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Splitting hybrid Make-To-Order and Make-To-Stock demand profiles

Wolfgang Garn,James Aitken

The Surrey Business School, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom

Abstract

In this paper a demand time series is analysed to support Make-To-Stock (MTS) and Make-To-Order(MTO) production decisions. Using a purely MTS production strategy based on the given demand can leadto unnecessarily high inventory levels thus it is necessaryto identify likely MTO episodes.

This research proposes a novel outlier detection algorithmbased on special density measures. We dividethe time series’ histogram into three clusters. One with frequent-low volume covers MTS items whilst asecond accounts for high volumes which is dedicated to MTO items. The third cluster resides between theprevious two with its elements being assigned to either the MTO or MTS class. The algorithm can be appliedto a variety of time series such as stationary and non-stationary ones.

We use empirical data from manufacturing to study the extentof inventory savings. The percentage ofMTO items is reflected in the inventory savings which were shown to be an average of 18.1%.

Keywords: demand analysis; time series; outlier detection; production strategy; Make-To-Order(MTO);Make-To-Stock(MTS);

1. Introduction

Research into production systems has generallycharacterized and modeled them as either make-to-order (MTO) or make-to-stock (MTS). We proposethe following definitions. Amake-to-order productis a product where the required quantity is manufac-tured after receiving a sales order. MTO productsare commonly identified by low average demand anda high coefficient of variation (Soman et al., 2007).A make-to-stock productis a product where itemsare manufactured on anticipated demand. A concretesales order may not exist. Usually the required quan-tity is derived from forecasts.

Presenting the operating choice of production sys-tems as a choice between MTO or MTS simplifiesthe discussion but does not reflect current production

✩

Tel.: +44(0)1483 68 2005; fax:+44(0)1483 68 9511.Email address:

{w.garn,james.aitken}@surrey.ac.uk (WolfgangGarn,James Aitken)

dynamics. Fewer and fewer firms can be classified aspurely MTS or MTO in practice (Christopher, 2010;Soman et al., 2006; Aitken et al., 2003). Investigat-ing and modeling the combined MTS-MTO chal-lenge has had limited research with only a few papersexploring some aspects of the problem (Soman et al.,2006; Rajagopalan, 2002). Where capacity exists formanufacturers it can be expedient to separate prod-ucts between MTO and MTS in terms of planningand control. The literature highlights the benefits ofa focusing/isolating production of MTO and MTS interms of changeovers, bottleneck reduction, processvariation and costs (Schmenner, 2004). However,separating products between the two approaches isnot possible for many firms. Sharing and schedul-ing finite capacity between MTS and MTO prod-ucts is a major challenge for many organisations(Kerkkanen, 2007). This paper investigates how or-ganisations manage the MTS-MTO dynamic in thecontext of a food manufacturing business. The foodsector predominately services supermarkets and isunder growing pressure to increase the number of

Preprint submitted to arXiv April 15, 2015

stock keeping units (SKUs), reduce lead-times andmanage the delivery of an increasing heterogeneousservice demand across customers. The growing com-plexity of operating in the food sector has increasedthe incidences of shared capacity between MTO andMTS. The sector offers the opportunity of investigat-ing the combined MTS-MTO scheduling challengein the context of finite capacity faced with high de-mand variability products classified as either MTOor MTS.

Within the food sector companies arrange bulksales, promotions or marketing events that impact onthe demand pattern of products. These events arenot always visible to the production planners lead-ing to unplanned surges in demand creating unstableproduction schedules and diminishing service levels.Unplanned surges can lead to product being purelyproduced via a MTS process when they actually re-quire a MTO production strategy. Ignoring this of-ten results in the depletion of MTS produced inven-tory for regular sales and subsequently unplannedchanges in production (Schmenner, 2004). We intro-duce a new approach, which identifies MTO quanti-ties within an otherwise MTS classified product. Theobjective of our paper is to present a method thatcan support the identification of changes in statusbetween MTS and MTO. Identification of changescan motivate a MTO strategy for products which aretreated as MTS, a hybrid approach, providing the ad-vantage of a production schedule which reduces in-ventory and improves customer service. The casestudy demonstrates that applying our new methodled to reduced inventory levels of 18.1% on aver-age for previously pure MTS classified products. Theproposed new method automatically identifies MTOitems as “outliers” within a time series, allowingthe absence of order records. The novelty of themethod is the usage of clustering demand frequencyextracted from time series.

Our paper is organized as follows; after intro-ducing the case study firm we review the literatureon MTS-MTO and MTO/MTS in the section threeand then turn in section four to the new proposedmethod for the identification of change in productstatus between MTS, MTO and MTO/MTS. Sectionfive presents the results from the modeling and im-plementation of the new approach in the case study

Raw Material Cleaning & sorting Intermediary Packaging Finished Goods

Figure 1: Production process.

firm followed by discussions on the significance ofidentifying and managing the status change betweenMTO and MTS. Section six presents the conclusionsand suggestions for future work in this area of grow-ing importance for operation managers.

2. Company and Process Overview

The case study firm produces over 250 differentproducts derived from five raw materials. The rawmaterials are cleaned and sorted leading to the pro-duction of eight intermediary semi-finished productswhich are stored in material handling silos awaitingrelease to the appropriate production lines for pack-ing. Storage of the semi finished products was lim-ited to 48 hours due to bacterial and decay issues.The variety of different packaging options generatedin excess of 250 finished products for sale to the re-tail and catering market segments. The productionprocess for the food processing business is shown infigure 1, The manufacturing process had been facedwith the challenges of growing sales, increased sup-ply chain complexity and falling service levels of abroadening heterogeneous customer base. The resultof the increasingly variable demand on the manufac-turing operation was the conversion of the produc-tion and planning control schedule from a plan witha three week time horizon to a reactive customer or-der list. The reactive planning and control modusoperandi had forced manufacturing into an increas-ing number of unplanned changeovers and diminish-ing productivity, effectively reducing the availablecapacity in the packaging operation. The firm hadmoved from a position of flexible spare capacity to abottleneck over a three year period due to increasedcomplexity and reduction in schedule stability.

