment of monetary resources
Inventories affect virtually all aspects of a company’s daily operations
Inventories represent a lethal “weapon”
Example: Dell, Wal-Mart, Zara
Importance of Inventory
Inventory Management – Victor Araman
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To meet anticipated customer demand
To protect against stock-outs
To take advantage of economic order cycles
To maintain independence of operations
To allow for smooth and flexible production operations
To hedge against inflation and price increases
To take advantage of quantity discounts
Why Do Companies Hold Inventory?
Inventory Management – Victor Araman
Inventory Sales Ratio
Inventory Management – Victor Araman
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Inventory Sales Ratio
Inventory Management – Victor Araman
Impact of Inventory on Valuation
Inventory Management – Victor Araman
Abnormal inventory growth vs. On year ahead earnings
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Inventory Management – Victor Araman
WSJ-09-09-04
Why Do Companies Hold Inventory?
Inventory Management – Victor Araman
Average aggregate inventory value:
– Average of the total value of all items held in inventory
Weeks of supply =
Inventory turns =
Some of these measures can be customized for specific
settings/industry
– Retail: sales per sqm of shelf space
– Restaurant: sales per available seat-hour
– Media: sales per slot per impression
weekper Sold Goods of Cost
valueinventory aggregate Average
valueinventory aggregate Average
weekper Sold Goods of Cost
Inventory Measures
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Inventory Management – Victor Araman
Common industry benchmark
Example (K-Mart: 2002)
– Inventory value = 4.825 B $
– Cost of Goods Sold = 26.258 B $/year
– Average time to turn a dollar (cost) to a dollar
= 4.825/26.258 year = 0.183 years = 67 days. (Little’s law)
• What is the financial significance of this time?
• Kmart improved this figure from 88 days in 1998.
– Kmart Inventory Turns in 2002 = (1/0.183) = 5.44 Turns/year
Example (Walmart: 2002)
– Inventory value = 22.75 B$, COGS = 171.56 B $
– Time to turn a dollar = 43 days
– Inventory Turns = 7.7
Inventory Turns
Inventory Management – Victor Araman
Consider a retailer whose inventory holding cost is 0.3 $/$/year (we will discuss the components of inventory costs later)
– That is, incur 30 cents to hold one unit of a good that costs 1 $ for 1 year
– Say, this retailer turns inventory 4 times per year
– So, on average, each unit stays in inventory for (1/4) of a year
– So, the cost that the retailer incurs just due to holding inventory is 30/4 = 7.5 cents per dollar
– In other words, when we buy a product for $100 at this retailer, $7.5 are paid towards the retailer’s inventory holding costs
Inventory Turns: Importance
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Inventory Management – Victor Araman
Think about profit margins for two Retailers (A and B) in the same market (selling the same products)
– If Retailer A turns 4 times per year, 7.5 cents is the inventory cost/$.
– If Retailer B turns 8 times per year, only 3.75 cents is the inventory cost per $ (by better Inventory management)
– All else being the same, the profit margin of B is 3.75 % higher than A!
– Typically, net profits in the retail industry can be as low as 2 % !
