ie563_project_paper oct5.edited

IE563 Term Project (2010 Winter)

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Estimating Cost Savings of Risk-Pooling for an HP DeskJet

Printer Case Study

Takeaki Toma

School of Mechanical, Industrial and Manufacturing Engineering

Oregon State University

Corvallis, OR 97331-2407

Mylie Tong

School of Mechanical, Industrial and Manufacturing Engineering

Oregon State University

Corvallis, OR 97331-2407

Abstract In this paper, we estimated the cost-saving effect of designing a product family by applying

delayed product differentiation (DPD). We estimated the expected cost saving from DPD with

HP printers. We used EOQ, inventory service function, and variance reduction modeling for

estimating the cost savings. We concluded that the cost saving provided by DPD was significant

regardless of IRR and order cost value.

Keywords Supply Chain Management (SCM), Inventory Control, Economic Order Quantity (EOQ), Risk-

pooling, Postponement, Design for Logistics (DFL), and Delayed Product Differentiation (DPD)


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Contents

1. Introduction .......................................................................................................................................... 2

1.1 Hewlett-Packard (HP) DeskJet Printer Case Study ........................................................................ 2

1.2 Problem Statement ............................................................................................................................. 3

2. Methodologies ...................................................................................................................................... 3

2.1 Risk-Pooling and delayed-production-differentiation (DPD) ............................................................ 3

2.2 Available Data and Assumptions ....................................................................................................... 5

2.3 Mathematical Models ....................................................................................................................... 6

3.2 Change of EOQ sizes ........................................................................................................................ 9

3.3 Change of safety stock levels ........................................................................................................... 10

3.4 Change of the total annual cost (TAC) ............................................................................................ 11

4. Discussion (Analysis of the result) ..................................................................................................... 12

4.1 Sensitivity Analysis of order cost Cp ........................................................................................... 12

4.2 Sensitivity Analysis of IRR ............................................................................................................. 14

4.2 Demand Correlations .................................................................................................................... 16

5. Conclusion and Recommendation ...................................................................................................... 18

References ................................................................................................................................................. 19

Appendices ................................................................................................................................................ 19

Spread-sheet modeling .............................................................................................................................. 20


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1. Introduction Although Economic Order Quantity (EOQ) model could be a powerful technique for inventory

control, it assumes accurate demand forecasting. However demand forecasting is a difficult task,

even with sophisticated forecasting techniques and powerful computers. Risk pooling is a

powerful technique for uncertain demand situation in a supply chain. Our study attempts to

estimate the cost-saving effect with Hewlett-Packard’s DeskJet printer case study [1].

1.1 Hewlett-Packard (HP) DeskJet Printer Case Study

In the 1990s, HP needed to reduce the inventory level of DeskJet Printer without sacrificing

service levels for customers in the supply chain. The DeskJet products were a series of ink-jet

printers introduced by HP in the late 80s that became one of their most popular products. With

the steady increase of sales, the available spaces and locations for inventory couldn’t grow to

meet the market demands. The competition with other companies moved from the technical side

to more general business criteria such as cost, reliability, quality, and availability. Specifically,

HP was facing increasing pressure to high levels of availability of their products because the

retailers of HP wanted to carry as little inventory as possible. The forecasting error was serious

problem in the European market. There were product shortages for some models while the

inventory of other models piled up.

HP solved the inventory problem in a creative way. They have redesigned the whole DeskJet

printer family in such a way that generic family inkjet products were manufactured in a

Vancouver factory. Those inkjet printers were sent to European supply chain where they were

customized for each country's specifications (This is called "Delayed Product Differentiation" or

DPD). Because the same inkjet printer inventories are used, the surplus and shortage of inkjet

printer demands are canceled out ("Risk-Pooling") [2]. The DPD is not the only method to

achieve the risk-pooling. The risk-pooling could be also achieved by other techniques such as

aggregating the distributed inventory to larger integrated inventory, or constructing a “virtual”

integrated inventory by sharing the inventory information [1].


