Advanced Engineering Informatics 26 (2012) 46–54

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Advanced Engineering Informatics

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Production risk management system with demand probability distribution

Kenji Tanaka a,⇑, Hiromichi Akimoto a, Masato Inoue b

a Department of Systems Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japanb Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Tokyo, 1-5-1, Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 March 2011Received in revised form 1 June 2011Accepted 1 July 2011Available online 16 August 2011

Keywords:ForecastingNM methodDecision supportRisk managementProduction planningBook retailing

1474-0346/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.aei.2011.07.002

⇑ Corresponding author. Tel.: +81 3 5841 6523; faxE-mail address: kenji_tanaka@sys.t.u-tokyo.ac.jp (

As market globalization has changed the nature of their business, the types of products are multiplied bycustomizing in order to seize each market segment. Moreover, model lifecycle have been shortened byreleasing new models for stimulating customers. That makes it difficult to control the proper timingand volume of the product supply. Manufactures face the overstock risks and stock shortage risks. Eachproduct needs its customized supply control to keep profitability. This study proposes a reproductiondecision support system that measures demand risks through a sales forecasting method. This systemgives manufactures the proper volume and timing guidance for daily reproduction of products. The sys-tem is applied to the case of a Japanese publisher. A three-month operational test of the system proved itable to provide the optimized supply volume options based on manufacturer’s decision strategies. Theratio of surplus stock decreased from 40% to 34% as a result.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

As market globalization has changed the scale of manufacturers’business, market demand uncertainty has become too large andtoo complex to manage. Manufacturers, like those in the area ofconsumer products, suffer enormous demand volatility and thenlose not only their business opportunity but also profitability be-cause of overproduction and surplus inventory. Even bestsellingproducts can cause financial loss through the product lifecycle,and this phenomenon is known as the ‘‘Tamagotchi overproduc-tion’’ in Japan. Tamagotchi was one of the famous record-breakingbest-sold portable game products in Asia, and the manufacturer re-ported a loss of 600 million USD because of the surplus stock of theproduct. That loss caused a serious financial problem for the man-ufacturer. More than 100 types of Tamagotchi models were sold,and the it was almost impossible to verify the sales result of eachproduct and decide customized proper reproduction volume for it.The manufacturer was so sensitive to that stock shortage, due tolost sales opportunity, that it made the decision for large-scalereproduction of all products of the tamagotch series. However,when the inventory was replenished, the product sales hadreached their peak and then suddenly plummeted. Thus the man-ufacturer faced serious surplus stock problems.

A newly released product’s sales trend characteristically has asudden peaks and a sudden plummet feature, which means thatit is nonlinear. The feature causes a demand–supply phase lag

ll rights reserved.

: +81 3 5841 6522.K. Tanaka).

(Fig. 1). It is extremely difficult to seize the product-specific vol-ume and timing to reproduce the products according to its sales re-sults. To seize and manage each demand uncertainty of products,the product specific approach is necessary.

Some existing research reports on management in uncertainbusiness environments. Kono and Mizumachi [16] proposed a prof-it sensitivity analysis under uncertainties for production capacitysurplus and shortage. Leung et al. [18] developed an optimizationmodel for production planning of perishable products, managinguncertain environments. These proposed risk measurement mod-els, however, do not deal with time value and forecasting. Demandcertainties and forecast values improve with the passage of time.They are two of the most important factors that should be consid-ered [3,20].

Accurate demand forecasting plays an important role both inmanufacturing and retail operations [1,8,19,26]. Fisher and Raman[13] reported that quick response to early sales results with fore-casting error distribution contributes to demand risk reduction.