Inventory Turns: Importance
Inventory Management – Victor Araman
Compare:
Wal-Mart : 7.54 turns per year
K-Mart : 5.44 turns per year
Inventory Turns in the Retail Sector
20%
25%
30%
35%
40%
45%
0 5 10 15
Gro
ss M
arg
in
Inventory Turns
11
Inventory Management – Victor Araman
Divides on-hand inventory into 3 classes
– A class, B class, C class
Basis is usually annual $ volume
– $ volume = Annual demand x Unit cost
Policies based on ABC analysis
– Develop class A suppliers more
– Give tighter physical control of A items
– Forecast A items more carefully
ABC Analysis
Inventory Management – Victor Araman
0
20
40
60
80
100
0 50 100
% of Inventory Items
% Annual $ Usage
A
B C
Class % $ Vol % Items
A 80 15 B 15 30
C 5 55
Classifying Items as ABC
80-20 rule
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Ordering cost. (per order/transaction)
– cost incurred each time an order is placed with a supplier or production is ordered with its own shop
Holding cost. (per unit of inventory per unit time)
– cost associated with maintaining an item in inventory until it is used or sold
Stockout or shortage cost. (per unit of lost sale)
– occurs when the demand for an item exceeds its supply
Item cost. (per unit of inventory)
– Under constant demand: becomes relevant if a quantity discount is available
Inventory Decisions Driven by Cost
Inventory Management – Victor Araman
Inventory Management – Victor Araman
Housing costs
Material handling costs
Labor cost from extra handling
Investment costs
Pilferage, scrap, and obsolescence
6% (3 - 10%)
3% (1 - 3.5%) 3% (3 - 5%) 11% (6 - 24%)
3% (2 - 5%)
(Approximate Ranges)
Inventory Holding Costs
Category Cost as % of Inventory Value
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Inventory Management – Victor Araman
A First Look at Inventory Management
– Motivation
Continuous Replenishment Model
– Economic Order Quantity (EOQ)
– EOQ variants
Periodic Review Model
– News Vendor
– LL Bean (see other slides)
Supply Chain Inventory
Agenda
Inventory Management – Victor Araman
Economic Order Quantity - EOQ
Time
Inventory Level
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Single product or item
Demand rate known and constant
Item produced in lots, or purchased in orders
Each lot or order received in single delivery
Lead time known and constant
Ordering, or setup costs are constant
No backorders are allowed
No quantity discounts are allowed
Model Assumptions
Economic Order Quantity (EOQ)
Inventory Management – Victor Araman
Inventory Management – Victor Araman
Demand = D units per year
Ordering cost = S dollars per order placed
Holding cost = H dollars per unit per year
Order quantity = Q units
Data & Costs Formulation
– Holding Cost = H Q/2 per year
– Ordering Cost = S D/Q per year
– Total Cost = H Q/2 + S D/Q
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Inventory Management – Victor Araman
Order Quantity (Q)
Annual Cost
Order (Setup) Cost Curve
Q*
Optimal Order Quantity
H Q/2
S D/Q
EOQ Model: How Much to Order?
Inventory Management – Victor Araman
EOQ: When to Order?
Time
Inventory Level
Average
Inventory
Q* / 2
ROP Reorder Point
LT
Lead Time
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solution) (EOQ
)TC(
*
H
DSQ
QH
Q
DSQ
2
2
Solution of the EOQ Problem
Total Cost
Optimal Quantity
Inventory Management – Victor Araman
Expected Number of Orders
Expected Time between orders
Optimal Order Quantity
Reordering Point
Inventory Management – Victor Araman
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
LT = Lead time in days
EOQ Model Equations
= Q* H
2 × D × S = N D
Q*
ROP = d × LT Working Days per year = T
N
Working days / Year = d
D
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What if?
What if management is concerned by costs of
emissions?
What if there are discounts based on the order
quantity?
What if demand or/and lead times are NOT
deterministic?
Inventory Management – Victor Araman
EOQ Adjusted – Costs of Emissions
Inventory Management – Victor Araman
Cost of reducing emissions
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Out of Stock At Supermarkets
Inventory Management - Victor Araman
Inventory Management - Victor Araman
Safety Stock
Time
Inventory Level
ROP
P(Stockout)
dLT SS
Service
Level
Frequency
Avg dLT
Place order
Lead Time
ROP
Q
EOQ Adjusted – Demand Uncertainty
Avg dLT
Receive order
SS
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Inventory Management - Victor Araman
How much & when to order ?
Uncertain demand (and possibly uncertain lead time)
– Lead Time Demand: Demand during leadtime
– Leadtime demand follows normal distribution (forecasting)
– Continuous replenishment
What is a service level? What is the differ
– What is the difference between a service level and a fill rate?
How is the service level linked to the Safety Stock?
– Service level = 1 - Probability of stockout
– Higher service level means more safety stock
– More safety stock means higher ROP
– ROP = Avg of leadtime demand + safety stock
Service Level & Safety Stock
Inventory Management - Victor Araman
Leadtime demand is a normal distribution with an average
and standard deviation
Decide on your TARGET Service Level
– Likelihood that leadtime demand is smaller than ROP is a service
level
– Example: SL = 99% means that you leave a 1% chance of stock-out
during any cycle
Find the corresponding level of inventory: ROP – ROP = Avg dLT + Safety Stock
ROP Avg dLT
Normal
Using Excel the ROP is
ROP = NORMINV(SL, Avg dLT, stdev)
Leadtime Demand
Safety Stock Computation
Service
Level
20
Inventory Management - Victor Araman
Demand during lead-time for one brand of TV is normally
distributed with a mean of 36 TVs and a standard deviation of 15
TVs. What safety stock should be carried for a 90% service level?
