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Introduction to StochasticIntroduction to Stochastic Inventory Models and SupplyInventory Models and Supply
Contracts
David Simchi-Levi
Professor of Engineering SystemsMassachusetts Institute of TechnologyMassachusetts Institute of Technology
�
�
�
Outline of the Presentation � Introduction
� The Effect of Demand Uncertainty( S) li �(s,S) Policy�Supply Contracts�Risk PoolingRisk Pooling
� Practical Issues in Inventory Practical Issues in Inventory Management
©Copyright 2002 D. Simchi-Levi
Sources:Plants vendors
portsRegional warehouses:
Stocking points
Field warehouses:Stocking points
Customers, demand
centers sinks
Transportation costsTransportation costs
Inventory & warehousingcosts
Inventory & warehousingcosts
Production/purchasecosts
Supply
Image by MIT OpenCourseWare.
Goals:Goals: Reduce Cost, Improve Service
• By effectively managing inventory: – Xerox eliminated $700 million inventory from its supply chain – Wal-Mart became the largest retail company utilizing
efficient inventory managementefficient inventory management – GM has reduced parts inventory and transportation costs by
26% annually
©Copyright 2002 D. Simchi-Levi
Goals:Goals: Reduce Cost, Improve Service
• By not managing inventory successfully – In 1994, “IBM continues to struggle with shortages in their
ThinkPad line” (WSJ, Oct 7, 1994) – In 1993, “Liz Claiborne said its unexpected earning decline is Liz Claiborne said its unexpected earning decline isIn 1993,
the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993)
– I 1993 “D ll C t di t l St k l DIn 1993, “Dell Computers predicts a loss; Stock plunges. Dellll acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)
©Copyright 2002 D. Simchi-Levi
j
Understanding Inventory • The inventory policy is affected by:
– Demand Characteristics
– Lead Time
– Number of Products – Objectives
• Service level • Minimize costs
– Cost Structure
©Copyright 2002 D. Simchi-Levi
The Effect ofThe Effect of Demand Uncertainty
• Most companies treat the world as if it were predictable: – Production and inventory planning are based on
forecasts of demand made far in advance of the selling season
– CCompaniies are aware of demandd uncertaintyf d i when they create a forecast, but they design their planning process as if the forecast truly representsplanning process as if the forecast truly represents reality
©Copyright 2002 D. Simchi-Levi
Demand Forecast • The three principles of all forecasting
t h itechniques: – Forecasting is always wrong – The longer the forecast horizon the worst is the
forecast – Aggregate forecasts are more accurate
©Copyright 2002 D. Simchi-Levi
The Effect ofThe Effect of Demand Uncertainty
• Most companies treat the world as if it were predidicttable:bl – Production and inventory planning are based on forecasts of
demand made far in advance of the selling seasondemand made far in advance of the selling season – Companies are aware of demand uncertainty when they
create a forecast, but they design their planning process as if th f t t l t litifthe forecast truly represents reality
• Recent technological advances have increased the level of demand uncertainty:level of demand uncertainty: – Short product life cycles – Increasing product varietyyg p
©Copyright 2002 D. Simchi-Levi
SnowTime Sporting Goods • Fashion items have short life cycles, high
vari tiety off competitorstit • SnowTime Sporting Goods
– New designs are completed – One production opportunity – BBasedd on pastt salles, kknowlleddge of th f the iinddusttry,
and economic conditions, the marketing department has a probabilistic forecastdepartment has a probabilistic forecast
– The forecast averages about 13,000, but there is a chance that demand will be greater or less than thithis.
©Copyright 2002 D. Simchi-Levi
Supply Chain Time Lines
Jan 00 Jan 01 Jan 02 Design Production Retailing
Feb 00 Sep 00 Feb 01 Sep 01p pProduction
©Copyright 2002 D. Simchi-Levi
SnowTime Sporting Goods • Fashion items have short life cycles, high
vari tiety off competitorstit • SnowTime Sporting Goods
– New designs are completed – One production opportunity – BBasedd on pastt salles, kknowlleddge of th f the iinddusttry,
and economic conditions, the marketing department has a probabilistic forecastdepartment has a probabilistic forecast
– The forecast averages about 13,000, but there is a chance that demand will be greater or less than thithis.
