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Product Availability
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Level of product availability
Also referred as customer service level.
Is measured using the cycle service level or fillrate.
Is high to improve the responsiveness andattract customers.
But high level requires large inventories. These large inventories tend to raise cost for SC.
Therefore, SC needs to balance between level ofinventory and cost of inventory.
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Factors affecting optimal level ofproduct availability
Before understanding factors considerone example of a storekeeper who sells
jacket.
He buys the stock for entire seasonssupply of jacket before start of sellingseason.
High level of product availability requireslarge number of jackets.
It is likely to satisfy all demands. However, it results in a large number of
unsold jackets at the end of season.
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Example
On the other hand, low level of productavailability results in few unsold
jackets.
In this scenario, a loss of potentialcustomers has to bear.
Must balance the loss from having toomany unsold jackets and lost profitfrom turning away customers.
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12-5
Mattel, Inc. & Toys R Us
Mattel was hurt last year by inventory cutbacks at Toys RUs, and officials are also eager to avoid a repeat of the 1998Thanksgiving weekend. Mattel had expected to ship a lot ofmerchandise after the weekend, but retailers, wary of
excess inventory, stopped ordering from Mattel. That led thecompany to report a $500 million sales shortfall in the lastweeks of the year ... For the crucial holiday selling seasonthis year, Mattel said it will require retailers to place their fullorders before Thanksgiving. And, for the first time, the
company will no longer take reorders in December, Ms.Barad said. This will enable Mattel to tailor production moreclosely to demand and avoid building inventory for ordersthat don't come.
- Wall Street Journal, Feb. 18, 1999
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12-6
Key Questions
How much should Toys R Us ordergiven demand uncertainty?
How much should Mattel order? Will Mattels action help or hurt
profitability?
What actions can improve supply chainprofitability?
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Importance of the Levelof Product Availability
Product availability measured by cycle service level or fill rate Also referred to as the customer service level Product availability affects supply chain responsiveness Trade-off:
High levels of product availability increased responsiveness andhigher revenues
High levels of product availability increased inventory levels andhigher costs
Product availability is related to profit objectives, and strategicand competitive issues (e.g., Nordstrom, power plants,
supermarkets, e-commerce retailers) What is the level of fill rate or cycle service level that will result
in maximum supply chain profits?
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Factors Affecting the OptimalLevel of Product Availability
Cost of overstocking
Cost of understocking
Possible scenarios Seasonal items with a single order in a season
One-time orders in the presence of quantitydiscounts
Continuously stocked items Demand during stockout is backlogged
Demand during stockout is lost
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Cost
of overstocking = C0 Is the loss incurred by a firm for each unsold
unit at the end of selling season.
of understocking = Cu Is the margin lost by a firm for each lost sale
from current and future sales if customer doesnot return.
Two factors that affect optimal level of
product availability. Cost of overstocking
Cost of understocking
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Optimal level of product
availability Makes sense in the context of demand
uncertainty.
Firms have forecast a consensus estimate ofdemand without any measure of uncertainty.
Now they have better appreciation foruncertainty.
Incorporation of uncertainty and optimal levelof product availability can increase profit.
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ExampleDemand distribution for jackets
Demand Di(*100) Probability Cumulative probability ofdemand being Dior less
probability of demandbeing greater then Di
4 0.01 0.01 0.99
5 0.02 0.03 0.97
6 0.04 0.07 0.93
7 0.08 0.15 0.85
8 0.09 0.24 0.76
9 0.11 0.35 0.65
10 0.16 0.51 0.49
11 0.20 0.71 0.29
12 0.11 0.82 0.18
13 0. 10 0.92 0.08
14 0.04 0.96 0.04
15 0.02 0.98 0.02
16 0.01 0.99 0.01
17 0.01 1.00 0.00
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Example Expected profit from ordering a thousands of jacket
=$49,900
Potential outcome to buy 100 more jackets If extra 100 are sold, then profit=$5,500
If 100 units are send to outlet, then loss=$500
From table, there is 0.49 probability that demand is 1100 or higherand a 0.51 probability that demand will be 1000 or less.
Expected profit=$5,500Xprob[Demand1,100]
-$500Xprob[Demand
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Optimal cycle service levelfor seasonal items
Focus on seasonal product whereleftover items must be disposed at theend of season.
Input:C0: cost of overstocking = c-s
Cu: cost of understocking =p-c
CSL*=optimal cycle service level
O*=corresponding optimal order size
CSL*=probability that demand during seasonwill be at or below O*.