On the other hand, there are few practical methods for salesforecasting for short lifecycle products. Ko et al. [15] pointed outthat there is no perfect solution available to solve these problemsdue to the uncertainty and difficulty in predicting market demand.This is one of the reasons why the forecast model is not used forexisting risk measurement approaches to production. Chu andZhang [9] claimed linear methods as one of the major limitationsof traditional methods. Users are unable to consider the complexrelationships in the data for those forecasts, except for seasonalanalysis. Therefore, there has been research on a nonlinear model-ing approach to neural networks [12,21]. However, the opposite

0

20

40

60

80

100

120

140

160

180

05 06 07 08 09 10 11 12 01 020

300

600

Stock(Left axis)

(Units) (Units)

Dead Stock

Sales(right axis)

Sales Peak

Stock Peak

Phase Lag

Stock Peak

Phase Lag

Fig. 1. Sales-stock phase lag (example: business title in 2005).

Sample Product Data

Sales datecategory

Target products Daily Data

Sales, Supply, Return,Date category

Sales forecast (long term, short term

Evaluate Risks ofReproduction volume

options

Decide Product localoptimized volume

Knowledge Based Grouping

Filtering Irregular Products

NM coefficient tables

Business boundaryconditions

Select product i

Pre-set Flow Daily Main Flow

Probability distribution table

- Target ratio of surplus- Minimum production lot- Production Utilization

Evaluate Products Risk Portfolio

Finished all products?

Reproduction Volume

YesNo

Stock forecast (based on the sales forecast)

The major contributions of this study

Fig. 2. The flow of the system.

K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54 47

results are reported [2,10,14]. Their findings reveal that a neuralnetwork is not superior to the time series models even if the dataare nonlinear. In the latter half of the 2000s, some other trials forcombining methods (e.g., clustering technique, decision support,or other existing forecasting method) have reported successful re-sults [4–7,11,17,26,27]. Tanaka [23], and Tanak and Miyata [24],also developed ‘‘the NM method’’, an empirical sales forecastingmethod that deals with time marching sales results and providesa sales forecast just a few days after the products’ release. Theseadvances enable us to measure risks based on the forecastingmethod’s probability distribution [25]. In this study, introducingthe concept of two time points in a product’s lifecycle, two typesof risks are defined. This provides a proposed volume and timingof reproduction of specific products based on risk taking strategies,even just few days after product release.

The main objective of this study is to propose a production riskmanagement system with demand probability distribution basedon the NM method proposed by Tanaka [23], and Tanak and Miyata[24]. In order to obtain the objectives, two new elements are devel-oped: a modification of the NM method and a measurement meth-od of demand uncertainty risk. The practical verification test of thissystem will be stated as a case study. This system was applied tothe case of a Japanese publisher, and three months’ operationaltesting has been done. The system succeeded in reduction of thesurplus loss by 13%.

The rest of this paper consists of three sections. Section 2 ex-plains the whole flow of the system and then the developed ele-ments in this study. In Section 3, this model is applied to aJapanese publisher’s case and verify its performance. The conclu-sion is presented in Section 4.

2. Production risk management system

2.1. System workflow

The basic flow of the proposed model in this research is illus-trated in Fig. 2. There are two flows in the system; one is thepre-set flow for setting the forecasting coefficient based on thesample data and the other is the daily main flow.

The pre-set flow is the preparation process of coefficients forsales forecasting and probability distribution for risk measuringwith the sample product data. Sample product data is the resultof daily sales of past products in previous years. The products aredivided into groups whose elements show a similar sales trendthroughout the products’ lifetime. Firstly, the groups are deter-mined by experts’ knowledge. Secondly, the some products ofirregular sales trend are eliminated from the original groups.

The daily main flow gives us the reproduction volume of thetarget products on that day. The target products’ daily data consistsof two kinds of up-to-date data on on-going products: sales dataand production volume data of the target products. The product i(Pi) is selected as the first step. Then, the long- and short-term salesforecasts of Pi are calculated with the ‘‘NM method’’ [23,24]. In thismodel long term means the days between the present day and theend of the product’s expected lifecycle. Its forecast means esti-mated accumulated sales volume of Pi throughout the lifecycle.Short term means the days of minimum lead time between repro-duction decision and market inventory replenishment. Additionalitems cannot be supplied during the period. At step three, twokinds of risks are evaluated based on the probability distributiontable. Opportunity loss risk and surplus loss risk are caused byreproduction volume decisions. So next the local optimized volumeoption of reproduction for Pi is determined. These four steps are re-lated to Pi local risk management.