The case study company reflects the food man-ufacturing sector which has come under increasingpressure from supermarkets and distributors to di-minish the homogenisation of their offerings, re-duce lead-times, increase promotions, shorten prod-uct life-cycles and provide more frequent deliv-

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eries (Fisher et al., 1999; Taylor and Fearne, 2006;Squire et al., 2009). The continually changing envi-ronment that the food manufacturers operate withinhas made the management of processes throughthe application of forecasting methods difficult.The inaccuracies of forecasting in the food sec-tor have been found to have a significant impacton the performance and efficiency of the operation(Taylor and Fearne, 2006; Aghazadeh, 2004). Man-ufacturing a large number of products through apure MTS approach and putting them into inven-tory is not viable because of unpredictable demandand shelf-life (Soman et al., 2007). Due to increas-ing volatility the effectiveness and returns from in-creased investment on forecasting could be viewedas futile (Christopher, 2010) rendering the pure MTSapproach ineffective. In order to improve the perfor-mance of the operation the case study firm decidedto alter its approach to planning and control of MTOand MTS categorised products

3. Literature Review

3.1. MTS and MTO

Make-To-Stock (MTS) systems are described interms of low variety and high volume that aredriven through forecasts (Rafiei and Rabbani, 2011;Soman et al., 2004). Operationally the issues thatare in focus for this system are lot size determi-nation, accuracy of forecasting and inventory con-trol (Soman et al., 2006). A MTS approach isused for manufacturing items which are standard-ized with high volume, regular demand and are de-livered to customers from stock (Birou et al., 2011;Chang and Lu, 2010; Kerkkanen, 2007). The pre-ferred option for firms is to move from a MTS to aMTO system of production linked to a change in phi-losophy from a push to pull approach (Birou et al.,2011; Jodlbauer, 2008). MTO products are out-lined in terms of customised items with low averagevolumes and irregular demand (Birou et al., 2011;Kerkkanen, 2007). The uncertainty linked to MTOproducts places planning and control process in apivotal and time-sensitive critical role within firms(Corti et al., 2006). Reducing lead-times and im-proving the reliability of due dates, in the context

of demand uncertainty, has been a focus for sev-eral researchers in developing models that can sup-port firms in their decision making to optimize pro-duction schedules and performance (Zaerpour et al.,2009; Jodlbauer, 2008; Sawik, 2006).

An alternative approach to managing the pres-sure related to reducing lead-times and growing un-certainty in demand is through the development ofa hybrid MTS/MTO approach. The approach at-tempts to harness the strengths of the pure MTOand MTS systems (Federgruen and Katalan, 1999).Through operating a MTS system in the downstreamsections of the operations parts can be producedthat are subsequently assembled in the MTO sec-tion when orders are received (Rafiei and Rabbani,2011). Heuristic models have been developed tocontrol and schedule production activities to supportthe portioning problem and successfully operate thehybrid approach (Chang et al., 2003; Rajagopalan,2002). The splitting of the operation reflects theconcept of “postponement which has successfullybeen applied in many sectors where it is possible tostore semi-finished products or modular parts await-ing orders before assembling the final product with-out any detritus effect on quality (Zaerpour et al.,2009; Kerkkanen, 2007). The option to build semi-finished product and store the materials until an orderis received has limited application in the food pro-cessing sector. Strict food storage guidelines, bac-terial control challenges and short shelf-life renderthe opportunity for utilizing a hybrid MTS/MTO ap-proach, through semi-finished products, difficult ifnot illegal (Johnston et al., 2003). However the mix-ing of the MTO and MTS approaches has merit out-side of the “postponement concept. Firms in the foodsector dynamically move from a MTS to MTO statusto manage short term changes in demand operating ahybrid MTS/MTO approach not based on “postpone-ment”.

MTS/MTO processes enjoy popularity in industryand find themselves implemented in software sys-tems. Enterprise resource planning systems such asSAP, Microsoft Dynamics and Oracle’s JD Edwardsaccommodate strategies for MTS and MTO prod-ucts. For instance SAP has a detailed default processflow for handling MTO products. The user is forcedto distinguish a product to be either of MTO or MTS

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type. That means products of hybrid character lead totwo product records, which evolve into two demandand production time series. In this paper we developan alternative approach that reverses the process byhaving one demand time series for a hybrid productand splitting it up into MTO and MTS items for pro-duction planning and control. Some researchers havebegun tackling the challenge of modeling MTS/MTOsystems and to analytically decide whether a prod-uct should be classified as MTS or MTO through thelens of demand analysis. The methodology sectionbuilds on this earlier approach through the applica-tion of outlier detection techniques leading to the in-troduction of the new method developed to dynami-cally identify MTO and MTS product categories.