What is the appropriate reorder point?
Based on available information, the daily demand for CD-ROM
drives averages 10 units (normally distributed), with a standard
deviation of 1 drive. The lead-time is exactly 5 days. Management
wants a 97% service level. What safety stock should be carried?
What is the appropriate reorder point?
Probabilistic Model: Examples
Inventory Management – Victor Araman
A First Look at Inventory Management
– Motivation
Continuous Replenishment Model
– Economic Order Quantity (EOQ)
– EOQ variants
Periodic Review Model
– News Vendor
– LL Bean (see other slides)
Supply Chain Inventory
Agenda
21
Inventory Management: The Newsvendor model
Inventory Management – Victor Araman
Single
Order
Demand
Uncertainty
Fixed
Price
Too
many?
Selling Newspapers…
Economic parameters
– buy at w = € 1
– sell at r = € 1.5
– salvage at s = € 0.05
Inventory Management – Victor Araman
Random demand
– a distribution is available
(with an average 300 and a
standard deviation 100 units)
The too much/too little problem
Order too much and there is a loss due to unsold newspapers Order too little and you lose potential sales (and profits)
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Market Uncertainty & Ex-Ante Bet
There are consequences of getting this bet wrong
The expected profit maximization balances the “too
much too little” costs Inventory Management – Victor Araman
Brief Comparative Analysis
Inventory Management – Victor Araman
Long lifecycle products with stationary demand
No demand uncertainty
Tradeoff between setup and
holding costs, driven by the
frequency of ordering
Short lifecycle products – One shot
items
– can be stocked only once at the beginning of the selling season)
Considerable demand uncertainty
Tradeoff between
– costs of excess leftover inventory (overstocking, holding or disposal costs)
– excess demand (stockout costs)
Examples
– fashion clothing | toys | computer games | music albums | books, consumer electronics
EOQ The “Newsvendor” model
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Inventory Management - Victor Araman
Overage cost per unit Co is the (opportunity) cost of one unit of
excess inventory (“over” ordering)
– What if you had ordered one fewer unit?
– Overage cost = Cost – Salvage value = w – s
• What if additional cost is required to dispose of a leftover inventory?
– Co = € 0.95
Underage cost per unit Cu is the (opportunity) cost of one unit of lost
sales (“under” ordering)
– What if you had ordered one additional unit?
– Underage cost = Price – Cost = r – w
• what if a goodwill cost or penalty cost is incurred in addition to the
lost margin?
– Cu = € 0.50
The Newsvendor Concept
The Newsvendor Order Quantity Q
We define the critical ratio
CR = 𝐶𝑢
𝐶𝑢+𝐶𝑜
CR measures the balance of power between marginal costs of
shortage and leftover
– how worse or better is too little compared to too much
Inventory Management – Victor Araman
Demand
Probability
Distribution
Q Avg
Dmd
Critical Ratio
CR
Risk of
leftover Risk of
shortage
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News Boy – Victor F. Araman
Expected Profit
If Q < D : Revenues = r Q ;
If Q > D : Revenues = r D ; Salvage value = s (Q – D )
Profit = r min{D , Q} + s (Q – D )+ – w Q
Penalty cost = p = 0
r x Sales s x Leftover
News Boy – Victor F. Araman
Cost of Demand Uncertainty
Gr(Q) = (r - w) E(D - Q)+ + (w – S) E(Q - D)+
Profit = r min{D , Q} + s (Q – D )+ - w Q
Cu : under-ordering
cost or lost margin Expected Lost
Sales Co : over-ordering cost
or the overage cost Expected leftover
The mismatch Cost
x
x
Risk free profit Mismatch Cost
Expected Profit
Pr (Q) = (r – w) ED – Gr (Q)
Simple
manipulations
25
0
10
20
30
40
50
60
70
80
0 800 1600 2400 3200 4000 4800 5600 6400
Ex
pecte
d g
ain
or
loss
.