The remaining steps deal with product risk portfolio manage-ment. If there are other products, evaluate these risks on eachproduct. As all the products’ risks are obtained, the total risk as aportfolio are evaluated. With the evaluation of each product’s vol-ume options, the prioritization among products is decided accord-ing to manufacturers’ strategy. Finally, the decision onreproduction volume is reached.

2.2. NM forecasting model

Tanaka [23], and Tanak and Miyata [24] proposed the NM fore-casting model which is based on experts’ knowledge. NM forecast-ing method and its probability distribution are adopted as aforecasting method in this study. The NM method is a knowl-edge-utilizing accumulated sales forecasting method. It provides

Expected Lifecycle

Rate of Sales Accomplished (%)

Dr(r)

r%

(days)

Fig. 4. Ds(r) model.

48 K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54

us with not only short-term forecasts, but also with long-termaccumulated sales forecasts. Using the empirical correlation be-tween a specific date pair for sales results among the relevantgroup products, the target forecast is calculated. This method pre-dicts the Mth day accumulated sales forecast based on the Nth dayaccumulated sales result. The correlation between the Mth daysales result and Nth day forecast is determined by the empiricaldata of the relevant product groups. Relevant groups are preparedin two patterns; grouping by existing categories, or by new groupscollected by experts’ knowledge; key words, topics, target custom-ers, and other features. Thus, the experts define the relevant groupfor Pi among existing products sales data.The forecast of accumu-lated Mth day sales of Pi on the Nth day XiN(M) is,

XiNðMÞ ¼ CðNMgroup; N;MÞ � RiN ð1Þ

Here, Mth and Nth are the numbers of days after Pi has been re-leased. RiN is the accumulated sales result of the Pi on the Nth dayafter its release. C(NMgroup, N, M) is NM coefficient of the Mth dayforecast from the Nth day result in the reference group; NMgroup.NMgroup is the specific products’ group which is used for salesforecasting of Pi.C(NMgroup, N, M) is determined by,

CðNMgroup; N;MÞ ¼kPkj¼1

RjM � RjN

!�

Pkj¼1RjM

� ��Pk

j¼1RjN

� �

kPk

j¼1ðRjNÞ2

� ��

Pkj¼1ðRjMÞ

2� �2

ð2Þ

Here, k is the number of products in the NMgroup, and eachNth–Mth pair has the NM coefficient. Reference NMgroups aredetermined by the experts’ knowledge of the products’ typicalattributes: series, prices, and so on. According to the adoptedgrouping rule, NM coefficient tables are calculated by Eq. (2).NMtable is the matrix table of coefficients of Nth and Mth in theNMgroup. Based on the sample sales results, the NM coefficient ta-ble and its probability distribution are prepared. The probabilitydistribution table of each group is also calculated by aggregatingthe NM sample forecasting error.

2.3. Filtering irregular sales trend products for relevant group

The grouping of products by the experts’ knowledge enables usto obtain the NMgroups for the target products before their salesrelease [23,25], and provides the sales forecast even immediatelyafter the product’ sales release. There is, however, a problem ofaccuracy if products in NM groups are mischaracterized by the ex-perts. The accuracy of the NM forecasting depends on the similarityof the sales trends between the product and the titles in the

Fig. 3. Filtering by day of sales accom

NMgroup. There are some cases that NMgroups include irregularproducts and thus decrease accuracy. In this study, the filteringgrouping method is adopted in order to manage those accuracyproblems.