3.2. Outlier detection techniques

Demand analysis has been utilised to cate-gorise products into MTS and MTO families.D’Alessandro and Baveja (2000) suggested that ananalysis through the prism of demand variability andaverage weekly demand products can be categorisedas MTO or MTS. A fair amount of literature in thisfield utilises the coefficient of variation (CoV):

cv =σ

µ, (1)

which is the ratio of standard deviationσ and meanµ. Products with low demand variability and “highvolume” were classed as MTS, remaining productswere viewed as MTO. A typical characterisation ofa MTO product is its low average demand and highvariation.Some researchers have stated that a coef-ficient of variation on or below 0.5 may be usedto classify a product as MTS. The authors have notfound any definitive method in the literature, whichcomputes the likeliness of a product falling into theMTS or MTO category. Determining where the cut-off point is for demand variability and the portion-ing of products into MTO or MTS based on theCoV factor can be subjective and difficult to deter-mine (Soman et al., 2007). Recent research has chal-lenged the validity of applying of CoV as a lensto allocate MTS or MTO status due to the frequentchanges in CoV for products as market and their de-mands change quickly altering a product categoriza-tion (Godsell and Kharlmanov, 2012). The low av-

erage demand could be deceiving because large, un-forecasted, orders can shift the average to any level.The ratio of the sample standard deviation to thesample mean overcomes this problem. However,trends can affect this ratio. Removing the linear trendleads to improvements.

In practice operations need to derive a productionstrategy that accommodates MTS and MTO from asingle demand profile. We will assume that outliersrepresent MTO items. Hence, we have to consid-ered outliers in time series. Lewis (1975) reviewsdemand analysis in his extensive work where he dis-cusses demand impulses in the context of adaptiveforecasting He emphasises that “unusual demandsstill have to be dealt with” indicating the relevanceof outlier detection. Silver and Peterson (1985) alsoacknowledge that “temporary change in demand pat-tern” such as promotions should be filtered out be-fore forecasting.Removing identified outliers will re-duce the variation of the MTS classified product thusreducing subsequent inventory.

Atkinson et al. (1997) suggested ways of check-ing fitted models to possible shocks and introduceda new type of intervention analysis, which uses anextra parameter for the outlier. This is equivalent todeleting the outlier and observing the residual sumof squares in a regression model. A considerableamount of literature about outlier detections refersto Fox (1972), which introduces likelihood ratios.Fox looks at stationary time series and proposes twotypes of errors. The first type deals with recordingerror or “isolated independent cross execution” thatare independent of other observations. The secondtype of “outliers” affects consecutive observations -known as additives or innovations. Our work focuseson the first type, which is commonly addressed asshock in the time series literature. Time series analy-sis usually relies on predictive causality, the oppositeof what we aim to do.

Hawkins (1980) discusses the identification of out-liers in great detail and defines them as: “An outlieris an observation which deviates so much from theother observations as to arouse suspicions that it wasgenerated by a different mechanism”. It is conve-nient to introduce abasic model, which is univariate,assumes one “normal” generating mechanism andthat outliers are rare observations. Barnett and Lewis

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(1994) similarly define anoutlier in a set of data tobe “an observation (or subset of observations) whichappears to be inconsistent with the remainder of thatset of data”. On the other handcontaminantsare ob-servations which are not “genuine members” of themain distribution. Extremes could be outliers or con-taminants. Assume that the actual distributionF isknown for a sorted samplex1, x2, . . . , xn. x1 and xn

are the sample extremes, which might be outliers.However, outliers are extreme values. Contaminantsinterfere with the original distributionF and maystem from another distributionG. This could resultin extreme values wrongly identified as outliers. Anintuitive model could assume that a demand time se-ries is made up of a MTS distributionF and a MTOdistributionG.

A variety of methods have been devised to de-tect outliers. Typically these techniques fall intotwo categories: model based and proximity basedapproaches (Kriegel et al., 2010). Model based ap-proaches can use statistical tests, depth considera-tions and deviation analysis. Proximity based tech-niques usually use distance measures or density as-pects. Chen et al. (2010) compare outlier detectiontechniques in regards of of performance. They anal-ysed statistics-based, distance-based and density-based approaches. Model based approaches havebeen extensively investigated by Hawkins (1980).Most of these models assume normal distributeddata; however, all samples in the case study re-ject this assumption. We will focus our review onproximity based techniques. Distance based ap-proaches have the basic assumption that data has adense neighbourhood. This allows identification ofoutliers due to their distance from the neighbour-hood. Knorr and Ng (1998, 1999) have discussedsuch algorithms based on iodizes, nested-loops andgrids. Thek-nearest neighbour method was adaptedfor outlier detection by Ramaswamy et al. (2000),Angiulli and Pizzuti (2002) and many more. Prox-imity techniques based on density usually assumethat the density around an outlier is different toits neighbours. Breunig et al. (1999, 2000) use theconcept of the Local Outlier Factor that overcomesthe issue of clusters having different densities. Re-lated to this concept are the works from Tang et al.(2002) and Jin et al. (2001). A further improve-

ment was achieved by Jin et al. (2006) by usingsymmetric neighbourhood relationships. Cao et al.(2010) developed a density-based algorithm to iden-tify outliers. They introduced a density-similarity-neighbourhood factor which suggests the likelinessof the data to be an outlier. Another interesting ap-proach which uses a local outlier correlation inte-gral on anǫ neighbourhood is Papadimitriou et al.(2003) work. Kriegel et al. (2010) mentioned thatcluster algorithms can be used to identify a noiseset/outliers. Multiple outliers similar to each otherwould form a cluster rather than being identified asnoise. Alan and Catal (2011) use thresholds to formmultiple clusters using proximity based outlier de-tection mechanisms. These techniques are insightfulbut were not designed for demand time series in par-ticular.

