ch 03 inventory management supply contracts and risk pooling
TRANSCRIPT
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InventoryManagement, Supply
Contracts and RiskPooling
Phil [email protected]
David Simchi-Levi
Philip Kaminsky
Edith Simchi-Levi
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Outline of the Presentation
Introduction to Inventory Management
The Effect of Demand Uncertainty
(s,S) Policy Periodic Review Policy
Supply Contracts
Risk Pooling
Centralized vs. Decentralized Systems
Practical Issues in Inventory Management
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Supply
Sources:plants
vendorsports
RegionalWarehouses:
stockingpoints
FieldWarehouses:stocking
points
Customers,demandcenterssinks
Production/purchasecosts
Inventory &warehousingcosts
Transportationcosts Inventory &
warehousingcosts
Transportationcosts
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Inventory
Where do we hold inventory? Suppliers and manufacturers warehouses and distribution centers
retailers Types of Inventory
WIP raw materials finished goods
Why do we hold inventory? Economies of scale Uncertainty in supply and demand Lead Time, Capacity limitations
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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 management
GM has reduced parts inventory andtransportation costs by 26% annually
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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 the consequence of higher than anticipatedexcess inventory (WSJ, July 15, 1993)
In 1993, Dell Computers predicts a loss; Stock plunges.Dell acknowledged that the company was sharply off inits forecast of demand, resulting in inventory writedowns (WSJ, August 1993)
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Understanding Inventory
The inventory policy is affected by:
Demand Characteristics
Lead Time
Number of Products
Objectives
Service levelMinimize costs
Cost Structure
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Cost Structure
Order costs Fixed
Variable Holding Costs
Insurance
Maintenance and Handling
Taxes Opportunity Costs
Obsolescence
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EOQ: A Simple Model*
Book Store Mug Sales
Demand is constant, at 20 units a week
Fixed order cost of $12.00, no lead time
Holding cost of 25% of inventory valueannually
Mugs cost $1.00, sell for $5.00 Question
How many, when to order?
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EOQ: A View of
Inventory*
Time
Inventory
Order
Size
Note:
No Stockouts
Order when no inventory
Order Size determines policy
Avg. Inven
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EOQ: Calculating Total
Cost* Purchase Cost Constant Holding Cost: (Avg. Inven) * (Holding Cost) Ordering (Setup Cost):
Number of Orders * Order Cost Goal: Find the Order Quantity that
Minimizes These Costs:
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EOQ:Total Cost*
0
20
40
60
80
100
120
140
160
0 500 1000 1500
Order Quantity
Co
Total Cost
Order Cost
Holding Cost
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EOQ: Optimal Order
Quantity* Optimal Quantity =
(2*Demand*Setup Cost)/holding cost
So for our problem, the optimal quantity is
316
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EOQ: Important
Observations* Tradeoffbetween set-up costs and holding costs
when determining order quantity. In fact, we order
so that these costs are equal per unit time Total Cost is not particularly sensitive to the
optimal order quantity
Order Quantity 50% 80% 90% 100% 110% 120% 150% 200%
Cost Increase 125% 103% 101% 100% 101% 102% 108% 125%
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The 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 sellingseason Companies are aware of demand uncertainty when they
create a forecast, but they design their planning processas if the forecast truly represents reality
Recent technological advances have increasedthe level of demand uncertainty: Short product life cycles Increasing product variety
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Demand Forecast
The three principles of all forecastingtechniques:
Forecasting is always wrong
The longer the forecast horizon the worst is the
forecast Aggregate forecasts are more accurate
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SnowTime Sporting
Goods Fashion items have short life cycles, high variety
of competitors
SnowTime Sporting Goods New designs are completed
One production opportunity
Based on past sales, knowledge of the industry, and
economic conditions, the marketing department has aprobabilistic forecast
The forecast averages about 13,000, but there is achance that demand will be greater or less than this.
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Supply Chain Time Lines
Jan 00 Jan 01 Jan 02
Feb 00 Sep00 Sep01
Design Production Retailing
Feb01Production
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SnowTime Demand
ScenariosDemand Scenarios
0%
5%
10%
15%
20%
25%30%
8000
10000
12000
14000
16000
18000
Sales
Probabili
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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
Profit =Revenue - Variable Cost - Fixed Cost + Salvage
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SnowTime Scenarios
Scenario One: Suppose 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 and demand ends up
being 11,000 jackets. Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000)
= $ 335,000
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SnowTime Best Solution
Find order quantity that maximizes weightedaverage profit.
