Expert Systems with Applications 42 (2015) 1773–1787

Contents lists available at ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

SPC forecasting system to mitigate the bullwhip effect and inventoryvariance in supply chains

http://dx.doi.org/10.1016/j.eswa.2014.09.0390957-4174/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Department of Mechanical and Aerospace Engineer-ing, University of Rome ‘‘La Sapienza’’, Via Eudossiana, 18, 00184 Rome, Italy. Tel.:+39 3282777914; fax: +39 0644585746.

E-mail addresses: francesco.costantino@uniroma1.it (F. Costantino), giulio.digravio@uniroma1.it (G. Di Gravio), ahmed.shaban@uniroma1.it, ahmed.shaban@fayoum.edu.eg (A. Shaban), massimo.tronci@uniroma1.it (M. Tronci).

Francesco Costantino a, Giulio Di Gravio a, Ahmed Shaban a,b,⇑, Massimo Tronci a

a Department of Mechanical and Aerospace Engineering, University of Rome ‘‘La Sapienza’’, Via Eudossiana, 18, 00184 Rome, Italyb Department of Industrial Engineering, Faculty of Engineering, Fayoum University, 63514 Fayoum, Egypt

a r t i c l e i n f o

Article history:Available online 30 September 2014

Keywords:Supply chainForecastingOrder-up-toBullwhip effectInventory varianceSPCControl chartSimulation

a b s t r a c t

Demand signal processing contributes significantly to the bullwhip effect and inventory instability insupply chains. Most previous studies have been attempting to evaluate the impact of available traditionalforecasting methods on the bullwhip effect. Recently, some researchers have employed SPC control chartsfor developing forecasting and inventory control systems that can regulate the reaction to short-runfluctuations in demand. This paper evaluates a SPC forecasting system denoted as SPC-FS that utilizesa control chart approach integrated with a set of simple decision rules to counteract the bullwhip effectwhilst keeping a competitive inventory performance. The performance of SPC-FS is evaluated and com-pared with moving average and exponential smoothing in a four-echelon supply chain employs theorder-up-to (OUT) inventory policy, through a simulation study. The results show that SPC-FS is superiorto the other traditional forecasting methods in terms of bullwhip effect and inventory variance underdifferent operational settings. The results confirm the previous researches that the moving averageachieves a lower bullwhip effect than the exponential smoothing, and we further extend this conclusionto the inventory variance.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The orders variability often increases as one moves up the sup-ply chain. This phenomenon is recognized as the bullwhip effectand has been observed in many industries (Klug, 2013; Lee,Padmanabhan, & Whang, 1997a; Zotteri, 2012). The bullwhip effectcan cause large consequences in supply chains such as stock outs,low service level, and extra transportation and capacity costs. Leeet al. (1997a), Lee, Padmanabhan, and Whang (1997b) identifiedfive operational causes of the bullwhip effect: demand signal pro-cessing, lead-time, order batching, price fluctuations and rationingand shortage gaming. Of our particular interest is the demand sig-nal processing which represents the practice of dynamically esti-mating the demand forecasts and subsequently updating theparameters of the inventory control policies (Dejonckheere,Disney, Lambrecht, & Towill, 2004). By doing that, short-run fluctu-ations maybe overreacted because of forecast updating causing

order variability amplification across the supply chain. Extensiveresearch has investigated the impact of the above-mentionedcauses utilizing three modeling approaches: statistical modeling,simulation modeling and control theoretic approach, showing thatthe bullwhip effect can be mitigated by selecting the proper fore-casting method (Chandra & Grabis, 2005; Chen, Drezner, Ryan, &Simchi-Levi, 2000; Chen, Ryan, & Simchi-Levi, 2000; Jaipuria &Mahapatra, 2014; Li, Disney, & Gaalman, 2014), proper orderingpolicy and smoothing (Costantino, Di Gravio, Shaban, & Tronci,2014a; Costantino, Di Gravio, Shaban, & Tronci, 2014b;Costantino, Di Gravio, Shaban, & Tronci, 2014e; Dejonckheere,Disney, Lambrecht, & Towill, 2003; Dejonckheere et al., 2004;Wright & Yuan, 2008), reducing the lead-time (Chen, Drezner,et al., 2000; Chen, Ryan, et al., 2000; Ciancimino, Cannella,Bruccoleri, & Framinan, 2012) and increasing the collaborationlevel (Babai, Ali, Boylan, & Syntetos, 2013; Cho & Lee, 2013;Ciancimino et al., 2012; Costantino, Di Gravio, Shaban, & Tronci,2014d, 2014e).