3.3. MTO cluster detection technique

In this work we propose a new technique whichis based on proximity and density. The novelty ofour approach is a distance measure operating on theprobability mass distribution that identifies MTS andMTO categories via clustering. Before we embarkon the details of this technique we give a first demandtaxonomy of hybrid MTS-MTO products:

1. MTO outliers

(a) Demand is high and infrequent(b) Demand is low and infrequent

2. MTO contaminants

(a) MTO and MTS demand distributions dif-fer

(b) MTO and MTS demand are similar

Type 1 (a) assumes that MTO items are characterisedby high demand and low frequency. This is the casewe will develop our techniques for. Type 1 (b) isnot important to us because we assume that MTSproduction will not be affected significantly as lowdemand can be served from inventory. Type 2 (a)allows a separation of the distributions when deter-mination of the parameters is a possibility. Type 2(b) constitutes a challenge and cannot be analysedwithout further information and will be discussed infuture research.

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4. Methodology

In this section we will introduce new methods,which help to classify what parts of the demandshould be used as MTS or MTO. Some of the the-oretical underpinnings were introduced in the previ-ous section, which motivated a discussion of outlierdetection techniques. Furthermore we derived a tax-onomy of hybrid MTS-MTO systems.

Here, we will propose our new MTS and MTOidentification method. This requires us to introducea novel series distance measure, which operates onhistograms and time series. We embed this distancemeasure into a cluster technique and derive three cat-egories. A new immediate neighbour detection tech-nique reduces these to the two final MTS and MTOcategories.

The methodology introduced in this research fo-cuses on type 1 demand profile. Our goal is to sep-arate the convoluted MTS-MTO demand. The firststep is the definition of an appropriate distance met-ric. A new city block metric that operates on a his-togram with frequenciesf = ( f1, . . . , fn) is proposed.

dst = | fs− ft| + α|cs − ct|, (2)

The distancedst betweens and t uses equidistantclassesc = (c1, . . . , cn) with d = ci+1 − ci > 0, i < n,whereci represents the centre of classi. Note thata scaling factorα was introduced. The factor is sup-ported by the following considerations. Assume eachclass contains only one observation then the unit dis-tance between classes seems appropriate. If eachclass contains ten observations a unit distance wouldbe inappropriate, because the class distance is not inproportion to the frequency scale. This motivates theclass scaling factorα:

α =

∑nk=1 fk

(n− 1)d. (3)

Example 4.1 (scaled city block distance). Let fig-ure 2 (a) be the histogram derived from a demandtime series. Class two shows demand for two itemsoccurs 80 times/days. A total of 195 days were ob-served and placed into seven demand classes. Thescaling factor isα = 195/(7 − 1) = 32.5. Hence

the distance between s= (2, 80) and t = (5, 20) isdst = |80− 20| + 32.5|2 − 5| = 60+ 97.5 = 157.5.Note that the demand classes can be transformed torepresent other quantities (e.g. c1 could represent1200 items, c2 = 1300with d = 100)).

The problem with the above distance measure is thatfor instance the distance between two classes sepa-rated by another one could be shorter than the onenext to each other. As a result clusters could consistout of disconnected classes. We have overcome thisby introducing a novel“series” distance measure.The distance between classes next to each other is de-termined as before, i.e.dk,k+1 = | fk− fk+1|+α|ck−ck+1|.Note thatα|ck− ck+1| can be simplified to the averagefrequencyf . The distance between two classessandt with s< t is determined by adding up previous dis-tances:

dst =

t−1∑

k=s

dk,k+1. (4)

This can be expressed as a recursiondk,k+2 = dk,k+1 +

dk+1,k+2. All individual series distances form a corre-sponding matrixD = (dst). Example 2’s histogramhas similar characteristics to those observed in thecase study, i.e. classes with low demand occur morefrequently than those with high demand (a type 1MTS-MTO hybrid). These distance measures areused to build an agglomerative hierarchical clustertree. We use the Unweighted Pair Group Methodwith Arithmetic Mean (UPGMA) to build a dendo-gram (binary tree) (Sokal and Michener, 1958).

Example 4.2 (Dendogram). We continue the previ-ous example and build an agglomerative hierarchicalcluster tree (see figure 2 (b)). The average distancebetween class 1 and 2 is 62.5. The average distanceto class three from one and two isd13+d23

2 = 73.8. Thiscluster represents MTS items. Class 5 is in betweenthe MTS and MTO cluster.

In general the distance of two clustersS andO aredetermined by the average pair distances:

1nm

∑

s∈S

∑

o∈O

ds,o, (5)

where n and m are the number of elements inSand O respectively. A possibility to improve the

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Figure 2: Example (a) demand histogram showing scaled city block metric. (b) dendogram.

distance measures further is by considering holdingcosts, setup costs and shortage costs.

The procedure developed above is summarised inalgorithm 1. This procedure offers a systematic way

Algorithm 1 MTS/MTO cluster detectionRequire: equidistant time series of demandsy, no

major innovation in time seriesEnsure: MTO thresholdm, MTS thresholdM

1: remove linear trend from time seriesy and obtainy

2: transformy into histogram with classesci andcorresponding frequenciesfi

3: create series distance matrixD = (dst) usingequation (4)

4: determine hierarchical cluster tree using un-weighted average distances (see example 4.2).