Question: Will this quantity be less than,equal to, or greater than average demand?
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What to Make?
Question: Will this quantity be less than,equal to, or greater than average demand?
Average demand is 13,100 Look at marginal cost Vs. marginal profit
if extra jacket sold, profit is 125-80 = 45
if not sold, cost is 80-20 = 60
So we will make less than average
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SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profit
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SnowTime Expected
ProfitExpected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profit
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SnowTime:Important Observations
Tradeoff between ordering enough to meetdemand and ordering too much
Several quantities have the same average profit Average profit does not tell the whole story
Question: 9000 and 16000 unitslead to about the same averageprofit, so which do we prefer?
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SnowTime ExpectedProfit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profit
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Probability of Outcomes
0%
20%
40%
60%
80%
100%
-300
000
-100
000
1000
00
3000
00
5000
00
Revenue
Probability
Q=9000
Q=16000
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Key Insights from thisModel
The optimal order quantity is not necessarily equalto average forecast demand
The optimal quantity depends on the relationshipbetween marginal profit and marginal cost
As order quantity increases, average profit firstincreases and then decreases
As production quantity increases, risk increases.In other words, the probability of large gains and oflarge losses increases
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Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
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Demand Scenarios
Demand Scenarios
0%
5%
10%
15%
20%25%
30%
8000
1000
0
1200
0
14000
1600
0
1800
0
Sales
Probability
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Distributor ExpectedProfit
Expected Profit
0
100000
200000
300000
400000
500000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
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Distributor ExpectedProfit
Expected Profit
0
100000
200000
300000
400000
500000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
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Supply Contracts (cont.)
Distributor optimal order quantity is 12,000units
Distributor expected profit is $470,000 Manufacturer profit is $440,000 Supply Chain Profit is $910,000
Is there anything that the distributorand manufacturer can do to increasethe profit of both?
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Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
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Retailer Profit(Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
6
000
7
000
8
000
9
000
10
000
11
000
12
000
13
000
14
000
15
000
16
000
17
000
18
000
Order Quantity
RetailerP
rofit
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Retailer Profit(Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
6
000
7
000
8
000
9
000
10
000
11
000
12
000
13
000
14
000
15
000
16
000
17
000
18
000
Order Quantity
RetailerP
rofit
$513,800
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Manufacturer Profit(Buy Back=$55)
0
100,000
200,000
300,000400,000
500,000
600,000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
Production Quantity
Manufacturer
Profit
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Manufacturer Profit(Buy Back=$55)
0
100,000
200,000
300,000400,000
500,000
600,000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
Production Quantity
Manufacturer
Profit $471,900
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Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$??
Supply Contracts
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Retailer Profit(Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
15000
1600
0
1700
0
1800
0
Order Quantity
RetailerProfit
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Retailer Profit(Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
15000
1600
0
1700
0
1800
0
Order Quantity
RetailerProfit
$504,325
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Manufacturer Profit(Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
Production Quantity
Manufacturer
Profit
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Manufacturer Profit(Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
Production Quantity
Manufacturer
Profit
$481,375
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Supply Contracts
Strategy Retailer Manufacturer Total
Sequential Optimization 470,700 440,000 910,700Buyback 513,800 471,900 985,700
Revenue Sharing 504,325 481,375 985,700
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Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
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Supply Chain Profit
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
1500
0
1600
0
1700
0
1800
0
Production Quantity
SupplyChain
Profit
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Supply Chain Profit
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
Production Quantity
SupplyChain
Profit $1,014,500
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Supply Contracts
Strategy Retailer Manufacturer Total
Sequential Optimization 470,700 440,000 910,700Buyback 513,800 471,900 985,700
Revenue Sharing 504,325 481,375 985,700
Global Optimization 1,014,500
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Supply Contracts: KeyInsights
Effective supply contracts allow supplychain partners to replace sequential
optimization by global optimization Buy Back and Revenue Sharing contracts
achieve this objective through risk sharing
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Supply Contracts: CaseStudy
Example: Demand for a movie newly releasedvideo cassette typically starts high and decreasesrapidly
Peak demand last about 10 weeks Blockbuster purchases a copy from a studio for
$65 and rent for $3 Hence, retailer must rent the tape at least 22 times
before earning profit Retailers cannot justify purchasing enough to
cover the peak demand In 1998, 20% of surveyed customers reported that they
could not rent the movie they wanted
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Supply Contracts: CaseStudy
Starting in 1998 Blockbuster entered a revenuesharing agreement with the major studios Studio charges $8 per copy
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 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 retailer, Hollywood Entertainment Corp has 5%market share)
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Other Contracts
Quantity Flexibility Contracts
Supplier provides full refund for returned items
as long as the number of returns is no largerthan a certain quantity
Sales Rebate Contracts
Supplier provides direct incentive for the retailerto increase sales by means of a rebate paid bythe supplier for any item sold above a certainquantity
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SnowTime Costs: InitialInventory
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
Profit =Revenue - Variable Cost - Fixed Cost + Salvage
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SnowTime ExpectedProfit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Profi
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Initial Inventory
Suppose that one of the jacket designs is a modelproduced last year.