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1.2 Problem Statement

Although, risk-pooling is known to be a technique to reduce the inventory level while meeting

customer demand, its initiation and deployment would not be straightforward. We assume it

requires close communication and cooperation between several internal and external departments

and organizations including sales, design, manufacturing, and retailers in the supply chain.

Nevertheless, our hypothesis is that the DPD has a great cost-saving effect.

The goal of our term project was to estimate the expected cost saving of the HP printer based on

the available information and sensitivity analysis. In the methodology section, the mechanism

of DFL of HP’s case study and risk-pooling mathematical modeling are introduced. In section

three, the spreadsheet estimation results were presented. In section four, the assumptions were

analyzed, and section five summarized the analysis results and recommendations.

2. Methodologies In this section, we introduce the methodology used to solve the above problem. First, we present

the details of DPD approach used at HP. Second, we introduce the OR tools to model and

support the manager’s decision.

2.1 Risk-Pooling and delayed-production-differentiation (DPD)

In this subsection, the mechanism of risk-pooling and delayed-production-differentiation (DPD)

techniques used by HP is introduced. Risk-pooling is a variation reduction technique widely

used for financial portfolio, insurance, and supply chain management [2]. It shows that

variability of integrated variance is usually much smaller than the separate variances. Table1 is

an average demand sample data of DeskJet at the Europe. The monthly demand information of

six different printer type (A, AA, AB, AQ, AU, and AY) of the same printer family is shown.

The integrated demand of each month shows that the integrated demand is the sum of the

average demand faced by each printer type. However, the variability of the integrated demand is

much smaller than the combined variabilities. We notice that the coefficient of variation “CV”


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(standard deviation divided by average) is smaller at the integrated demand than separated

demand of each option.

The effect of risk-pooling is clear in safety stock amount. If we have safety stock for each printer

option for the same α level (α =0.05), then the summation of the safety stock of each printer

options is,

=++++=−∗=∑=

38...20607581)1(1112

1

ασ tSSm

pSeparate 3,489 (units)…(1)

On the other hand, the pooled demand’s safety stock is,

=−∗= )1(11 ασ tSS poolPool 2,313 (units)…(2)

Thus, the difference of (1) and (2) could be possible target of cost saving, which is,

=−=− 313,2489,3pooledSeparate SSSS 1176 (units)…(3)

In the 1990s, HP used the risk-pooling method. They redesigned the DeskJet product family so

that the demand variance of each printer option was pooled. Practically, HP postponed the final

assembly process that customizes the DeskJet printer to meet the local language and power

supply requirements needed for the regional countries. Since the last stage of customization is

postponed, this is called “delayed product differentiation” (DPD).


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2.2 Available Data and Assumptions

Table1 shows the actual European market of demand information for HP’s DeskJet printer.

Table 1 Demand Information (Adopted from the reference [1]), P174, Table 8.1)

Table 2 shows the estimated parameters. The procurement cost Cp was estimated from the

shipping and handling cost of Amazon.com. The unit manufacturing cost was obtained from the

cost estimation report from Cypres Lab Corporation [4]. The internal rate of return (IRR) was

estimated from the typical high-tech company's expected IRR. It was assumed that the holding

cost could be estimated by multiplying the unit manufacturing cost and the IRR. Since we were

not confident of the point estimates of Cp and IRR value, we conducted sensitivity analysis.

Table 2 Information Table Items Values Information Sources

Product Name HP DeskJet

3940 series

HP

www.hp.com

Demand Information Table-1 Deskjet demand data sample from Reference[1]

Procurement cost Cp $26.29 Shipping & Handling cost of similar HP primer from Amazon.com

Unit Manufacturing

Cost V

$54.48 Cypres Lab~ Cost estimation for HP DeskJet 3940

http://www.cypress-labs.com/pdf/HPDeskjet3940-part1.pdf

Internal Rate of Return 35% From Google with keyword “what is the typical internal rate of return for

high-tech company”, we obtained the IRR between 35%~50%.