©Copyright 2002 D. Simchi-Levi
8000
100
120
0 1
0
SnowTime Demand Scenarios
Demand ScenariosDemand Scenarios
25% 30%
ity
10% 15% 20% 25%
Pro
babi
li
0% 5%
10%
0 0 0 0 0 0
00 0014
000
1600 80
0
SalesSales
©Copyright 2002 D. Simchi-Levi
SnowTime Costs • Production cost per unit (C): $80 • Selling price per unit (S): $125 • Salvage value per unit (V): $20 • Fixed production cost (F): $100,000 • Q is production quantity, D demand
• ProfitProfit = Revenue - Variable Cost - Fixed Cost + SalvageSalvage
©Copyright 2002 D. Simchi-Levi
SnowTime Best Solution
• Find order qquantityy that maximizes weighted average profit.
•• Question: Will this quantity be less Question: Will this quantity be less than, equal to, or greater than average d d? demand?
©Copyright 2002 D. Simchi-Levi
What to Make? • Question: Will this quantity be less
than equal to or greater than average than, equal to, or greater than average demand?
• Average demand is 13,100 • Look at marginal cost Vs marginalLook at marginal cost Vs. marginal
profit – ifif exttra jjackkett soldld, profitfit i is 125125-8080 = 4545 – if not sold, cost is 80-20 = 60
• So we will make less than average ©Copyright 2002 D. Simchi-Levi
– = - -
SnowTime Scenarios • Scenario One:
– Suppose you make 12 000 jackets andSuppose you make 12,000 jackets and demand ends up being 13,000 jackets.
– Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000
• Scenario Two: – Suppose you make 12 000 jackets andSuppose you make 12,000 jackets and
demand ends up being 11,000 jackets.– Profit = 125(11 000) - 80(12 000) - 100 000 + Profit 125(11,000) 80(12,000) 100,000 +
20(1000) = $ 335,000 ©Copyright 2002 D. Simchi-Levi
SnowTime Expected Profit
Expected ProfitExpected Profit
$400,000
$200 000
$300,000
Proof
it
$100,000
$200,000
$0 8000 12000 16000 20000
Order Quantity Order Quantity
©Copyright 2002 D. Simchi-Levi
SnowTime Expected Profit
Expected ProfitExpected Profit
$400,000
$200 000
$300,000
Proof
it
$100,000
$200,000
$0 8000 12000 16000 20000
Order Quantity Order Quantity
©Copyright 2002 D. Simchi-Levi
SnowTime Expected Profit
Expected ProfitExpected Profit
$400,000
$200 000
$300,000
ofit
$100,000
$200,000
Pro
$0 8000 12000 16000 20000
Order Quantity Order Quantity
©Copyright 2002 D. Simchi-Levi
SnowTime:SnowTime: Important Observations
• Tradeoff between ordering enough to meet demand and ordering too much
• Several qquantities have the same averagge profit
• Average profit does not tell the whole storyAverage profit does not tell the whole story
• Q ti 9000 d 16000 Question: 9000 and 16000 unitits lead to about the same average profitfit, so whi hich do we preffer?h d ?
©Copyright 2002 D. Simchi-Levi
0 0 00
0
000
0000
0000
0000
-300
0 -1
00 0
100 0
0
300 0
0
500 0
0
Probability of Outcomes
100%
60%
80%
100%
Q=9000
20%
40%
60% Q=9000 Q=16000
0%
20%
Prob
abibilit
y
Cost
©Copyright 2002 D. Simchi-Levi
Key Insights from this Model • The optimal order quantity is not necessarily
equal to average forecast demandequal to average forecast demand • The optimal quantity depends on the
l ti hi b t i l fit drelationship between marginal profit and marginal cost
• As order quantity increases, average profit first increases and then decreases
• As production quantity increases, risk increases. In other words,, the pprobabilityy of large gains and of large losses increases
©Copyright 2002 D. Simchi-Levi
Supply Contracts
©Copyright 2002 D. Simchi-Levi
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost = $35
Wholesale Price = $80
Selling Price = $125Salvage Price = $20
Variable Production Cost = $100,000
20:00
20:00
Image by MIT OpenCourseWare.