Some inventory is left from last year Assume the same demand pattern as before If only old inventory is sold, no setup cost
Question: If there are 7000 units remaining, whatshould SnowTime do? What should they do ifthere are 10,000 remaining?
I iti l I t d
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Initial Inventory andProfit
0
100000
200000
300000
400000
500000
5000
6500
8000
9500
1100
0
1250
0
1400
0
1550
0
Pr oduction Quan
Profit
I iti l I t d
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Initial Inventory andProfit
0
100000
200000
300000
400000
500000
5000
6500
8000
9500
1100
0
1250
0
1400
0
1550
0
Pr oduction Quan
Profit
I iti l I t d
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Initial Inventory andProfit
0
100000
200000
300000
400000
500000
5000
6500
8000
9500
1100
0
1250
0
1400
0
1550
0
Pr oduction Quan
Profit
I iti l I t d
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Initial Inventory andProfit
0
100000
200000300000
400000
500000
5
000
6
000
7
000
8
000
9
000
10
000
11
000
12
000
13
000
14
000
15
000
16
000
Production Quant
Profi
t
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(s, S) Policies
For some starting inventory levels, it is better tonot start production
If we start, we always produce to the same level Thus, we use an (s,S) policy. If the inventory level
is below s, we produce up to S. s 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 ordering,transportation, or manufacturing
A M lti P i d I t
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A Multi-Period InventoryModel
Often, there are multiple reorder opportunities
Consider a central distribution facility which ordersfrom a manufacturer and delivers to retailers. Thedistributor periodically places orders to replenishits inventory
R i d
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Reminder:The Normal Distribution
0 10 20 30 40 50 60Average = 30
Standard Deviation = 5
Standard Deviation = 10
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The DC holds inventory to:
Satisfy demand during lead time
Protect against demanduncertainty
Balance fixed costs and holdingcosts
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The Multi-Period Continuous
Review Inventory Model Normally distributed random demand Fixed order cost plus a cost proportional to amount
ordered. Inventory cost is charged per item per unit time If an order arrives and there is no inventory, the order is
lost The distributor has a required service level. This is
expressed as the the likelihood that the distributor willnot stock out during lead time.
Intuitively, how will this effect our policy?
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A View of (s, S) Policy
Time
In
ventory
Le
ve
l
S
s
0
Lead
Time
Lead
Time
Inventory Position
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The (s,S) Policy
(s, S) Policy: Whenever the inventoryposition drops below a certain level, s, we
order to raise the inventory position to levelS. The reorder point is a function of:
The Lead Time
Average demand Demand variability
Service level
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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 K = fixed cost SL = service level (for example, 95%). This implies that the
probability of stocking out is 100%-SL (for example, 5%) Also, the Inventory Position at any time is the actual
inventory plus items already ordered, but not yet delivered.
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Analysis
The reorder point (s) has two components: To account for average demand during lead time:
LT AVG To account for deviations from average (we call this safety stock)
z STD LTwhere z is chosen from statistical tables to ensure that the probability ofstockouts during leadtime is100%-SL.
Since there is a fixed cost, we order more than up to the reorderpoint:
Q=(2 K AVG)/h The total order-up-to level is:
S=Q+s
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Example
The distributor has historically observed weekly demand of:AVG = 44.6 STD = 32.1
Replenishment lead time is 2 weeks, and desired service
level SL = 97% Average demand during lead time is:
44.6 2 = 89.2 Safety 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
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Example, Cont.
Weekly inventory holding cost: .87
Therefore, Q=679
Order-up-to level thus equals: Reorder Point + Q = 176+679 = 855
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Periodic Review
Suppose the distributor placesorders every month
What policy should the distributoruse?
What about the fixed cost?
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Base-Stock Policy
Inv
entory
Le
vel
Time
Base-stock
Level
0
InventoryPosition
r r
L L L
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Periodic Review Policy
Each review echelon, inventory position israised to the base-stock level.