Holding cost $19.068/year The Unit manufacturing cost multiplies the internal rate of return


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2.3 Mathematical Models

With an assistance of an OR handbook [2], we estimated the cost-saving amount by the

following six steps. At the first step, we estimated the risk-pooled demand variance. The

"pooled" demand at month mwas estimated as,

∑=

=6

1,,

ˆp

pmmpooled dd …(4)

And the pooled demand variance was estimated as,

∑ ∑∑=

−

= +=

+=n

p

N

i

N

ijjDLTiDLTijiDLTmpooled

1

1

1 1,,

2,, 2 σσρσσ …(5)

Where, ijρ is the correlation coefficient of the demand between regions i and j .

At the second step, we estimated the Economic Order Quantity jQ as,

H

PJJj C

CAQ ∗∗=2 … (6)

At the third step, we estimated the safety stock jS and reorder point jR for each product option

type of HP printer in Europe ( 6,5,4,3,2,1=j for option A, AA, AB, AQ, AU and AY). Here, we

used the service function developed by R.G. Brown [3]. We set the target service level as 98%,

j

j

j

jj

QQSLZE

σσ 100*)98100(

100*)100(

)(−

=−

= …(7)

From the service function table, we estimated the jZ value as,

( ) LowerLowerjLowerUpper

LowerUpperj ZZEZE

ZEZEZZ

Z +−−

−= )()(

)()(…(8)

Where, the Z and E(Z) values were obtained from the service function adopted from source[3].

We estimated the service stock as,

jjj ZS σ∗= …(9)

And the reorder point as,


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)( jjjj ZdSdR σ∗+=+= …(10)

At the fourth step, the Total Annual Cost (excluding the manufacturing cost jAv • ) was

estimated as,

Hj

Pj

jj C

QC

QA

TAC2

+= …(11)

At the fifth step, the cost saving from the reduced safety stock kSafetyStocCS was estimated by,

pooledj

jkSafetyStoc SSCS −=∑=

6

1

…(12)

Also, the cost savings of the total annual cost TACCS was estimated by,

pooledj

jTAC TACTACCS −=∑=

6

1

…(13)


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3. Cost Saving Estimation We run a Monte-Carlo spreadsheet simulation with Table1 demand data and Table2 parameters based on the mathematical models shown above. In this section, the estimation results are summarized.

3.1 Variation Reduction Effect

Figure 1shows the monthly demand average and CV for each printer option. We noticed that the

product type AB had a high average demand, while demands for other product types were

relatively small. On the other hand, the coefficient of variation (CV) was high for products that

have small demand such as the product type A (217%), AA (49%), AQ(51%), and AU(52%).

The CV of risk-pooled demand was the lowest (27%) among all. This graph clearly shows the

risk pooling effect of DPD methodology.

Figure 1 Monthly demand average, standard deviation and CV for each printer option

217%

49% 36%51% 52%

34% 27%0%

50%

100%

150%

200%

250%

-‐

5,000

10,000

15,000

20,000

25,000

Average de

mand (Units)

Summary of average demand and CV

Monthly Average CV


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3.2 Change of EOQ sizes

Figure 2 shows the EOQ size comparison between “Non Risk-Pooled” and “Risk-Pooled". The

"Non Risk-Pooled” column indicates the EOQ value without implementing the delayed product

differentiation, and the “Risk-Pooled" column shows the one with the delayed production

differentiation. As we see the graph, the aggregated EOQ lot sizes decrease from 1650 to 876

(47% reduction) after implementing the delayed production differentiation.

Figure 2 EOQ size comparison

876

0200400600800

10001200140016001800

Non Risk Pooled Risk Pooled

EOQ size comparison

Delayed Product Differentiation

AY

AU

AQ

AB

AA

A


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3.3 Change of safety stock levels

Figure 3 shows the safety stock comparison between “Non Risk-Pooled” and “Risk-Pooled”.