010
012
0
0 1
0
Demand Scenarios
Demand ScenariosDemand Scenarios
25% 30%
ity
10% 15% 20% 25%
Pro
babi
li
0% 5%
10%
0 0 0 0 0 0
800 00 00
1400
016
00 800
Sales Sales
©Copyright 2002 D. Simchi-Levi
Distributor Expected Profit Expected Profit
400000
500000
100000
200000
300000
0
100000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
©Copyright 2002 D. Simchi-Levi
Distributor Expected Profit Expected Profit
400000
500000
100000
200000
300000
0
100000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
©Copyright 2002 D. Simchi-Levi
Supply Contracts (cont.)
• Distributor opptimal order qquantityy is 12,000 units
• Distributor expected profit is $470 000• Distributor expected profit is $470,000
• Manufacturer profit is $440,000 • Supply Chain Profit is $910,000
–IS there anything that the distributor andIS there anything that the distributor and manufacturer can do to increase the profit of both?
©Copyright 2002 D. Simchi-Levi
Supply Contracts
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost = $35
Wholesale Price = $80
Selling Price = $125Salvage Price = $20
Variable Production Cost = $100,000
20:00
20:00
©Copyright 2002 D. Simchi-Levi
Image by MIT OpenCourseWare.
Retailer ProfiRetailer Profit (Buy Back=$55)
600,000
300 000
400,000
500,000
r Pro
fit
100,000
200,000
300,000
Reta
ile
0
6000
7000
800
000 00 00 00 00
160
018
00
090
00 0
100
1 10
120
130
140
150 00
1700
0
Order QuantityOrder Quantity
©Copyright 2002 D. Simchi-Levi
600 0
7000
8000
9000
10
000
1100
012
000
1300
014
000
1500
016
000
1700
018
000
Retailer ProfiRetailer Profit (Buy Back=$55)
600,000 $513 800
300 000
400,000
500,000
r Pro
fit
$513,800
100,000
200,000
300,000
Reta
ile
0
Order QuantityOrder Quantity
©Copyright 2002 D. Simchi-Levi
Manufacturer ProfitManufacturer Profit (Buy Back=$55)
600 , 000
400, 000
500, 000
,
rer
Prof
it
100 000
200, 000
300, 000
Man
ufac
tur
0
100 , 000
6000
70
00
8000
90
00
1000
0 11
000
1200
0 13
000
1400
0 15
000
1600
0 17
000
1800
0
M
6 7 8 9 10
11
12
13
14
15
16
17
18
Production Quantity
©Copyright 2002 D. Simchi-Levi
Manufacturer ProfitManufacturer Profit (Buy Back=$55)
600 , 000
400, 000
500, 000
,
rer
Prof
it $471,900
100 000
200, 000
300, 000
Man
ufac
tur
0
100 , 000
6000
70
00
8000
90
00
1000
0 11
000
1200
0 13
000
1400
0 15
000
1600
0 17
000
1800
0
M
6 7 8 9 10
11
12
13
14
15
16
17
18
Production Quantity
©Copyright 2002 D. Simchi-Levi
Supply Contracts
©Copyright 2002 D. Simchi-Levi
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost = $35
Wholesale Price = $80
Selling Price = $125Salvage Price = $20
Variable Production Cost = $100,000
20:00
20:00
Image by MIT OpenCourseWare.
Retailer ProfiRetailer Profit (Wholesale Price $70, RS 15%)
600,000
400,000
500,000
,
Pro
fit
100 000
200,000
300,000
Ret
aile
r P
0
100,000
6000
7000
8000
9000
0000 00
020
0030
0040
0050
0060
0070
0080
00
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
Order Quantity
©Copyright 2002 D. Simchi-Levi
Retailer ProfiRetailer Profit (Wholesale Price $70, RS 15%)
600,000 $504 325
400,000
500,000
,
Pro
fit
$504,325
100 000
200,000
300,000
Ret
aile
r P
0
100,000
6000
7000
8000
9000
0000 00
020
0030
0040
0050
0060
0070
0080
00
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
Order Quantity
©Copyright 2002 D. Simchi-Levi
6 7 8 9 10
11
12
13
14
15
16
17
18
Manufacturer ProfitManufacturer Profit (Wholesale Price $70, RS 15%)
700,000
400 0 00
500, 000
600, 000
,
rer P
rofit
100 0 00
200, 000
300, 000
400 , 000
Man
ufac
tur
0
100 , 000
6000
70
00
8000
90
00
1000
0 11
000
1200
0 13
000
1400
0 15
000
1600
0 17
000
1800
0
M
Production Quantity
©Copyright 2002 D. Simchi-Levi
6 7 8 9 10
11
12
13
14
15
16
17
18
Manufacturer ProfitManufacturer Profit (Wholesale Price $70, RS 15%)
700,000
400 0 00
500, 000
600, 000
,
rer P
rofit
$481,375
100 0 00
200, 000
300, 000
400 , 000
Man
ufac
tur
0
100 , 000
6000
70
00
8000
90
00
1000
0 11
000
1200
0 13
000
1400
0 15
000
1600
0 17
000
1800
0
M
Production Quantity
©Copyright 2002 D. Simchi-Levi
Supply Contracts
Strategy Retailer Manufacturer Total Sequential Optimization 470,700 440,000 910,700 Buyback 513,800 471,900 985,700 Revenue Sharing 504,325 481,375 985,700
©Copyright 2002 D. Simchi-Levi
Supply Contracts
©Copyright 2002 D. Simchi-Levi
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost = $35
Wholesale Price = $80
Selling Price = $125Salvage Price = $20
Variable Production Cost = $100,000
20:00
20:00
Image by MIT OpenCourseWare.