The base-stock level includes twocomponents: Average demand during r+L days (the time until
the next order arrives):(r+L)*AVG
Safety stock during that time:z*STD*r+L
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Market Two
Risk Pooling
Consider these two systems:
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier WarehouseMarket One
Market Two
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Risk Pooling
For the same service level, which systemwill require more inventory? Why?
For the same total inventory level, whichsystem will have better service? Why?
What are the factors that affect these
answers?
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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 centralizedsystem
1 week lead time
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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,
Market 2
2 4 0 0 3 1 0 0
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Risk Pooling Example
Warehouse
Market 1
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Risk Pooling Example
Warehouse Product AVG STD CV s S Avg.
Inven.
%
Dec.
Market 1 A 39.3 13.2 .34 65 197 91
Market 2 A 38.6 12.0 .31 62 193 88
Market 1 B 1.125 1.36 1.21 4 29 14
Market 2 B 1.25 1.58 1.26 5 29 15
Cent. A 77.9 20.7 .27 118 304 132 36%
Cent B 2.375 1.9 .81 6 39 20 43%
Risk Pooling:
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Risk Pooling:Important Observations
Centralizing inventory control reduces bothsafety stock and average inventory level for
the same service level. This works best for
High coefficient of variation, which increases
required safety stock. Negatively correlated demand. Why?
What other kinds of risk pooling will we see?
Risk Pooling:
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Risk Pooling:
Types of Risk Pooling*
Risk Pooling Across Markets Risk Pooling Across Products
Risk Pooling Across Time Daily order up to quantity is:
LT AVG + z AVG LT
10 1211 13 14 15
Demands
Orders
To Centralize or not to
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To Centralize or not toCentralize
What is the effect on:
Safety stock?
Service level? Overhead?
Lead time?
Transportation Costs?
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Centralized Decision
Supplier
Warehouse
Retailers
Centralized Systems*
Centralized Distribution
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Centralized DistributionSystems*
Question: How much inventory should managementkeep at each location?
A good strategy:
The retailer raises inventory to level Sreach period The supplier raises the sum of inventory in the
retailer and supplier warehouses and in transit to Ss
If there is not enough inventory in the warehouse to
meet all demands from retailers, it is allocated sothat the service level at each of the retailers will beequal.
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Changes In Inventory
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Changes In InventoryTurnover
Inventory turnover ratio =annual sales/avg. inventory level
Inventory turns increased by 30% from 1995to 1998 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 five yearperiod ending in year 2000.
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Indus
Inventory Turnover Ratio
Factors that Drive
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Factors that DriveReduction in Inventory
Top management emphasis on inventoryreduction (19%)
Reduce the Number of SKUs in the warehouse(10%) Improved forecasting (7%) Use of sophisticated inventory management
software (6%) Coordination among supply chain members (6%) Others
Factors that Drive Inventory
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Factors that Drive InventoryTurns Increase
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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Forecasting
Recall the three rules Nevertheless, forecast is critical
General Overview: Judgment methods
Market research methods
Time Series methods Causal methods
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Judgment Methods
Assemble the opinion of experts Sales-force composite combines
salespeoples estimates Panels of experts internal, external, both Delphi method
Each member surveyed Opinions are compiled
Each member is given the opportunity tochange his opinion
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Market Research Methods
Particularly valuable for developingforecasts of newly introduced products
Market testing Focus groups assembled. Responses tested.
Extrapolations to rest of market made.
Market surveys Data gathered from potential customers
Interviews, phone-surveys, written surveys, etc.
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Time Series Methods
Past data is used to estimate future data Examples include
Moving averages average of some previous demand points.
Exponential Smoothing more recent points receive more weight Methods for data with trends: Regression analysis fits line to data Holts method combines exponential smoothing concepts with the
ability to follow a trend
Methods for data with seasonality Seasonal decomposition methods (seasonal patterns removed) Winters method: advanced approach based on exponential smoothing
Complex methods (not clear that these work better)
C
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Causal Methods
Forecasts are generated based on dataother than the data being predicted
Examples include: Inflation rates
GNP
Unemployment rates Weather
Sales of other products
Selecting the Appropriate
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Selecting the AppropriateApproach:
What is the purpose of the forecast? Gross or detailed estimates?
What are the dynamics of the system being forecast? Is it sensitive to economic data?
Is it seasonal? Trending? How important is the past in estimating the future? Different approaches may be appropriate for different
stages of the product lifecycle: Testing and intro: market research methods, judgment methods Rapid growth: time series methods Mature: time series, causal methods (particularly for long-range
planning) It is typically effective to combine approaches