The “Non Risk-Pooled” column indicates the safety stock value before implementing the delayed

product differentiation, and the “Risk-Pooled” column indicates the one with after the delayed

production differentiation was implemented. As we see the graph, the safety stock value

decreased from 26,383 to 17,690 (33% reduction) after implementing the delayed production

differentiation.

Figure 3 Safety Stock Comparison

17690

0

5000

10000

15000

20000

25000

30000


Safety Stock Comaprison


AY

AU

AQ

AB

AA

A


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3.4 Change of the total annual cost (TAC)

Figure 4 shows the total annual cost comparison between “Non Risk-Pooled” and “Risk-Pooled”.

As we see the graph, the Total Annual Cost (TAC) decreased from 31,462 to 16,696 (47%

reduction) after implementing the delayed production differentiation.

Figure 4 Total Annual Cost Comparison

$16,696

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000


Total Annual Cost comprison


AY

AU

AQ

AB

AA

A


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4. Discussion (Analysis of the result) We estimated the mean value of the Cp and IRR with risk-pooling methodology. However, we

do not know if the assumptions will not be changed. In this section, we conducted a sensitivity

analysis of the two parameter assumptions and demand correlation.

4.1 Sensitivity Analysis of order cost Cp

Figure 5 shows the sensitivity analysis result of the order cost (Cp) for the total annual cost with

fixed IRR rate of 35%. Here, it should be noted that TAC value was based on the formula (11)

excluding the manufacturing cost, since the variable production costs were canceled out

∑=

∗=∗6

1jjpool AvAv when we calculated the difference between pooled and non-pooled TAC

amounts. Non Risk-Pooled line indicated the supply chain inventory system before

implementing the delayed product differentiation (DPD). Risk-Pooled line indicates the one

with delayed production differentiation. As we see the graph, the TAC value and slope of “Risk-

Pooled” were much smaller than the one of Non Risk-Pooled. 53% of steady cost savings was

estimated regardless of order cost. Since the delayed product differentiation requires less

frequency of orders, its TAC was always smaller, and a high level of robust cost-saving was

estimated. The expected saving cost of TAC was $9,107 at Cp=$10, and $28,797 at Cp=$100.

Figure 5 Sensitivity Analysis of Order cost Cp for Total Annual Cost (TAC)


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Figure 6 shows the sensitivity analysis result of order cost (Cp) for the safety stock amount. We

noticed two things. First, as the order cost (Cp) increases, the safety stock amount decreases.

This is because when the Cp increases, the EOQ size will be increased. If EOQ batch size will

be larger, naturally it has the buffer effect against the stock-out risks with less safety stock.

Second, Risk-Pooled was always significantly smaller than the Non Risk-Pooled, we could

always expect the cost saving by PDP. Since the DPD pools the variance of demand, we can

handle the demand variation with less stock. Between the order cost range of $10 and $100, the

DPD had minimum 28%, maximum 36%, and average 32% of cost reduction effect for the total

annual cost of inventory management. The expected saving cost of safety stock was $639,373 for

the order cost of $10, and $486,787 for order cost of $100 respectively.

Figure 6 Sensitivity Analysis of Cp for Safety Stock


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4.2 Sensitivity Analysis of IRR

Figure 7 shows the sensitivity analysis of IRR for safety stock. As same as the sensitivity

analysis of Cp, the “Risk-Pooled" line was always lower than the Non Risk-Pooled line. Also,

the safety stock values were almost flat and not significantly affected by the change of the IRR.

Therefore, steady cost saving was expected regardless of IRR. Between the IRR range of 35%

and 50%, we have minimum $532,341, maximum $600,462, and average $559,110 cost savings

was expected from the safety stock for this printer family.