60
70
80
9 3 6 80
Supply Chain Profit
1,200,000
800,000
1,000,000
, ,
in P
rofit
200 000
400,000
600,000
uppl
y C
ha
0
200,000
6000
7000
8000
9000
0000
1000
2000
3000
4000
5000
6000
7000
8000
Su
010
011
0 12
01
014
015
01
0 17
01
Production Quantity
©Copyright 2002 D. Simchi-Levi
60
70
80
9 3 6 80
Supply Chain Profit
1,200,000 $1 014 500
800,000
1,000,000
, ,
in P
rofit
$1,014,500
200 000
400,000
600,000
uppl
y C
ha
0
200,000
6000
7000
8000
9000
0000
1000
2000
3000
4000
5000
6000
7000
8000
Su
010
011
0 12
01
014
015
01
0 17
01
Production Quantity
©Copyright 2002 D. Simchi-Levi
Supply Contracts
Strategy Retailer Manufacturer Total Sequential Optimization 470,700 440,000 910,700 Buyback Buyback 513 800 513,800 471 900 471,900 985 700 985,700 Revenue Sharing 504,325 481,375 985,700 Global Optimization 1,014,500
©Copyright 2002 D. Simchi-Levi
Supply Contracts: Key Insights
• Effective supppplyy contracts allow supplypp y chain partners to replace sequential optimization by global optimization optimization by global optimization
• Buy Back and Revenue Sharing contracts achihieve thithis objecti tive thth roughh riskbj i k sharing
• No one has an incentive to deviate from the contract terms from the contract terms
©Copyright 2002 D. Simchi-Levi
Supply Contracts: Case Study • Example: Demand for a movie newly released video
cassette typically starts high and decreases rapidlycassette typically starts high and decreases rapidly– Peak demand last about 10 weeks
• Blockbuster purchases a copy from a studio for $65Blockbuster purchases a copy from a studio for $65 and rent for $3 – Hence, retailer must rent the tape at least 22 times before
earning profitearning profit • Retailers cannot justify purchasing enough to cover
the ppeak demand – In 1998, 20% of surveyed customers reported that they
could not rent the movie they wanted
©Copyright 2002 D. Simchi-Levi
– -
Supply Contracts: Case Study • Starting in 1998 Blockbuster entered a revenue sharing
agreementt with th ith the major sttudiosj di– Studio charges $8 per copy – Blockbuster pays 30-45% of its rental income Blockbuster pays 30 45% of its rental income
• Even if Blockbuster keeps only half of the rental income, the breakeven point is 6 rental per copythe breakeven point is 6 rental per copy
• The impact of revenue sharing on Blockbuster was dramatic – Rentals increased by 75% in test markets – Market share increased from 25% to 31% (The 2nd largest
ret il tailer, HHollywood E d Entterttaiinment C t Corp has 5% 5% market shhare)ll h k t )
©Copyright 2002 D. Simchi-Levi
t t
What are the drawbacks of RS? • Administrative Cost
L it b ht b th i d d t id t il h– Lawsuit brought by three independent video retailers who complained that they had been excluded from receiving the benefits of revenue sharing was dismissed (June 2002)
– Th W l Di C h d Bl kb iThe Walt Disney Company has sued Blockbuster accusing them of cheating its video unit of approximately $120 million under a four year revenue sharing agreement (January 2003)
• Impact on sales effort – Retailers have incentive to push products with higher profit
marginsmargins – Automotive industry: automobile sales depends on retail effort
©Copyright 2002 D. Simchi-Levi
What are the drawbacks of RS? • Retailer may carry substitute or