In particular, previous researches have attempted to quantifythe contribution of various forecasting methods to the bullwhipeffect. The periodic review order-up-to (R,S) policy (OUT) is widelyapplied in practice and therefore most previous studies haveadopted it to investigate the impact of the available traditionalforecasting methods on the bullwhip effect (Li et al., 2014). In this

1774 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

policy, the order is generated to recover the gap between the targetand current levels of inventory position, where the target level isdynamically updated with demand forecast every review period.Chen, Drezner, et al. (2000) have quantified statistically the bull-whip effect in a two-stage supply chain (single supply chain con-sisting of a demand point (customer), a stocking point (retailer),and an outside supplier/manufacturer) employs OUT with movingaverage (MA) and experiencing autoregressive AR(1) demand pro-cess. They have further extended this analysis to the exponentialsmoothing (ES) showing that, if both methods are set to achievethe same forecasting accuracy, then ES produces higher bullwhipeffect (Chen, Ryan, et al., 2000). Dejonckheere et al. (2003, 2004)have confirmed these results through a control theoretic approach.Zhang (2004) has found statistically that the bullwhip effect mea-sures under MA, ES and minimum mean-squared error (MMSE)have distinct properties in relation to lead-time and demandparameters. Ma, Wang, Che, Huang, and Xu (2013) derived bull-whip effect and inventory variance for MMSE, MA and ES underprice sensitive demand. Li et al. (2014) quantified and comparedthe bullwhip effect under Naïve, MA, ES, Holts method and damp-ened trend method. Further related research on the effect of tradi-tional forecasting methods can be found in Bandyopadhyay andBhattacharya (2013), Bayraktar, Lenny Koh, Gunasekaran, Sari,and Tatoglu (2008), Kelepouris, Miliotis, and Pramatari (2008)and Wright and Yuan (2008). Table 1 summarizes the related liter-ature to this study.

The majority of the previous studies have been focusing only oncharacterizing the impact of the available traditional forecastingmethods (time series models) on the bullwhip effect with limitedideas for novel forecasting systems (see also, Table 1). However,most recently, some researchers have attempted to developimproved forecasting systems based on artificial intelligence tech-niques (AI) and compared them against the traditional methods interms of bullwhip effect measures (Campuzano-Bolarín, Mula, &Peidro, 2013; Jaipuria & Mahapatra, 2014). Although implementingartificial intelligence methods may improve forecasting perfor-mance, they have limited usage, require advanced level of knowl-edge, and practitioners always prefer easy-to-use managementtools. Table 1 also indicates limited research has been focusingon both the bullwhip effect and inventory variance while evaluat-ing the available forecasting methods (Hussain, Shome, & Lee,2012; Ma et al., 2013). In supply chains, both downstream andupstream echelons have different interests in forecast updatingwhere upstream echelons desire forecasting method chosen bythe downstream echelons to smooth the bullwhip effect whilethe downstream echelons has an interest in minimizing inventoryvariance (Ma et al., 2013). In general, there is a lack of studies thathave attempted to develop bullwhip effect solutions without majorimplementation effort (Chandra & Grabis, 2005). This is the mainobjective of this research as we attempt to present and evaluatean easy-to-implement forecasting system that can counteract thebullwhip effect without affecting inventory performance.

The classical forecasting approach looks at demand forecastingand inventory management as two independent stages withoutinteractions, which may cause a sub-optimal performance of thewhole system (Babai et al., 2013). In inventory systems (e.g.,OUT), the target inventory level is dynamically updated withdemand forecast (over the lead-time) leading to variation inreplenishment orders that induces the bullwhip effect, however,maintaining a fixed target level or reducing its variability wouldmitigate or eliminate the bullwhip effect, respectively. In tradi-tional forecasting systems such as MA and ES, that are commonlyused in practice, the sensitivity to demand changes can only becontrolled through a single smoothing dimension. They are rigidsystems to allow controlling the trade-off between responsiveness(following the demand changes very closely) to keep desired

service level and mitigating the bullwhip effect through avoidingover/under-reaction to demand changes (Dejonckheere et al.,2003, 2004). Therefore, forecasting should be protected from theover/under-reaction to short-run fluctuations in demand/incomingorder without affecting inventory performance (Jaipuria &Mahapatra, 2014). This protection can be achieved by embeddinga simple monitoring tool to the forecasting system such as controlcharts to regulate forecasting sensitivity to demand changes(Costantino et al., 2014e). Control charts have recently beenemployed successfully to develop easy-to-implement forecastingand inventory control systems for dynamic environments like sup-ply chains as can be found in Pfohl, Cullmann, and Stölzle (1999),Lee and Wu (2006), Cheng and Chou (2008), Kurano, McKay, andBlack (2014) and Costantino et al. (2014a, 2014b, 2014e).