Figure 7 Sensitivity Analysis of IRR for Safety Stock

Non Risk-‐pooled

Risk-‐Pooled

Cost Savings

$-‐$200,000 $400,000 $600,000 $800,000

$1,000,000 $1,200,000 $1,400,000 $1,600,000 $1,800,000 $2,000,000

35% 36% 37% 38% 39% 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% 50%

US$

Internal Rate of Return (IRR) %

Sensitivity Analysis of IRR for Safety Stock


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Figure 8 shows the sensitivity analysis of IRR for the TAC. This graph also showed that steady

cost saving was expected regardless of IRR rate. The minimum expected cost saving amount was

$ 14,766 when IRR was 35%, the maximum was $17,649 when IRR was 50%.

Figure 8 Sensitivity Analysis of IRR for Total Annual Cost (TAC)

The sensitivity analysis indicated that HP could expect the cost reduction of at least $486,787 by

reducing the reduced safety stock, and $9,107 by TAC for this product family per year in

European market by implementing the risk-pooling strategy.

Non Risk-‐pooled

Risk-‐Pooled

Cost Savings

$-‐$5,000 $10,000 $15,000 $20,000 $25,000 $30,000 $35,000 $40,000

35% 36% 37% 38% 39% 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% 50%

Total Annual Cost (TAC) $

Internal Rate of Return (IRR) %

Sensitivity Analysis of IRR for TAC


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4.2 Demand Correlations

What would happen if the correlations between the demand of product types changes? Fiugre10

shows the correlations between the model "AY" and other printer models from Table1, where

there were both positive and negative correlations. According to the OR handbook [2], when

there is no correlation (i.e., ijρ =0), then the pooled demand variance formula (5) will be reduced

to,

∑= 2,, iDLTpooledDLT σσ …(14)

Due to the triangle inequality,

∑∑=

≤=N

iiDLTiDLTpooledDLT

1,

2,, σσσ ,…(15)

Therefore,

unpooled

N

iiDLTpooledDLTpooled SSZZSS =∗≤∗= ∑

=1,, σσ αα

…(16)

Formula (16) indicates that safety stock of risk-pooling is smaller or at least equal to non risk-

pooled one. For example, when there is a perfect positive correlation ( ijρ which is regarded as

the worst case scenario), the risk-pooled safety stock becomes equal to the one of no risk-pooled

as Figure 10. However, i in case the safety stock is estimated by the service level target with

formula (7) and (8), we could have even more inventory level as Figure 11.


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Figure 9 Correlation of demand between model “AY” and other printer models

Figure 10 Safety stock level estimated by pooledDLTZ ,σα ∗ ( 1=ρ )

-‐0.18

0.54

0.22

-‐0.16

0.27

-‐0.30

-‐0.20

-‐0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

A AA AB AQ AU

Correlation

Correlation between model "AY" and each model

Pooled, 21,765

-‐

5,000

10,000

15,000

20,000

25,000

Unpooled Pooled

Safety Stock Level

Safety Stock Level when Correla3on=1


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Figure 11 Safety Stock Level calculated based on the target service level ( 1=ijρ )

5. Conclusion and Recommendation

In this paper, we hypothesized that the saving cost by DPD is large. We estimated its cost

reduction amount based on the available information and sensitivity analysis. EOQ, inventory

service function, and variance reduction models were used for estimating the cost savings. Our

analysis showed that HP could expect 32% cost reduction in safety stock, and 47% cost

reduction in the inventory total annual cost (TAC). Sensitivity analysis showed demand

correlation should be small for a successful DPD deployment.

25,865

27,689

24,500

25,000

25,500

26,000

26,500

27,000

27,500

28,000

Non-‐Riskpooled Riskpooled

Safety Stock level when Perfect Correlation (p=1)


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References [1] Simchi-Levi. D., Kaminsky. Ph., and Simchi-Levi. E., “Designing and managing supply

chain”, 2000, McGraw-Hill Higher Education

[2] A. Ravi Ravindran, “Operations Research and Management Science Handbook”, 2008, CRC

Press (PP.22-41~22-44)

[3] R.G. Brown, “Decision Rules for Inventory Management”, New York: Holt, Rinehart &

Winston, 1967, pp.95-103.