The left side of Fig. 3 shows the transition of each r (rate of salesaccomplished compared to the accumulated sales of the expectedlifecycle) of the products in the NMgroup, as determined by the ex-perts’ knowledge. In this example, literature is the category ofproduct. There are products which show a different transition com-pared to others. Those products are filtered by introducing Ds(r).This is the indicator of the Days of Sales Accomplished of the prod-ucts to r [%] (Fig. 4).

The Filtering condition is defined as Dsmin < Ds(r) < Dsmax. Here,Dsmax and Dsmin are the upper and lower limit of Ds(r), respec-tively. The right side of Fig. 3 shows the filtering example of a lit-erature category group under the condition of 0 < Ds(70) < 60. Inthis filtering example case, the minor products with a constantsales trend are separated from the major products with early salespeaks.

The flow of the filtering grouping method is indicated in Fig. 5.At first, the NMgroup in which accuracy should be improved is se-lected. The NMgroup by the experts’ knowledge is called the origi-nal NMgroup. Secondly, the sales results of the products in theoriginal NMgroup are picked up from the sample data. Thirdly,the parameters of filtering condition (r, Dsmax, Dsmin) are set. Basedon the filtering condition (Dsmin < Ds(r) < Dsmax), irregular productsare eliminated from the original NMgroup and the products of thefiltered NMgroup are fixed. The NM coefficient table of the filteredNMgroup under the condition of Dsmin < Ds(r) < Dsmax is calculatedwith the sales result of fixed products. The accuracy of the filteredNMgroup is verified with MAPE (Mean Absolute Percentile ofError). The verification condition of (Nth, Mth) pair is set according

plished (e.g., literature category).

Pick up the sales results of the products in the NMgroup

(Original NM group)

Set each parameter of Filtering Condition

r,Dsmax, Dsmin

Filter each productDrmin<Ds(r)< Drmax

Fix the products of filtered NM group

Calculate the NMcoefficient table with the obtained products

Select the NMgroup

NM coefficient tablesProbability Distribution tables

Of “Filtered” NM group

Verify the accuracy of filtered NM group with MAPE

Change Parameter?

Sample POS dataTitle, Category,

Sales, date

Verification TitleData

Title, Category,Sales, date

Fig. 5. Filtering irregular products.

Sales ForecastWith Probability Distribution

Product Timeafter release(days)

70%

20%

Resultt0

Salesresult

Accumulated Sales

10%

Forecast

Probability

Fig. 6. Forecast probability distribution.

K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54 49

to the business rules. In the Japanese book industry, for example,the Nth day is set on the first decision day of the reproduction,and the Mth day is set on the day of the expected lifecycle. Throughthe verification of each set of the parameters (r, Dsmax, Dsmin), theset with the best MAPE performance is adopted.

2.4. Risk measurement model

Manufacturers continually have to determine if they shouldproduce a particular product. Two types of risks caused by repro-duction decisions—opportunity loss risk and surplus loss risk aredefined. Opportunity loss risk is an intangible risk that is causedby stock shortage. Surplus loss risk is a cost of retirement at theend of the product lifecycle because of overstock.

Fig. 6 shows the sales forecast with probability distribution, andFig. 4 has indicated the basic concept of these two risks. The waverays indicate average possible demand trends in the future. If the

demand rises above the supplied production volume, it gives riseto opportunity loss. If the demand moves below the productionvolume, it gives rise to surplus loss risk. These risks are measuredusing the colored area in Fig. 7. These risks are measured using theprobability function of product i (PiN+n(x), PiN+last(x)). PiN+n(x) [%] is aprobability function that represents n days forward forecast prob-ability distribution of the NM group on the Nth day. The opportu-nity loss risk of product i (Pi) on the Nth day is expressed byRiskOppLossi, and is expressed as in Eqs. (3) and (4).