complementary products from other suppliers – One supplier offers revenue sharing while
the other does not • Substitute products: retail will push the product
with high margin • CCompllementtary prodductts: rettail iler may di discountt
the product offered under revenue sharing to motivate sales of the other product motivate sales of the other product
©Copyright 2002 D. Simchi-Levi
SnowTime Costs: Initial Inventory • Production cost per unit (C): $80 • Selling price per unit (S): $125 • Salvage value per unit (V): $20 • Fixed production cost (F): $100,000 • Q is production quantity, D demand
• ProfitProfit = Revenue - Variable Cost - Fixed Cost + SalvageSalvage
©Copyright 2002 D. Simchi-Levi
SnowTime Expected Profit
Expected ProfitExpected Profit
$400,000
$200 000
$300,000
Proof
it
$100,000
$200,000
$0 8000 12000 16000 20000
Order Quantity Order Quantity
©Copyright 2002 D. Simchi-Levi
Initial Inventory • Suppose that one of the jacket designs is a
model produced last year. • Some inventoryy is left from last yyear • Assume the same demand pattern as before
• If only old inventory is sold If only old inventory is sold, no setup cost• no setup cost
• Question: If there are 7000 units remaining, what should SnowTime do? What should they do if there are 10,000 remaining?
©Copyright 2002 D. Simchi-Levi
Initial Inventory and Profit
500000
300000 400000 500000
it
100000 200000 300000
Prof
i
0
000 500 000 500
00 00 00 00
50006500800095001100012500 1400015500
Production Quantityy
©Copyright 2002 D. Simchi-Levi
Initial Inventory and Profit
500000
300000 400000 500000
it
100000 200000 300000
Prof
i
0
000 500 000 500
00 00 00 00
50006500800095001100012500 1400015500
Production Quantityy
©Copyright 2002 D. Simchi-Levi
Initial Inventory and Profit
500000
300000 400000 500000
it
100000 200000 300000
Prof
i
0
000 500 000 500
00 00 00 00
50006500800095001100012500 1400015500
Production Quantityy
©Copyright 2002 D. Simchi-Levi
Initial Inventory and Profit
500000
300000 400000 500000
t
100000 200000 300000
Prof
i
0 100000
00
00
00
00
00
00
00
00
00
00
00
00
500
600
700
800
900
1000
11
00
1200
13
00
1400
15
00
1600
Production Quantity Production Quantity
©Copyright 2002 D. Simchi-Levi
eo n e o e p
(s, S) Policies • For some starting inventory levels, it is better to not
st ttart prodducti tion • If we start, we always produce to the same level • h ( Ss, ) li f h i lThus, we use an ( S) policy. If the inventory level i l is
below s, we produce up to S. • i the de point d S i th d to le els is the reorder point, and S is the order-up-to level• The difference between the two levels is driven by
the fixed costs associated with orderingthe fixed costs associated with ordering, transportation, or manufacturing
©Copyright 2002 D. Simchi-Levi
o pe o p o e o ep en
A Multi-Period Inventory Model
• Often, there are multiple reorder opportunities
• Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The di dist ib tributtor periiodidi ll cally pll eaces ordders tto replenil ishh it its inventory
©Copyright 2002 D. Simchi-Levi
•
Case Study: Electronic ComponentCase Study: Electronic Component Distributor
• Electronic Compponent Distributor • Parent company HQ in Japan with
worldworld-wide manufacturingwide manufacturing • All products manufactured by parent
company One central warehouse in U SOne central warehouse in U.S.