5: extract three clusters from the tree, identifyingMTO and MTS thresholds

of identifying initial MTS and MTO thresholds. Itmay be the case that a product has no MTO products.However, the above procedure will always identify apotential MTO class. In such cases we suggest tofall back to classic service level strategies. For in-stance ensuring that predicted demand is fulfilled in95% of the time periods. We require that there are no“major” innovations in the time series. However, thatissue and a solution are addressed in the followingsection. The first step is the remove of linear trend.This is a first approximation which can be followed

with higher order trend removals in accordance to aTaylor series development. Next a histogram is de-rived. We would like to suggest as future work touse Kernel Density Functions. Botev et al. (2010)have proposed a method which has the advantage ofbeing free of an underlying normal distribution as-sumption. Step 3 and 4 were already explained inthis section. The last step identifies the MTO andMTS thresholds by using the agglomerative hierar-chical clustering that identifies three clusters. Theintroduced distance ensures that the clusters are ad-jacent rather than overlapping.

4.1. Time series

In the previous section we have introduced a tech-nique to identify MTO items; assuming a hybridMTS-MTO time series. Removing MTO items fromthe hybrid time series will improve subsequent timeseries analysis for the remaining MTS items. This inturn causes savings in the holding costs. The produc-tion schedule can be determined via solving the Eco-nomic Lot Scheduling Problem. Alternatively gen-eral time series analysis and forecasting techniquescan be used to determine the anticipated demand andderive a production schedule.

Let us consider three theoretical cases of time se-ries shapes: (1) constant demand; (2) linear increas-ing demand; and (3) demand undergoes an innova-tion. The first case leads to histograms with a sin-gle class of high frequency, which is identified asMTO or MTS. This is in accordance to our empir-

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ical expectations, i.e. either orders are known inadvance or excellent predictability. That means nofurther information is required to make a decision.The second case leads automatically to case one af-ter trend removal. Not removing the trend wouldequipartition the histogram, suggesting wrongly thathigher demand consists out of MTO items. The thirdcase is a change in trend (innovation), which lineartrend removal would not cope with. However, anadditional preprocessing step to the previously intro-duced procedure 1 is able to transform case three intocase one or two. Finding the innovation is achievedby using a weighted average intra-cluster distancemeasure (weighted pair group method with averag-ing, WPGMA) instead of the average measure. Firstthe series distance (equation 4) is determined for thetime seriesy. This is followed by the WPGMA clus-tering and identifying two clusters.

The boundary between the two clusters identifiesthe innovation. This is the cut-off point, that meanswe can use the remaining observations for cluster-ing and identifying MTO items using algorithm 1.Hence, we will improve the MTS demand predic-tions for the shortened time-series. Certainly thequestion remains open, what is a “major break”? Ourmethod divides the time series into two parts, whichallows several approaches to find an answer. Twoapproaches could be used to answer the question:(1) comparing the angle between the trend lines; (2)expectation and variance considerations of the twoparts.

4.2. Summary

An decision support system was developed thatclassifies MTO and MTS items. To be more spe-cific the proposed method transforms a time into ahistogram. The histogram is further processed us-ing a cluster detection technique that identified MTOand MTS categories. The success of this clusteringis ensured by the proposed distance measure.

In practice there are several issues, which stillneed to be dealt with. The next section will look atthose and add a few additionally required techniques,which are better understood through the applicationof actual data.

5. Case study results

The background of the case study company wasgiven in the introduction and elaborated on the factthat there are 250 products to be manufactured. Ini-tially we will focus on one particular product, andlater discuss a set of ten products which were pro-duced on the same production line. This will makeuse of the methodology introduced in the previoussection. This section will give us a good understand-ing of the data, and introduce one more requiredtechnique motivated by the case study’s practical re-quirements. This technique is an approach for prac-titioners and suggests an approach to dissolve theMTS or MTO “grey zone”.

5.1. Product categories

Figure 3 (a) shows the demand profile for prod-uct G01SL over a period of two years (n = 104weeks). It displays the frequencies of MTS/MTOitems in 20 classes (bins). This histogram was de-rived from the time series displayed in figure 4 (a).The time series consists of equidistant demand ob-servationsy = y1, y2, . . . , yn, i.e. yi is the number ofitems moved from the central warehouse (see section2) to the customer in weeki. A high variability canbe observed. A moving average of four weeks (blackline) is shown and approximates a monthly demandprofile. The linear trend (red line) shows that the de-mand is non-stationary.

The coefficient of variation xs = 1.1 suggests a

product being predominantly MTS. Here ¯x is thesample mean ands is the sample standard devia-tion. MTO items are visible by computing thez-scorez = x−x

s . This identifies two weeks as outlierswhich have az-score above 3.1. They are highlightedin figure 4 (see dashed red lines). To be more pre-cise week 73 and 82 have az-scores ofz73 = 6.5andz82 = 3.8 respectively. That means for a normaldistribution this would not be expected in 99.9% ofthe cases. Despite the correct identification it shouldbe noted that the KolmogorovSmirnov test does notconfirm a normal distribution.

Considering figure 3 the demand can be dividedinto three categories: MTO, MTS and a third one.Algorithm 1 identifies these categories using the hi-erarchical agglomerative clustering (see section 3.3).

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y dataNormalt−distributionLogistic

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Figure 3: Product G01SL (a) Probability density and mass of demand identifying MTO and MTS, (b) Dendogram.

The clusters were created using the series city blockdistance (equation 4). Figure 3 (b) visualises andquantifies the intra cluster distances. The MTO cat-egory occurs in two weeks with quantities 25,650(12.8%). MTS comprises 88.5% weeks and a to-tal quantity of 125,041 (62.3%). The third category(MTO or MTS) happens in 9.6% weeks with a quan-tity of 49,935 (24.9%).