RiskOppLossiðDSiN ; SiNÞ ¼ NumOppLossiðDSiN ; SiNÞ � GrossProfiti ð3Þ

NumOppLossiðDSiN; SiNÞ ¼Z 1

SiNþDSiPiNþnðxÞ � jx� ðSiN þ DSiÞjdx ð4Þ

SiN (units) is the volume of the Pi already supplied on the Nthday. DSiN represents the added volume of production for Pi onthe Nth day and is going to be supplied to the market n days laterthan the Nth day. n (days) is the shortest supply lead time ex-pressed in days. GrossProfiti (JPY) is the gross profit per one itemof Pi, and x (units) is a variable of the total production volume.NumOppLossi(DSiN,SiN) is the volume of opportunity loss units thatis caused by the inventory shortage.

On the other hand, the risk of surplus loss of Pi on the Nth dayafter release, RiskSrpLossi, is also defined as in Eq. (6) and the leftfigure of Fig. 8.

RiskSrpLossiðDSuN; SuNÞi ¼ NumSrpLossiðDSiN; SiNÞ � CostperItemi

ð5Þ

The number of surplus losses at the end of the expected lifecy-cle of Pi, NumSrpLossi, is expressed as in Eq. (6) and the middle fig-ure of Fig. 8.

NumSrpLossðDSNi; SNiÞ ¼Z SNþDSN

0PiNþlastðxÞ � jSN þ DS� xjdx ð6Þ

wherein Eq. (6), last is the remaining days of the product lifecycle.CostperItemi is the cost on retirement loss per unit of product i.The expected return of product i is defined as ExpectedReturni,which is also calculated as in Eqs. (7) and (8) and the right figureof Fig. 8.

ExpectedReturniðDSiN ; SiNÞ¼ ExpectedNumReturniðDSiN; SiNÞ � GrossProfiti ð7Þ

ExpectedNumReturniðDSiN ; SiNÞ

¼Z SiNþDSiN

0x � ð1� PiNþlastðxÞÞdx

þZ 1

SiNþDSiN

ðSiN þ DSiNÞð1� PiNþlastðxÞÞdx ð8Þ

The evaluation of the risk-return efficiency of each DSiN optioncan be obtained with these risk and return measurement methods.Opportunity loss risk, surplus loss risk, and expected return of Pi

depend on the volume of DSiN. The more DSiN increases, the moreRiskSrpLoss increases at an accelerating pace. RiskOppLossi, how-ever, decreases gradually as DSiN increases. The total risk showsa gradual increase after a minimum peak. On the other hand, theExpectedReturni increases gradually, with its increments decreasinggradually. There are three production decision strategies: total riskminimizing, expected return and risk gap value maximizing, andrisk-return ratio maximizing. Depending on the risk strategy, Pi lo-cal optimized volume option DSiN should be provided (Fig. 9). DSiNis indicated for manufacturers as the providing chart of DSiN vol-ume option at Nth day for manufacturers (Fig. 10).

Sales Forecast

Timeafter release(days)

Long termPiN+last(x)

Opportunity Loss

Surplus Loss

Nth

Presentlast

Expected Lifecycle

Supply Lead time

Forecast Probability DistributionShort term

0

SalesResult

PiN+n(x)

N+n

(Units)

SN

DecidedReproductionVolume

SNSN+ SN

Present Supply Volume

Decided Supply Volume

Fig. 7. Two types of risks defined.

Fig. 8. Opportunity loss risk, surplus loss risk and expected return (units).

(JPY)

0

Surplus Loss Risk

Expected Return

Opportunity Loss Risk

Total Risk

(items)

Present

Minimum Risk

Max. Return-Risk Gap

Max. Risk-Return Ratio

Ret

urno

r Ris

k

SiN Volume Option

Fig. 9. Risk Return evaluation (product local).

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

113

120

127

134

141

148

155

162

169

176

Acc

umur

ated

Item

s (it

ems)

Supply Forecasst

Supply Result

Sales Forecast

Sales Result

+ SiN Volume Option

PresentDay(Nth )

TargetDay

(Mth )

(Days after release)

Fig. 10. Example of the providing chart of DSiN volume option at Nth day formanufacture (product local).