©Copyright 2002 D. Simchi-Levi
•
a
Case Study: The Supply Chain OutboundInbound
Distributor Factoryy
End UserDC DC
4) Production 1) OrderPlanningg 3) Order
ProcessingProcessingProcessing
2) Forecasting ReplenishmentReplenishment Order Flow Order Flow
Product Flow ©Copyright 2002 D. Simchi-Levi
0
AprMay Ju
n Ju
lAugSep OctNovDec Ja
nFeb Mar
Demand Variability: Example 1
P d t D Product Demandd
225250
150
75 100
150 125 104
100 150 200
Demand (000's) 75
50 61 48 53 45
0 50
100(000's)
M hMonth
©Copyright 2002 D. Simchi-Levi
Demand Variability: Example 1 Histogram for Value of Orders Placed in a Week
20
25
ncy
5
10
15
Freq
uen
0
$25,0
00
$50,0
00
$75,0
00
00,00
0
25,00
0
50,00
0
75,00
0
00,00
0
$25
$50
$75
$100
$125
$150
$175
$200
Value of Orders Placed in a Week
©Copyright 2002 D. Simchi-Levi
Reminder:Reminder: The Normal Distribution
St d d D i ti 5Standard Deviation = 5
Standard Deviation = 10Standard Deviation 10
0 10 20 30 40 50 60
Average = 30
0 10 20 30 40 50 60
©Copyright 2002 D. Simchi-Levi
The DC holds inventory to:
•• Satisfy demand during lead time Satisfy demand during lead time
• Protect against demand uncertainty
• Balance fixed costs and holding costs
©Copyright 2002 D. Simchi-Levi
e o
•
The Multi-Period Inventory Model • Normally distributed random demand • Fixed order cost plus a cost proportional to amount
ordered. • Inventory cost iis chhargedd per iitem per uniit tiime • If an order arrives and there is no inventory, the
o d i torder is lol st • The distributor has a required service level. This is
expressed as the the likelihood that the distributorexpressed as the the likelihood that the distributor will not stock out during lead time.
• IntuitivelyIntuitively, how will this effect our policy?how will this effect our policy?
©Copyright 2002 D. Simchi-Levi
A View of (s, S) Policy In
vent
oory
Levve
l
SS
s
Inventory Position
Lead Time LeadTime
0 Time
©Copyright 2002 D. Simchi-Levi
The (s,S) Policy • (s, S) Policy: Whenever the inventory position
drops below a certain level, s, we order to raise the inventory position to level S.
• The reorder point is a function of: – The Lead Time – Average demand – Demand variabilityDemand variability – Service level
©Copyright 2002 D. Simchi-Levi
Notation • AVG = average daily demand • STD = standard deviation of daily demand • LT = replenishment lead time in days • h = holding cost of one unit for one day • SL = service level (for example, 95%). This implies
that the probability of stocking out is 100%-SL (for example, 5%)
• AlAlso, ththe IInventtory PPositi ition att any ti time iis th the actual inventory plus items already ordered, but not yet delivered yet delivered.
©Copyright 2002 D. Simchi-Levi
Analysis • The reorder point has two components:
– To account for average demand during lead time: LT×AVG
– To account for deviations from average (we call this safetyTo account for deviations from average (we call this safety stock)
z × STD × √LT where z is chosen from statistical tables to ensure that thewhere z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is 100%-SL.
©Copyright 2002 D. Simchi-Levi
Example • The distributor has historically observed weekly
ddemandd off: AVG = 44.6 STD = 32.1
Replenishment lead time is 2 weeks and desired Replenishment lead time is 2 weeks, and desired service level SL = 97%
• Average demand during lead time is:Average demand during lead time is: 44.6 × 2 = 89.2
• Safetyy Stock is: 1.88 × 32.1 × √2 = 85.3
• Reorder point is thus 175, or about 3.9 weeks of supply at warehouse and in the pipeline
©Copyright 2002 D. Simchi-Levi
Fixed Order Schedule
• Suppppose the distributor pplaces orders everyy month
• What policy should the distributor use?
• What about the fixed cost?
©Copyright 2002 D. Simchi-Levi
Base-Stock Policy Target Inventory
Units Expected UBUnits Expected UB
,
r1 r2 r3 Time
Expected LB
L L L
©Copyright 2002 D. Simchi-Levi
Risk Pooling • Consider these two systems:
Supplier
Warehouse One Market One
Market Two Warehouse Two
Market One
M k t T
Supplier Warehouse
Market Two
©Copyright 2002 D. Simchi-Levi
Risk Pooling • For the same service level, which system will
require more inventory? Why? • For the same total inventoryy level ,, which
system will have better service? Why?