Expected marginal benefit
of understocking
Expected marginal loss
of overstocking
Marginal Analysis: Balancing the Risks
Ordering one more unit
Inventory Management – Victor Araman
Q+1
Q X
X – Cu
X + Co
D > Q
D ≤ Q
(X – Cu) x Prob{D > Q }
+
(X + Co) x Prob{D ≤ Q }
As more units are ordered the average benefit from
ordering one unit decreases (it becomes more likely
to be left with inventory)
while the average loss of ordering one more unit
increases (it becomes less likely to be short in
inventory)
X – Cu Prob{D > Q } + Co Prob{D ≤ Q }
Q+1 is better than Q if
Co Prob{D ≤ Q } < Cu Prob{D > Q
Inventory Management - Victor Araman
Optimal Rule
Expected cost of ordering one extra unit = Expected cost of ordering one less unit
So, the optimal quantity solves for
C0 P(D ≤ Q) = Cu P(D > Q)
The quantity 𝐶𝑢
𝐶𝑢+𝐶𝑜 is known as the critical ratio.
In the newspaper example: critical ratio = 0.5/(0.95+0.5) = 0.345
Cost UnderageCost Overage
Cost UnderageQ}P{Demand
Newsvendor Cost Tradeoff
26
Inventory Management - Victor Araman
Demand
Probability Distribution
Q Average
Demand
Newsvendor: Optimal Quantity to order
Critical Ratio
Risk of leftover
Risk of shortage
A Normal Distribution
If demand distribution is normal Use Excel
Inventory Management – Victor Araman
Q m =300
CR
0.345
s =100
Q* = Norminv(CR, m , s)
= Norminv(0.345,300,100)
= 260
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Financial Performance
If seller orders the newsvendor quantity Q*
– What should the seller expect in terms of profits ?
– What about averages sales?
– How many units will be discounted on average (salvage)?
– How much money is left on the table? (i.e. What is the fraction of
demand unmet?)
Once lost sales are evaluated the rest follow trivially
For normal distribution lost sales is known
– tables that provide the values of lost sales
– excel functions that give the exact value of lost sales
If demand is not normal. Harder to get (need simulation)
Inventory Management – Victor Araman
Average Lost Sales
Suppose demand can take one of these values
D belongs to {0,10, 20,…190, 200}
Suppose Q=120
What is the average lost sales?
– If D<=Q : No lost sales = 0
– If D = 130, lost sales = D - Q= 10
– If D = 140, lost sales = D - Q = 20
Average Lost Sales
= 10 x P(D=130) + 20 x P(D=140) + … + 80 x P(D=200)
Inventory Management – Victor Araman
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Average Lost Sales for Normal Dist.
Available information
– Demand (D) is Normal with avg: ED = 300 and stdev sD = 100
– Assuming the previous economic parameters
– then CR = 0.325 and Q = 260
Formula for Average Loss Sales
sD x L(z)
– s is the standard deviation (given)
– z = (Q – ED) / sD e.g. z = (260-300)/100 = – 0.4
L(z) = normdist(z, 0, 1, 0) – z x (1 - normdist(z, 0, 1, 1))
e.g. L(-0.4) = 0.63 and Average Lost Sales = 100 x 0.63 = 63
Inventory Management – Victor Araman
The Rest Indeed Follows
Sales + Lost Sales = Demand
Avg Sales = Avg Demand – Avg Lost Sales = 300 – 63 = 237units
Leftover Inventory + Sales = Q
Avg leftover inventory = Q – Avg Sales = 260 – 237=23units
Average Profit
Price x Avg Sales + Salvage x Avg Leftover Inv. – Cost * Q
= (Price – Cost) x Avg Sales – (Cost – Salvage) x Avg Leftover Inv.
= (1.5-1)*237-(1-0.06)*23 = $96.88 ~ $97
Inventory Management – Victor Araman
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Inventory Management - Victor Araman
Fare: New York - Chicago Wednesday to Friday
0
200
400
600
800
1000
1200
1400
US
$
August September October
0
200
400
600
800
1000
1200
1400
US
$
Fare: New York - Chicago Thursday to Saturday
August September October
Wednesday-Friday fares are 15-20% higher than Thursday-Saturday fares!