[4] Cypres Lab, “Cost estimation for HP DeskJet 3940”,

http://www.cypress-labs.com/pdf/HPDeskjet3940-part1.pdf

Appendices Figure 1 Monthly demand average, standard deviation and CV for each printer option ............................ 8 Figure 2 EOQ size comparison ................................................................................................................... 9 Figure 3 Safety Stock Comparison ........................................................................................................... 10 Figure 4 Total Annual Cost Comparison .................................................................................................. 11 Figure 5 Sensitivity Analysis of Order cost Cp for Total Annual Cost (TAC) ......................................... 12 Figure 6 Sensitivity Analysis of Cp for Safety Stock ............................................................................... 13 Figure 7 Sensitivity Analysis of IRR for Safety Stock .............................................................................. 14 Figure 8 Sensitivity Analysis of IRR for Total Annual Cost (TAC) ........................................................ 15 Figure 9 Correlation of demand between model “AY” and other printer models ..................................... 17 Figure 10 Safety stock level estimated by pooledDLTZ ,σα ∗ ( 1=ρ ) ......................................................... 17

Figure 11 Safety Stock Level calculated based on the target service level ( 1=ijρ ) ............................... 18

Figure 12 Summary Statistics of the demand data (Cp=26.29, IRR=35%) ............................................... 20 Figure 13 The conversion from E(Z) value to Z value by interpolating the service level table ................ 20 Figure 14 EOQ Size Data ......................................................................................................................... 20 Figure 15 Safety Stock size (Cp=$26.29, IRR=35%, V=$54.48) ............................................................ 21 Figure 16 Total Annual Cost Comparison (Cp=$26.29, IRR=35%, V=$54.48) ........................................ 21 Figure 17 Sensitivity Analysis Data for Order cost (From Cp=$10 to Cp=$100), IRR=35%, V=$54.58) 22 Figure 18 Sensitivity Analysis of Internal Rate of Return for the Safety Stock and Total Annual Cost ... 22 Figure 19 Correlation of demand from the original data ........................................................................... 23 Figure 20 Data used for Correlation=1 cases ............................................................................................ 23 Figure 21 Service Level Function adopted from [3] .................................................................................. 23


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Spread-sheet modeling

Figure 12 Summary Statistics of the demand data (Cp=26.29, IRR=35%)

Figure 13 The conversion from E(Z) value to Z value by interpolating the service level table

Figure 14 EOQ Size Data

Option Monthly Average Stdev (sd) CV A(Annual Demand) Cp Ch EOQA 102 222 2.2 1228 26$ 19$ 58AA 420 204 0.5 5042 26$ 19$ 118AB 15830 5625 0.4 189961 26$ 19$ 724AQ 2301 1168 0.5 27614 26$ 19$ 276AU 4208 2205 0.5 50496 26$ 19$ 373AY 309 104 0.3 3703 26$ 19$ 101

Total(Risk Pool) 23170 6318 0.3 278044 26$ 19$ 876


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Figure 15 Safety Stock size (Cp=$26.29, IRR=35%, V=$54.48)

Figure 16 Total Annual Cost Comparison (Cp=$26.29, IRR=35%, V=$54.48)


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Figure 17 Sensitivity Analysis Data for Order cost (From Cp=$10 to Cp=$100), IRR=35%, V=$54.58)

Figure 18 Sensitivity Analysis of Internal Rate of Return for the Safety Stock and Total Annual Cost


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Figure 19 Correlation of demand from the original data

Figure 20 Data used for Correlation=1 cases

Figure 21 Service Level Function adopted from [3]

ie563_project_paper oct5.edited

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