50 K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54

2.5. Risk portfolio management model

Manufacturers determine reproduction DSiN under their limitedresources. It is important to manage their product portfolio risks.The total risk and return of product portfolio are expressed as inEqs. (9) and (10).

RiskPortfolio ¼X

i

ðRiskSrpLossi þ RiskOppLossiÞ ð9Þ

ReturnPortfolio ¼X

i

ExpectedReturni ð10Þ

Risk Portfolio should be kept below a company’s maximumallowable risk. The prioritization of products should be determined

according to this strategy. Plotting each product’s risk-return posi-tioning and potential volume options enables graphical compari-son over products (Fig. 11).

3. Case study

3.1. Verification of filtering method

According to annual report of the The Research Institute forPublications [22], over 60 thousand titles are released and approx-imately 40% of copies are returned to publishers as surplus-goodsin Japan. There are serious problems of misleading demand

Expe

cted

Ret

urn

(mil J

PY)

Product C(week3)

Product A(week4)Product B(week2)

Present

Chosen option

Present

Present

Present

00 10 20 30 40 50

Total Risk (RiskOppLoss + RiskSrpLoss) (mil JPY)

20

40

60

80

Fig. 11. Risk return evaluation (product portfolio).

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14(day)(days after release)

Original grouping

Filtering grouping

Fig. 13. The ratio of titles so that the absolute error is within ±30%.

K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54 51

uncertainty. Book sales is not seasonal nor cyclical, because theircustomers buy only once. Book is one of the most typical goodsthat has wide variety and short-lifecycle. The title specific custom-ized approach of demand management is inevitable.

The grouping method developed in the current study was veri-fied using actual data from a major book wholesaler in Japan. Thiscompany maintains a share of approximately 40% of the domesticmarket. Using 7661 titles in the paperback book category releasedin Japan from March 2003 to September 2006 as sample data, 1021titles released from October 2006 to March 2007 were verified.Assessment was performed of the ratio of titles so that the absoluteerror was within ±30% as the index of error assessment. This wasadopted based on the results of interviews with people in the pub-lishing industry.

The forecasting method using filtering is verified in the paper-back book category, which is one of the groups that has the prob-lem of mis-characterizing.

Original group by experts’ knowledge before release may in-clude a few titles (abnormal titles) with different sales trendsdue to human error in categorization, etc., causing a reduction inprecision.

By changing the parameter of Ds(r) by 5% to perform filtering ofpatterns, the optimal filtering with the highest forecasting preci-sion was sought. Fig. 12 and Fig. 13 shows the results. It can beseen that by obtaining the NM coefficient after removal of peculiartitles by filtering, the forecasting precision of the entire group wasimproved. In this group, the forecasting precision was improved by60% or more at maximum.

Original Grouping

(days)

(%)

Fig. 12. Filtering grouping in a

3.2. Verification of production risk management system

3.2.1. Conditions of verificationIn this section the performance of the proposed production risk

management system is verified by applying it to Japanese businesstitles that are published in Sept. 2006 by a middle size mid-sizedpublisher. Business book sales trends have a keen peak and suddenpeak outplummet. Publishers suffer a lot of costloss caused bythose features. Static sample data of 1351 business titles publishedin 2007–2008 are were used for preparing NM coefficient and itsprobability distribution. Those data are also provided by a Japaneseleading wholesaler and the publisher. Their minimum lead time forreplenishment n is 21 days, and the expected lifecycle is 182 days.The sales numbers is are changed by a fixed proportion because ofdata confidentiality. The product reference group is made by thetopic attribute among divided among 21 business groups createdby wholesaler experts. Table 1 is the prepared probability distribu-tion table of 2 weeks ahead forward forecast of stock investmenttopics among business titles. Table 2 shows a 182nd day forecast.The group has 151 titles. The top row expresses the weeks afterproducts’ release. The bottom two rows indicate the proportionof sample titles under absolutely certain probability rate. It showsforecast probability convergence as time goes on.