• What are the factors that affect theseWhat are the factors that affect theseanswers?
©Copyright 2002 D. Simchi-Levi
g
Risk Pooling Example • Compare the two systems:
– two products – maintain 97% service level – $60 order cost – $.27 weekly holding cost – $1.05 transportation cost per unit in decentralized
system, $1.10 in centralized system – 1 week lead time
©Copyright 2002 D. Simchi-Levi
Risk Pooling Example
Week 1 2 3 4 5 6 7 8
Prod A, Market 1
33 45 37 38 55 30 18 58
Prod A, Market 2
46 35 41 40 26 48 18 55
Prod B, Market 1
0 2 3 0 0 1 3 0
Product B Product B, Market 2
22 44 00 00 33 11 00 00
©Copyright 2002 D. Simchi-Levi
Risk Pooling Example Warehouse Product AVG STD CV
Market 1 A 39.3 13.2 .34
Market 2 A 38.6 12.0 .31
Market 1 B 1.125 1.36 1.21
Market 2 B 1.25 1.58 1.26
©Copyright 2002 D. Simchi-Levi
Risk Pooling Example Warehouse Product AVG STD CV s S Avg.
InvenInven. % Dec Dec.
Market 1 A 39.3 13.2 .34 65 158 91
Market 2 A 38.6 12.0 .31 62 154 88
Market 1 B 1.125 1.36 1.21 4 26 15 Market 2 B 1.25 1.58 1.26 5 27 15 Cent. A 77.9 20.7 .27 118 226 132 26% Cent B 2.375 1.9 .81 6 37 20 33%
©Copyright 2002 D. Simchi-Levi
Risk Pooling:Risk Pooling: Important Observations
• Centralizing inventory control reduces both safety stock and average inventory level for the same service level.
• This works best for – Higgh coefficient of variation,, which reduces
required safety stock. – Negatively correlated demand. Why?
• What other kinds of risk pooling will we see?
©Copyright 2002 D. Simchi-Levi
–
To Centralize or not to Centralize
• What is the effect on:– Safety stock? – Service level?Service level? – Overhead? – Lead time? – Transpportation Costs?
©Copyright 2002 D. Simchi-Levi
Inventory Management: Best Practice
• Periodic inventoryy review policy (59%)) p y ( • Tight management of usage rates, lead
times and safety stock (46%)times and safety stock (46%) • ABC approach (37%) • Reduced safety stock levels (34%) • Shift more inventory Shift more inventory, or inventory• or inventory
ownership, to suppliers (31%)• Quantitative approaches (33%)
©Copyright 2002 D. Simchi-Levi
to o e 3 o e a e
Changes In Inventory Turnover
• Inventoryy turns increased byy 30% from 1995 to 1998
• Inventory turns increased by 27% from• Inventory turns increased by 27% from 1998 to 2000
• Overall the increase is from 8.0 turns per year to over 13 per year over a fivepe yea pe yeayear period ending in year 2000.
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Industry
Inventory Turnover Ratio Upper
Quartile Median Lower
Quartile Dairy Products 34.4 19.3 9.2
Electronic Component 9.8 5.7 3.7 Electronic Computers 9 4 5 3 3 5 Electronic Computers 9.4 5.3 3.5
Books: publishing 9.8 2.4 1.3
Household audio & video equipment
6.2 3.4 2.3
Household electrical 8.0 5.0 3.8 appliances
8.0 5.0 3.8
Industrial chemical 10.3 6.6 4.4
©Copyright 2002 D. Simchi-Levi
Factors that Drive Reduction inFactors that Drive Reduction in Inventory
• Top management emphasis on inventory reduction (19%)(19%)
• Number of SKUs in the warehouse (10%) d f i %) • Improved forecasting ((7%)
• Use of sophisticated inventory management software (6%)(6%)
• Coordination among supply chain members (6%) • OthOthers
©Copyright 2002 D. Simchi-Levi
Factors that will Drive InventoryFactors that will Drive Inventory Turns Change by 2000
• Better software for inventory management (16.2%)• Reduced lead time (15%) • Improved forecasting (10.7%) • Application of SCM principals (9.6%) • More attention to inventory management (6.6%) • Reduction in SKU (5.1%) • Others
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ESD.273J / 1.270J Logistics and Supply Chain Management Fall 2009
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