Our objective is to get clarity about the third cate-gory. In order to achieve this we have to analyse theindividual weeks. We will use the symbolWs andWo to denote the MTS and MTO weeks respectively.The union of all weeks is abbreviated withW. Thatmeans the weeks within the MTS or MTO categoryareW \ (Ww ∪Wo). The weeks can be derived usingthe MTO and MTS demand threshold determined byalgorithm 1. Ultimately the intention is to end upwith the MTS and MTO categories only. We can as-sume that the MTS category is pure with an averagedemand of 1,359 items per week. The two weeksidentified as MTO occur in week 73 and 82 with de-mands of 15,700 and 9,950 respectively. A closerinvestigation of the MTO neighbours helps in decid-ing about which of the weeksWc

o should be addedto the current MTO weeksWo. Week 73 has onlyone neighbouring week with unusual high demand5,096 (classified within the MTS or MTO category).The other neighbouring weeks [69, 76]\{73, 74} havean average demand of 2,899. A similar scenario ishappening with week 82. Week 81 has a demandof 6,663 items. The surrounding 7 weeks window[78, 85] \ {81, 82} has an average demand of 1,542.The immediate neighbours of MTO from the MTSor MTO category have a demand volume of 5.9%.

We conclude that close to MTO identified weeks arelikely to be part of MTO category. The pure MTSsample mean underestimates the MTO neighbouringdemand and cannot be used for estimating the de-mand during the MTO weeks. These heuristic con-siderations are used to decide about the final MTSand MTO classes.

5.2. Final classification technique

Based on the above considerations we will intro-duce a decision support mechanism to get even moreclarity about MTS and MTO demand. We begin byusing the third category (containing MTS or MTOweeks) as candidates for the MTO category. A can-didateai is the tuple (wi , yi), wherewi is thei th weekandyi the corresponding demand. If a candidate isin the immediate neighbourhood (i.e.wi−1 or wi+1) ofa MTO identified week then the candidate becomespart of the MTO category. This is followed up recur-sively, i.e. a newly assigned MTO (ex-candidate) cancause candidates to be added to the MTO category.The set of MTO-candidate weeks identified this waywill be abbreviated withWc

o. For instance for prod-uct G01SL we only have two candidates, which areadded to the MTO category. Now we are in the posi-tion to create our final demand profiles for MTO andMTS items. The final MTO weeks areWo :=Wo∪Wc

o

and the MTS weeks areWs := W \ Wo. We assumethat weeks with MTO demand also have MTS de-mand, which is equal to the average MTS demandDs. Replacing the demand of the MTO weeksWo

with Ds gives us the time series displayed in figure 4,

9

10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

2500

3000

3500

4000

4500

week

dem

and

10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

2500

3000

3500

4000

4500

week

dem

and

(a) (b)

Figure 4: Product G01SL (a) hybrid time series, (b) MTS time series due to removal of MTO items.

which we abbreviate withys.

ysi =

yi if i ∈W \ Wo

Ds, if i ∈ Wo(6)

The other time series is obtained by taking the de-mand during the MTO weeksWs and reduce it byDs. It is zero except for the MTO weeks and its re-cursively added candidates.

yoi =

0 if i ∈W \ Wo

yi − Ds, if i ∈ Wo(7)

Of courseysi + yo

i is equal toyi.Considering product G01SL the final MTS de-

mand is 84.6%, which is an increase of 22.3% tothe pure MTS cluster demand. The MTO compo-nent has an apparent increase by 2.6% resulting ina demand of 15.4%. We use the word “apparent”because the MTO cluster demand contains demand,which we have estimated to beDs per week.

In summary this additional assignment techniquehas created a time series for MTS units and one forMTO units.

5.3. Practitioner approach and ten products

We will give a guideline for practitioners to decideabout MTO and MTS products/items in the absenceof programming tool. These guidelines were appliedto ten products. The timeseries for the ten productsproduced on the same manufacturing line are dis-played in figure 5. Results in regards to savings andCoV are discussed in this context. Here savings are

due to reduced holding cost, because the productionknows the fraction of MTO units. The argument isthat MTO items can be produced just in time. Thatmeans an improved planning process is possible.

The approach for practitioners is shown in algo-rithm 2. As a first step the CoV should be used. Table

Algorithm 2 Approach for practitionersRequire: Time series of demandsDEnsure: MTO thresholdm, MTS thresholdM

1: Analyse time series2: if no break in structure (innovation) “visible”

then3: Identify MTO and MTS thresholds by4: Create histogram with frequenciesfi and

quantity centresci.5: Determine deltas∆ between consecutive fre-

quenciesf1:n−1 − f2:n.6: MTS thresholdM is the quantity after the

maximal frequency change max∆7: MTO thresholdm is the quantity after the

next maximal frequency change8: else if break in structure identifiedthen9: additional analysis required (set traffic light

to orange)10: else if coefficient of covariation highthen11: MTO likely (alternatives: new product,

product discontinuation) set traffic light to red12: end if

1 gives the CoV for the ten products. Two of them re-veal a CoV significantly above the average (product4 and 10). The CoV was determined following the

10

20 40 60 80 1000

1000

2000

3000

4000

(1) G01SL

week

dem

and

2

20 40 60 80 1000

1000

2000

3000

4000

5000

6000

(2) G02SN

week

dem

and

2

20 40 60 80 1000

200

400

600

800

1000

(3) G03MH

week

dem

and

1.6

2

20 40 60 80 1000

10

20

30

40

50(4) R04TN

week

dem

and

4

20 40 60 80 1000

200

400

600

800

1000

1200

(5) G05MM

week

dem

and

2

20 40 60 80 1000

200

400

600

800

1000

1200

(6) O06MN

week

dem

and

1

20 40 60 80 1000

200

400

600

800(7) G07ML

week

dem

and

2

20 40 60 80 1000

1000

2000

3000

4000

(8) O08SN

week

dem

and

20 40 60 80 1000

200

400

600

(9) O09LN

week

dem

and

20 40 60 80 1000

200

400

600

(10) R10LN

week

dem

and

4

Weekly demandMoving average (period 5)Linear trendoutlier (z−score)Hybrid MTS/MTO profileVisible InnovationHigh CoV (MTO or new product)Number of z−scores (left)Backorder percentage (underneath)Innovation split