Yield Management in Action
Inventory Management - Victor Araman
“Yield Management: term used in many service industries
to describe techniques to allocate limited resources, such as
airplane seats or hotel rooms, among a variety of customers,
such as business or leisure travelers. – By adjusting this allocation a firm can optimize the total revenue or
"yield“ on the investment in capacity – Since these techniques are used by firms with extremely
perishable goods, or by firms with services that cannot be stored at
all, these concepts and tools are often called perishable asset
revenue management. – American Airlines credits yield management techniques for a
revenue increase of $500 million/year and Delta Airlines uses
similar systems to generate additional revenues of $300 million per
year.”
Yield Management
30
Inventory Management - Victor Araman
“Marriott Hotels credits its yield management system for
additional revenues of $100 million per year, with
relatively small increases in capacity and costs
Broadcasting companies use yield management to
determine how much inventory (advertising slots) to sell
now to the "upfront market" and how much to reserve
and perhaps sell later at a higher price to the "scatter
market’’
The core logic is similar to the newsvendor model
Yield Management
Inventory Management – Victor Araman
A First Look at Inventory Management
– Motivation
Continuous Replenishment Model
– Economic Order Quantity (EOQ)
– EOQ variants
Periodic Review Model
– News Vendor
– LL Bean (see other slides)
Supply Chain Inventory
Agenda
31
News Boy – Victor F. Araman
A Simple Supply Chain
The manufacturer’s profit is given by
Pm = (w – m) Q*
where, m is the production unit cost incurred by the
manufacturer and Q* is the optimal quantity ordered by the
retailer
Manufacturer Retailer End
consumer
r, D w, Q m
Supply Chain Inventory Insights
Double marginalization effect
Postponement strategies
Risk sharing and supply chain maximum value
Inventory Management – Victor Araman
Refer to Newsvendor Problems
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News Boy – Victor F. Araman
Supply Contracts: Real Options
Retailer buys q “call” options at unit cost c
– Call option: right to buy one unit at the exercise price x
– Options bought ahead of season, but exercised after demand is observed
– Induce the retailer to buy more units at the expense of sharing the risk (demand uncertainty)
Retailer’s Expected profit
pr(q) = E[(R - x) min{D, q}] – c q
Comparing to Original Newsvendor
Max Expected Profit
r min{D , Q} + s (Q – D )+ - w Q
Solution given by Critical Ratio
– Cu = r – w | Co = w – s
– CR = 𝐶𝑢
𝐶𝑢+𝐶𝑜
– P(D ≤ Q) = CR
– Q*= norminv(CF, Avg D, sD)
Profit Manufacturer
(w – m) Q*
Inventory Management – Victor Araman
Max Profit
(r - x) min{D, q} – c q
Set
r → r – x | w → c | s → 0
By analogy, solution must be given
by Critical Ratio
– ku = r – x – c | ko = c
– CF = 𝑘𝑢
𝑘𝑢+𝑘𝑜
– P(D ≤ q) = CF
– q*= norminv(CF, Avg D, sD)
Profit Manufacturer
E (c - m)q + x min{D, q} + S (q - D)+
Standard Newsvendor Newsvendor with Options
33
News Boy – Victor F. Araman
Retailer’s Expected Profit
Retailer’s Expected profit
pr(q) = E[(R - x) min{D, q}] – c q
Re-writing the profit
pr(q) = (R - x - c) ED – gr(q)
gr(q) = (R - x - c) E[(D - q)+] + c E[ (q - D)+] – ku = R - x - c : opportunity cost (too few options)
– k0 = c : opportunity cost (too many options)
gr(q*) = s (ku + k0) Normdist(Normsinv(ku /(ku + k0)),0,1,false)
News Boy – Victor F. Araman
Manufacturer’s Expected Profit
Expected profit
pm(q) = E[(c - M) q + x min{D, q} + S (q - D)+]
See notes for an Excel formulation of this profit under normal
demand!
Net revenues from
selling q options
Revenues from
exercised options Revenues from non-
exercised options
Leftover Sales
34
Inventory Management – Victor Araman
Inventory is the result of the imbalance between Supply and Demand
It serves as a buffer to – Smooth seasonality
– Reduce risk/cost of stockouts
– Alleviate production scheduling
– Take advantage of economies of scale
Inventory is not free
EOQ. Simple and Commonly used model – Tradeoff between setup and holding costs
Newsvendor. Commonly used for One Shot Items – Critical Ratio measures the imbalance between too much and too
little
Supply Chain Inventory
Key Learnings