3.2.2. Product local risk evaluationThe product local-optimized volume options of for the Title A at

14st 14th day are indicated in Table 3. The publisher’s actual repro-duction volume decision without this model was 330,000 items.That results in over 40% of surplus stock at the end of its the life-cycle. As reproduction volume option Si14 increases, surplus lossrisk increases at an accelerating pace. On the other hand, RiskOpp-Loss decreases as Si14 increases. The product’s local optimized

Filtering Grouping

(days)

(%)

paperback book category.

Table 1Probability distribution table (2 weeks ahead; k = 151 titles; NMgroup = ‘‘Business’’ and ‘‘the publisher titles’’).

Table 2Probability distribution table (182 days forecast; k = 151 titles; NMgroup = ‘‘Business’’ and ‘‘the publisher titles’’).

Table 3Product local optimized volume option (Title A at 14thday; price 1200JPY; GrossProfit 60%; total supply 18,000 items; sales result 15,000 items).

(Unit: 100 thousand JPY) Present Min total riskoption

Max risk-return efficiencyoption

Max absolute gap Risk-returnoption

Actual optiondecided

S Option (100 U) 0 90 150 240 330ExpectedReturn 105 150 162 183 194RiskSrpLoss 2 8 12 34 63RiskOppLoss 34 7 5 2 1Total Risk 35 15 17 36 , 64Risk-return abs. gap (net

return)70 135 145 147 , 130

Return/risk efficiency ratio 3.0 10.0 9.5 5.1 , 3.0

Improvement from actual optionTotal risk �45% �77% �74% �44% 0%Risk-return abs. gap (net

return)�46% 4% 11% 13% 0%

Return/risk efficiency ratio �2% 231% 214% 69% 0%

52 K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54

0

50

100

150

200

250

0 50 100 150 200

Min. Total Risk OptionMax Risk-Return Efficiency Option

Max Absolute Gap Risk-Return

Present at 14thday

Reproduction result

Expe

cted

Ret

urn

(100

thou

sand

JPY)

Total Risk (100thousand JPY)

Fig. 14. Risk-return evaluations of volume options of Title A at 14th day.

Past 1 yearResult

ActualOption

Decided

SystemOption

Recommend

Fig. 15. The result of reduction of surplus stock through three month operation test.

Table 4Product portfolio case conditions.

N-th day Week Price (JPY) Grossprofit (%)

SN (units) RN (units)

Title A 14 2 1000 60 180 102Title B 35 5 1200 60 180 98Title C 16 3 1100 50 280 101Title D 12 2 1600 50 146 81

0

50

100

150

200

250

300

0 20 40 60 80 100 120

Title A

Title B

Title C

Title D

Present SN

Min Risk SN

Fig. 16. Determining reproduction volume of each product by products portfoliomanagement (minimizing portfolio risk strategy, solid line in both figures repre-sents potential volume options; SN < SN+ SN < 400%⁄Xi182).

0

50

100

150

200

250

300

0 20 40 60 80 100 120

Title A

Title B

Title CTitle D

Take Risks until Publisher’s Limit Present SN

Chosen Option SNOption2 Option3 Option4

Fig. 17. Determine reproduction volume of each product by products portfoliomanagement (right: risk-return ratio leveling until the publisher’s risk limistrategy. Solid line in both figures represents potential volume optionsSN < SN+ SN < 400%�Xi182).