Figure 5: Time series showing the weekly demand.

removal of the linear trend as discussed in section4.1. Typically the removal of trend reduces the CoV,that means without removal a identification of MTOproducts is less reliable. Closer investigation of thetwo products reveals one as a new product being in-troduced and the other one as a pure MTO productwith low demand. We will identify them with a redtraffic light, in table 1, to indicate that no further in-vestigation into these two products will take place(see algorithm 2, thirdif clause).

As a second step the practitioner can visually iden-tify those time series showing an obvious innovationsuch as a break in structure or change in trend. Theseare marked with an orange traffic light in table 1. Inour case study product six, eight and nine were iden-tified. Algorithm 2 only suggests that further anal-ysis is required. In subsection 4.1 we introduced atime series clustering technique that allows to findthe innovation for such time series. Using the newmethod allows the remainder of the time series to beanalysed. Product six and eight remaining demandprofiles were identified as hybrid MTS-MTO. Theirestimated savings due to separate MTS and MTO

production are 8.9% and 15.0%. Product nine is clas-sified a MTO and no savings are possible.

The third step deals with the hybrid MTS-MTOcharacter of the demand profiles. It should be notedthat the proposed procedure omits or changes stepsaddressed in the original algorithm 1. The majorchanges are the trend removal and the clusteringtechnique. These adaptations lead to differences inthe savings of about 5%. The results obtained withalgorithm 1 are shown in table 1 and 2. As we can seethe savings are 18.1% on average. This is due to thereduced holding costs by assuming neglect able hold-ing costs for MTO items. That means MTO items areassumed to be produced just-in-time. Figure 6 visu-alises the MTS/MTO categories. The last sub-plotdisplays the coefficients of variation and their group-ings. The first table shows that the estimated savingsare in the range of 13.4% and 27.0%. Furthermorethe CoV reduced in all cases (compare CoV andCoV-S), which will result in additional savings due tothe reduced variation and increased production sta-bility. Here, CoV-S is the abbreviation for the coeffi-cient of variation for the MTS products, which varies

11

0 5000 10000 150000

5

10

15

20

25

(1) G01SL

quantity

#wee

ks

x=2345.3, cv=0.90

2

0 5000 100000

5

10

15(2) G02SN

quantity

#wee

ks

x=3499.3, cv=0.65

2

0 500 1000 1500 20000

5

10

15

20(3) G03MH

quantity

#wee

ks

x=502.4, cv=0.87

3

0 50 1000

20

40

60

80

100(4) R04TN

quantity

#wee

ks

x=3.1, cv=5.13

4

0 500 1000 1500 2000 25000

5

10

15(5) G05MM

quantity

#wee

ks

x=735.8, cv=0.74

2

0 500 1000 1500 20000

5

10

(6) O06MN

quantity

#wee

ksx=674.7, cv=0.71

1

0 500 1000 15000

5

10

15

(7) G07ML

quantity

#wee

ks

x=519.6, cv=0.64

0 2000 4000 60000

5

10

15

(8) O08SN

quantity

#wee

ks

x=1915.8, cv=0.84

0 500 10000

20

40

60

80

(9) O09LN

quantity

#wee

ks

x=170.8, cv=2.52

0 500 10000

20

40

60

80

(10) R10LN

quantity

#wee

ks

x=63.2, cv=3.86

4

100

102

104

0

1

2

3

4

5

6

1 2 3

4

5 6 7 8

9

10

average demand (logarithmic scale)

Coe

ff. o

f var

iatio

n

pure MTS weeksMTS−or−MTO weeksMTO weeksHybrid MTS/MTO profileMajor innovation in TSHigh CoV (MTO or new product)Number of z−scores (left)Backorder percentage (underneath)

Figure 6: histograms demonstrating the MTS, MTS or MTO and MTO identification (trend removal when green traffic light).

Table 1: Savings for products due to MTO item identification.Product TL Savings #weeksCoV CoV-S CoV-O BO zG01SL • 15.4% 104 1.10 0.79 5.70 0.04% 2G02SN • 13.4% 104 0.63 0.50 3.38 0.00% 2

G03MH • 22.6% 104 1.20 1.07 3.83 1.65% 2R04TN • 104 5.13 5.13 0.00% 4

G05MM • 27.0% 104 0.98 0.77 2.96 0.09% 2O06MN • 8.9% 44 0.52 0.45 3.66 0.00% 0G07ML • 24.2% 104 0.93 0.77 2.96 0.02% 2O08SN • 15.0% 48 0.40 0.32 1.98 0.00% 0O09LN • 43 1.73 4.86 1.73 0.00% 0R10LN • 104 3.86 3.86 0.00% 4

Average 18.1% 86.3 1.65 1.19 3.52 0.18% 1.8

between .77 and 1.07. CoV-O is the CoV for MTOproducts and varies between 2.96 and 5.70. A tech-nicality should be noted; there are weeks with neg-ative demand (back-orders, BO). In particular prod-uct three had a negative demand of 1.65%. For theclustering technique to work effectively back-ordersabove 0.3% were treated separately. We have dis-played the number of weeks as outlier via thez-scoremethod in the last column of table 1. These numbersare equal or below the MTO weeks which were iden-tified via algorithm 1. Thez-score assumes a nor-mal distribution; however, all ten products failed theKolmogorov-Smirnov and the Jarque-Bera test for

normality. Many outlier detection methods dependon the normal distribution (see section 3.2). The em-pirical data cannot support their relevance for thiscase study. This is in accordance with time seriesliterature in general, which attempts to find as a lastremainder normally distributed noise. Table 2 showsthe actual number of items per category.