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Optimal cycle service levelfor seasonal items
Rise in quantity from O* to O*+1 is withprobability 1-CSL* Expected profit of purchasing extra unit= (1-
CSL*)(p-c) If additional unit remains unsold if demand is
below O*
Expected cost of purchasing cost of extra
unit=CSL*(c-s) Expected marginal contribution of raising the
order size from O* to O*+1=(1-CSL*)(p-c)-CSL*(c-s)
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Optimal cycle servicelevel for seasonal items
Expected marginal cost=0 CSL*=probability (demandO*)= (p-c)/(p-s)
C0/(Cu+C0)=1/{1+(C0/Cu)}
Optimal CSL* is referred as critical fractile
If demand during season is normally distributed withmean and standard deviation , optimal orderquantity
O*=F-1(CSL*, , )
Expected profit=
Fs is the standard normal cumulative distribution function andfs is the standard normal density function
s sO O
p s F p s f
O(c s)F(O, , ) O(p c)[1 F(O, , )]
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Desired cycle service level forcontinuously stocked items
Focus on products such as detergent that areordered repeatedly.
Organization uses safety inventory to increase thelevel of safety inventory to avoid stocking out.
Left over detergent can be sold in next cycle.
However, holding cost is incurred form one cycle tonext cycle.
Two extreme scenarios All demands that arises when the product is out of stock is
backlogged and filled later
All demand arising when product is out of stock is lost.
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When Demand during stockoutis backlogged
No demand is lost, minimizing costs isequivalent to maximizing profit.
When store is out of stock, discount of Cu isprovided to each customer.
Ensures that each customer will return. Increase in safety inventory satisfies more orders
resulting in less backlogs Cost of holding inventory increases. Level of safety inventory that minimizes backlogs
and holding cost?? Optimal cycle service level CSL*=1-(HQ/DCu)
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Example
Input Q=400 gallons, ROP= 300 gallons, D=100
gallons, D=20, unit cost=$3, holding cost
as a fraction of cost h=0.2, cost of holdingone unit for one year=0.6 Lead time =2weeks
Cost of stocking out?? If all unfilled
demand is backlogged and carried over tonext cycle.
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Solution
Mean demand over lead time DL=DL=200gallons
Standard deviation of demand in lead time
CSL=F(ROP, DL, L) =F(300, 200, 28.3)
CSL=NORMDIST(300, 200, 28.3, 1)=0.9998
Imputed cost of stocking out Cu=HQ/(1-
CSL)Dyear=0.6*400/0.0002*5,200=230.8 pergallon
L D L 20 2 28.3
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When Demand during stock out is lost
Optimal cycle service level CSL*
CSL*=1-HQ/(HQ+DCu)
Cuis the cost of loosing one unit ofdemand during stockout period.
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Managerial levers to improveSC profitability Focus on actions that can be taken to improvethe SC profitability Two obvious managerial levers
1. Increasing the salvage value of each unit increases
profitability.2. Decreasing the margin lost from a stockoutincreases profitability.
Strategies to1. Increase to salvage value include selling outlet
stores so that left units are not merely discarded.2. To decrease the margin lost in a stockout include
arranging the backup sourcing so that customersare not lost forever.
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Importance of the Ratio of cost ofoverstocking and understocking
If this gets smaller, optimal level ofproduct availability increases.
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Another lever
Is to reduction of demand uncertainty.
By this, better supply and demand canbe matched by reducing over and
understocking. Means to reduce demand uncertainty.
Improved forecasting
Quick response Postponement
Tailored sourcing
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Improving forecast
Helps the demand planning informationsystems.
Can help a firm to increase itsprofitability while decreasing excessinventory overstock and sales lost dueto understocking.
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Improved Forecasts
Improved forecasts result in reduceduncertainty
Less uncertainty (lower R) results in
either: Lower levels of safety inventory (and costs) for
the same level of product availability, or
Higher product availability for the same levelof safety inventory, or
Both lower levels of safety inventory andhigher levels of product availabilityAn increase in forecast accuracy decreases both the overstocked
and understocked quantity and increases a firms profits.
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Impact of Improving Forecasts(Example)
Demand: Normally distributed with a meanof R= 350 and standard deviation of R=100
Purchase price = $100Retail price = $250
Disposal value = $85
Holding cost for season = $5
How many units should be ordered as Rchanges?
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Impact of Improving Forecasts
R O* Expected Overstock
ExpectedUnderstock
ExpectedProfit
150 526 186.7 8.6 $47,469
120 491 149.3 6.9 $48,476
90 456 112.0 5.2 $49,482
60 420 74.7 3.5 $50,488
30 385 37.3 1.7 $51,494
0 350 0 0 $52,500
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Quick response
Is the set of actions a supply chain takes thatleads in the reduction of lead time.
Decrease in lead time results in increase in
forecast accuracy. This allows them to better match with the
demand and increase in profitability.
