Product Availability

8/10/2019 Product Availability

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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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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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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

Product Availability

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