Clearly indicating that product one and two havesignificantly more demand than the other products.The table shows first the absolute total demand overtwo years (except for the products with orange trafficlights). These numbers were obtained using algo-rithm 1. They are also represented as volume per-centage. Using the recursive immediate neighbourapproach the MTS or MTO category was dissolvedresulting in the “final” two MTS and MTO cate-gories. An average of 81.9% MTS items were foundin the hybrid products. The last column of this tableshows the average absolute number of MTS items inthe final MTS category.

5.4. Comments

The food processing sector continues to face in-creasing product volatility and service heterogene-

12

Table 2: MTS and MTO volume per category.Product TL MTS MT-S/O MTO MTS% MT-S/O% MTO% fMTS fMTO fMTS% fMTO% mMTSG01SL • 125,041 49,935 25,650 62.3% 24.9% 12.8% 169,746 30,880 84.6% 15.4% 1,632G02SN • 183,955 145,144 52,282 48.2% 38.1% 13.7% 330,254 51,127 86.6% 13.4% 3,176

G03MH • 12,088 17,737 8,416 31.6% 46.4% 22.0% 29,582 8,660 77.4% 22.6% 284R04TN • 320 100.0% 320 100.0%

G05MM • 19,246 22,581 17,401 32.5% 38.1% 29.4% 43,224 16,004 73.0% 27.0% 416O06MN • 15,714 18,752 4,202 40.6% 48.5% 10.9% 35,217 3,452 91.1% 8.9% 800G07ML • 13,161 14,695 10,573 34.2% 38.2% 27.5% 29,138 9,291 75.8% 24.2% 280O08SN • 35,463 96,268 23,550 22.8% 62.0% 15.2% 132,044 23,237 85.0% 15.0% 2,751O09LN • 14,150 100.0% 14,150 100.0%R10LN • 6,576 100.0% 6,576 100.0%

Average 57,810 52,159 16,312 38.9% 42.3% 43.2% 109,886 16,370 81.9% 42.7% 1,334

ity altering the historical demand profiles of SKU’s.Scheduling and controlling products on the basis ofa pure MTS approach has found in the case studyfirm to be futile and costly. Historically categorisedMTS products regularly exhibited characteristics thatalign with a MTO approach rendering the produc-tion schedule redundant. Rush and exceptionallylarge orders were becoming the norm for the casestudy firm and were found to be difficult to managethrough standard planning and control procedures.The methodology outlined in this section representsthe modeling, analysis and subsequent implementa-tion of a new way of planning and controlling prod-ucts that demonstrate duality in their product cat-egorisation. The algorithm offers practitioners thepossibility to evaluate products and demand in termsof the production approach to be utilised to satisfydemand. The methodology above provides a supporttool for decision-making and scheduling of produc-tion at the SKU level that separates orders in terms ofMTO and MTS.The result for food processing firmshowed that a separate production of the MTO itemsled to a reduction of holding costs by 18.1% on aver-age.

6. Discussion and conclusion

This empirical research has demonstrated how todeal with the combined MTS-MTO situation in thecontext of finite capacity. To date the authors arenot aware of the existence of a published quantita-tive method which identifies MTO and MTS itemsautomatically within a hybrid demand time series.The paper has reported on the challenges and diffi-culties of splitting MTO and MTS demand profiles

to enable firms to manage fluctuations in customersdemand and profile. The developed methodologyprovides practitioners with the tools to revise theirorder history and correlate it with the demand timeseries. Specifically the method supports the identi-fication and scheduling of change in product statusbetween MTS, MTO and MTO/MTS that could im-prove customer service and reduce costs. The newmethodology has the potential to improve the per-formance of production planning and control withinthe food processing sector. The algorithm developedfor practitioners is the first step in aiding productionplanners in achieving a stable schedule when facedwith products exhibiting shifting categorisation sta-tus.

The developed methodology is a valuable contri-bution to the MTO-MTS literature as it addresses,empirically as well as mathematically, a problem thatplanners face on a regular basis. The interaction ef-fects of MTS-MTO demand characteristics with fi-nite capacity is an area that had been identified byseveral researchers as an important area for researchin planning and control. The data analysis from thestudy of ten products paints a complex picture of thedualistic nature of products in the food processingsector and suggests that further research is requiredto develop a stronger link between the developedmethodology and practice. Identifying the MTO orMTS status of demand and converting the informa-tion to develop a robust manufacturing schedule, inthe context of a dynamic MTO/MTS environment, isan area for future investigation.

Through the development and implementation ofthe new methodology two further research directionshave emerged. MTO and MTS demands that are sim-

13

ilar in distribution are a challenge that have still tobe researched and resolved in terms of the model.Identifying, segregating and managing the overlap indistributions requires further data collection over awider range of products and longer time-series. Inte-grating the single demand series for a hybrid productinto the enterprise resource planning (ERP) system isalso highlighted as an area for future research. Giventhe wide application of ERP systems in the food pro-cessing sector linking the algorithm to the main toolof production planners is a vital next step in develop-ing a pathway for successful application and imple-mentation of the new methodology.

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