K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54 53

volume options according to three strategies are follows; the fol-lowing: 90,000 U of minimizing total risk option, 150,000 U ofthe maximizing return-per-risk efficiency option, and 240,000 Uof the maximizing absolute total gap between expected returnand risk option. Since the probability distribution converges astime goes on, the risk decreases. The reproduction decision shouldbe as earlier early as possible in terms of efficiency. If the decisionis postponed, the effect is gradually degreasing decreases becauseof the opportunity loss. Thus, this model provides measured risksand returns with regard to production volume, and allows us todetermine which option to be taken under three possible strate-gies. Title A case gives us the possibilities of risk reduction com-pared to real decisions by determining proper production volume(Fig. 14).

t;

3.3. Publisher operational test

The operational testing of a Japanese publisher was held fromDecember 2009 to March 2010. The reproduction decisions of thebusiness titles released in the latter half of 2009 by the publisherwere tested with this system. We provided the optimum volumeoptions of reproduction for those titles, and the real volume op-tions were decided by the publisher considering such other busi-ness elements as factory utilization or their back orders frombook stores. We succeeded in reducing the surplus stock by 6%as a real result. If the system recommended volume options weretotally adopted, the surplus stock could be reduced by 7% (Fig. 15).

The production decision case of the publisher at 28th Jan 2009is was simulated with proposed the portfolio model. Four titlesincluding Title A are were under considering ofation for reproduc-tion (Table 4). All titles are belongs to the NMgroup of ‘‘Businesscategory and the publisher titles’’. Publisher’s affordable risk limitis 20 million JPY for these titles. The following prioritization policyis was applied. First, determine the reproduction volume under theminimizing the portfolio risk strategy, the most left option are

Table 5The evaluation result of portfolio volume options.

Strategy RiskPortifolio ReturnPortifolio

Present Present SN 96 308Option 1 Min. risk

option45 437

Option 2 Return-per-risk (10.5)

44 457

Option 3 Return-per-risk (5.5)

96 531

...... ...... ...... ......Option 4 Return-per-

risk (3.0)187 582 Publisher’s

risk limit

54 K. Tanaka et al. / Advanced Engineering Informatics 26 (2012) 46–54

chosen (Fig. 16). Second, the reproduction volume of each title wasincreased until reaching the risk limit under the maximizing re-turn-per-risk efficiency strategy. The options on the same gradientline are chosen (Fig. 17). The evaluation result of portfolio volumeoptions is indicated in Table 5. Present portfolio risk is 9.6 millionJPY and total return is 308 million JPY. Under the minimizing theportfolio risk strategy (Option 1), the portfolio risk was reduced55% from 9.6 to 4.5 million JPY, while the portfolio return increased42% from 30.8 to 43.7 million JPY. If they take their full risk limit of18.7 mil JPY (Option 4), the portfolio return increases 27.4 millionJPY, and the portfolio risk increase by 8.9 million JPY, while portfo-lio risk-return efficiency remains 3.3. This model proved that it canprovide products’ risk evaluation and obtain an optimized produc-tion volume option. The portfolio case indicates that the model canprovide the prioritization of products for reproduction, allowingfor their efficient resource allocation.

4. Conclusion

The proposed model provides a useful approach to manage de-mand uncertainties through measuring risks and expected returnby using the forecasting method. Two types of risks are definedand measured based on forecasting probability distribution byintroducing the expected lifecycle. This study proposes the on-time-marching reproduction risk management system especiallyfor new products. It enables us to make the demand uncertaintycontrollable. By introducing the concept of two milestones of aproduct lifecycle, two types of risks are defined and measured withthe demand probability distribution. With the risk evaluation mod-el, the model can provide the optimum reproduction volume basedon a company’s reproduction strategy. The model also indicates thecompanies’ product risk portfolio, which enables allocation ofresources efficiently based on allocation rules.

Using book sales data, the system was applied to a publisherreproduction case. The results indicate that it can provide the mea-sured risk and return just after product release. The trial showedbetter performance than what is actually being done for produc-tion management, and risks are more significantly managed. Anon-time demonstration experiment with publishers of the systemhas been done, and it proved to be able to provide the optimizedsupply volume options according to their decision strategies. Theratio of the surplus stock decreased from 40% to 34% as a result.

Conflict of interest

None of the authors have any conflicts of interest associatedwith this study.

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