Typically, buyers are able to make accurateforecasts once they have observed demandin first or second week in season.
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Quick Response Set of actions taken by managers to reduce lead time
Reduced lead time results in improved forecasts
Typical example of quick response is multiple orders in one seasonfor retail items (such as fashion clothing)
For example, a buyer can usually make very accurate forecasts afterthe first week or two in a season
Multiple orders are only possible if the lead time is reducedotherwise there wouldnt be enough time to get the later orders beforethe season ends
Benefits:
Lower order quantitiesless inventory, same product availability
Less overstock
Higher profits
If quick response allows multiple orders in the season, profitsincrease and the overstock quantity decreases.
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Example
Selling season is of 14 weeks. Replenishment time is 25 to 30 weeks.
Difficult for a buyer to make a accurateforecast of demand this far in advance.
This results in high demand uncertainty,leading the buyer in too many or too less unitseach year.
Consider a case where replenishment time
can reduce upto 6 weeks. Its results in entire seasons purchase in two
orders.
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Variation of profit and inventories with
forecast accuracy
Expected understock
Expected over stock
Expected profit
Standard deviation of forecast error
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Quick Response: MultipleOrders Per Season
Ordering shawls at a department store Selling season = 14 weeks
Cost per handbag = $40
Sale price = $150 Disposal price = $30
Holding cost = $2 per week
Expected weekly demand = 20 SD of weekly demand = 15
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Comparison of two policies
1. A single order must arrive at the beginningof the season to cover the entire seasonsdemand.
2. Two orders are placed in the season, one
arriving at the beginning of the season andother arriving at the beginning of the eightweek.
3. Now consider two instances
One where buyers forecast accuracy does notimprove for the second order and where itimproves and the SD can be reduced.
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Comparison
Single order: consists of a quantity ordered atthe beginning of season.
Two orders: consists of initial order quantity forfirst seven weeks followed by an order upto
level for the second week. Second round quantity should account for sales
during the first week and inventory remaining.
The quantity ordered in second round it thedifference between order up-to-level andinventory remaining after first week.
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Consequences of being able toplace a second order
1. Consequences1. The expected total quantity ordered during the season
with two orders is less than that with a single order for thesame cycle service level.
2. The average overstock to be disposed of at the end of thesales season is less if two orders are allowed.
3. The profits are higher when a second order is allowedduring the sales season.
Total quantity is broken up intomultiple smaller orders, the buyer isbetter able to match supply anddemand and increase profitability.
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Impact of Quick Response
Single Order Two Orders in Season ServiceLevel
OrderSize
EndingInvent.
Expect.Profit
InitialOrder
OULfor 2nd
Order
AverageTotalOrder
EndingInvent.
Expect.Profit
0.96 378 97 $23,624 209 209 349 69 $26,590
0.94 367 86 $24,034 201 201 342 60 $27,085
0.91 355 73 $24,617 193 193 332 52 $27,154
0.87 343 66 $24,386 184 184 319 43 $26,944
0.81 329 55 $24,609 174 174 313 36 $27,413
0.75 317 41 $25,205 166 166 302 32 $26,916
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Forecast Improves for SecondOrder (SD=3 Instead of 15)
Single Order Two Orders in Season
ServiceLevel
OrderSize
EndingInvent.
Expect.Profit
InitialOrder
OULfor 2nd
Order
AverageTotalOrder
EndingInvent.
Expect.Profit
0.96 378 96 $23,707 209 153 292 19 $27,007
0.94 367 84 $24,303 201 152 293 18 $27,371
0.91 355 76 $24,154 193 150 288 17 $26,946
0.87 343 63 $24,807 184 148 288 14 $27,583
0.81 329 52 $24,998 174 146 283 14 $27,162
0.75 317 44 $24,887 166 145 282 14 $27,268
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Postponement Delay of product differentiation until closer to the time of the sale
of the product All activities prior to product differentiation require aggregate
forecasts more accurate than individual product forecasts
Individual product forecasts are needed close to the time of saledemand is known with better accuracy (lower uncertainty)
Results in a better match of supply and demand
Valuable in e-commercetime lag between when an order isplaced and when customer receives the order (this delay isexpected by the customer and can be used for postponement)
Higher profits, better match of supply and demandPostponement allows a firm to increase profits and better match supply anddemand if the firm produces a large variety of products whose demand is notpositively correlated and is of about the same size.
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Postponement
Refers to the delay of productdifferentiation until closer to the sale ofproduct.
Aggregate forecasts are more accuratethen individual product forecasts.
Individual forecasts are required close to
the time of sale when demand is knownwith greater accuracy.
Allows a SC to better match SC demand.
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Postponement
A powerful managerial tool to increaseprofitability.
However, while using it production cost
would be higher than the case wherethere is no postponement.
Is valuable to for a firm that sells a
large variety of products with demand.
Value of Postponement:
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Value of Postponement:Benetton
For each color
Mean demand = 1,000; SD = 500 For each garment
Sale price = $50
Salvage value = $10
Production cost using Option 1 (long lead time) =$20
Production cost using Option 2 (uncoloredthread) = $22
What is the value of postponement? Expected profit increases from $94,576 to
$98,092
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Value of Postponementwith Dominant Product
Color with dominant demand: Mean =3,100, SD = 800
Other three colors: Mean = 300, SD = 200
Expected profit without postponement =$102,205
Expected profit with postponement =$99,872
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Tailored postponement A firm uses production with postponement to satisfy a
part of demand with the rest being satisfied without it. Produces higher profits then when no postponements
is used or all are produced using postponement.
A firm produces a portion of demand which is
uncertain, postponement significantly improves theforecasts accuracy.
Thus, allows a firm to increase its profitability by onlypostponing the uncertain part of the demand andproducing the predictable part at a lower cost without
postponement.
a ore os ponemen :
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a ore os ponemen :Benetton
Produce Q1units for each color using Option 1 and QA
units (aggregate) using Option 2 Results:
Q1= 800
QA= 1,550
Profit = $104,603
Tailored postponement allows a firm to increase profits bypostponing differentiation only for products with the mostuncertain demand; products with more predictable
demand are produced at lower cost without postponement
T il d S i
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Tailored SourcingA firm uses a combination of two supply
sources One is lower cost but is unable to deal with
uncertainty well
The other is more flexible, and can thereforedeal with uncertainty, but is higher cost
The two sources must focus on differentcapabilities
Depends on being able to have one sourcethat faces very low uncertainty and cantherefore reduce costs
Increase profits, better match supply and
demand
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Tailored sourcing
Firms uses a combination of two supply sources1. Focusing on cost but unable to handle the uncertainty.
2. Focusing on flexibility to handle uncertainty but at higher cost.
But, to be effective, having supply sources where oneserves as the backup to other is not sufficient.
The first should be required to supply the predictable portionof demand.
The second should be responsive and be required to supply
the uncertain portion of demand. Allows to better match supply and demand and increase of
profit.
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Tailored sourcing
Value depends on the reduction in costthat can be achieved.
Small benefitit may not be ideal.
May be volume based or product based
depending on source depending on thesource of uncertainty.
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Volume based
Tailored sourcing, the predictable part of aproducts demand is produced at an efficientfacility.
Should be considered by firms that havemoved a lot of their production overseas totake advantage of lower costs.
In this condition source with shorter lead timeis more profitable even if he is moreexpensive.
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Product based
Low volume product with uncertain demand areobtained from a flexible source while high volumeproduct with less demand uncertainty are obtained forman efficient source.
New products have a very uncertain demand while wellestablished products have more stable demand.
May be implemented with a flexible facility focusing onnew products and efficient facilities focusing on wellestablished products.
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Tailored Sourcing
Sourcing alternatives
Low cost, long lead time supplier
Cost = $245, Lead time = 9 weeks
High cost, short lead time supplier Cost = $250, Lead time = 1 week
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Tailored Sourcing Strategies
Fraction of demand from
overseas supplier
Annual Profi t
0% $37,250
50% $51,613
60% $53,027
100% $48,875
T il d S i M lti l
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Tailored Sourcing: MultipleSourcing Sites
Characteristic Primary Site Secondary Site
Manufacturing
Cost
High Low
Flexibility(Volume/Mix)
High Low
Responsiveness High Low
EngineeringSupport
High Low
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Dual Sourcing Strategies
Strategy Primary Site Secondary Site
Volume based
dual sourcing
Fluctuation Stable demand
Product baseddual sourcing
Unpredictableproducts,
Small batch
Predictable,large batch
productsModel baseddual sourcing
Newerproducts
Older stableproducts
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Setting Product Availability for MultipleProducts under Capacity Constraints
Single product order
Multiple product order
Decrease the order sizeAllocating the products
When ordering multiple products under a limited supply capacity,
the allocation of capacity to products should be based on theirexpected marginal contribution to profits.
This approach allocates a relatively higher fraction of capacity toproducts that have a high margin relative to their cost of
overstocking.
S tti O ti l L l f
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Setting Optimal Levels ofProduct Availability in Practice
Use an analytical framework to increaseprofits
Beware of preset levels of availability
Use approximate costs because profit-maximizing solutions are very robust
Estimate a range for the cost of stocking
out Ensure levels of product availability fit with
the strategy