In particular, Cheng and Chou (2008) contributed in ESWA withan integrated inventory control system that employs the ARMAand Shewart control charts with the western electric rules, todetermine the time and the quantity to order. However, theirinventory system produces replenishment order without differen-tiating between forecasting and inventory control. Costantino et al.(2014a, 2014b, 2014e) have alternatively developed and evaluatednovel inventory control systems that differentiate between fore-casting and inventory position control in which two control chartsare integrated to estimate expected demand and adjust inventoryposition (net inventory level + supply line inventory), respectively.The first control chart represents a simple and easy-to-implementforecasting mechanism to estimate the expected demand based onthe current variation of the incoming orders/demand through a setof decision rules without over/under-reaction to demand changes.The second control chart is employed to control the inventory posi-tion whilst allowing order smoothing. They evaluated this inven-tory control system in a multi-echelon supply chain throughsimulation and found that it is superior to the OUT policy inte-grated with MA under various operational settings. They havereported that their forecasting system, we denote as SPC-FS, canachieve a higher ordering and inventory stability than MA but indi-cated that further investigations are still needed. Specifically, theirresearch was mainly focused on the performance of the inventoryreplenishment policy as a whole and therefore the effectiveness ofSPC-FS has not been extensively characterized.

This research focuses mainly on the forecasting part of theirproposed system by integrating SPC-FS with OUT ordering systemand comparing its forecasting performance with other commonforecasting systems, i.e., MA and ES. This inventory system (SPC-FS + OUT) works as an expert system since it combines novel fore-casting system (SPC-FS) and traditional ordering policy (OUT) andSPC-FS’s rules can be tuned based on practitioners knowledge. TheMA and ES are selected as benchmark because of their popularityin practice and literature (see, Table 1). The popularity of MA andES in practice can generally be attributed to their ease of use, flex-ibility, and robustness in dealing with non-linear demand pro-cesses subject to the proper selection of their parameters(Costantino et al., 2014d; Silver, Peterson, & Pyke, 2000). ‘‘Empiri-cal research by Makridakis et al. (1982) has shown simple expo-nential smoothing to be a good choice for one-period-aheadforecasting. It was the preferred option from among 24 other com-monly used time series methods compared under a variety of accu-racy measures and theoretical models for the process underlyingthe observed time series’’ (Disney, Farasyn, Lambrecht, Towill, &de Velde, 2006). However, bullwhip effect research have shownthat MA produces lower bullwhip effect than ES, proving that fore-casting accuracy is different from forecasting performance ininventory systems (Babai et al., 2013). The parameters of MA andES can also be adjusted to achieve the same forecasting accuracyand thus they are very appropriate to conduct direct comparisonswith SPC-FS which can be considered a modified version of MA but

Table 1Related research on the impact of forecast updating on the bullwhip effect.

Methodology orderingpolicy

Forecastingmethod

Performancemeasures

Supplychainmodel

Demand model Focus of analysis

Chen, Drezner, et al.(2000) and Chen,Ryan, et al. (2000)

Statistical,simulation

OUT MA, ES Order variance Singlesupplychain,Multi-Echelon

AR Bullwhip effect quantification, impact oflead-time, forecast parameter andinformation sharing

Chatfield et al. (2004) Simulation OUT MA Order variance 4-Echelon i.i.d Impact of lead-time variation, informationsharing and information quality on thebullwhip effect

Dejonckheere et al.(2003)

Controltheoretic

OUT,smoothing

MA, ES,demandsignaling

Order variance Singlesupplychain

Sinusoidal, realdata, i.i.d. stepdemand

The bullwhip effect under differentforecasting methods with OUT, impact oforder smoothing

Dejonckheere et al.(2004)

Controltheoretic,simulation

OUT,smoothing

MA, ES,demandsignaling

Order variance 4-Echelon i.i.d Impact of forecasting, information sharingand order smoothing on the bullwhip effect

Zhang (2004) Statistical OUT MA, ES, MMSE Order variance Singlesupplychain

AR Impact of lead time and demandautocorrelation on the bullwhip underdifferent forecasting methods

Chandra and Grabis(2005)

Simulation OUT, MRP MA, ES, Naïve,autoregressive

Order variance,averageinventory level

Singlesupplychain

AR Impact of OUT and MRP approach withdifferent forecasting methods on thebullwhip effect

Disney et al. (2006) Controltheoretic

OUT,smoothing

Averagedemand, ES

Order variance,inventoryvariance, fill rate

Singlesupplychain

i.i.d, AR, MA,ARMA

Quantifying the bullwhip effect andinventory variance for i.i.d. and AR, MA andARMA demand

Bayraktar et al. (2008) Simulation OUT Tripleexponentialsmoothing

Order variance Singleelectronicsupplychain

Linear demandwith seasonalswings

Impact of seasonality, lead-time andforecasting parameters, and theirinteractions on the bullwhip effect

Kelepouris et al. (2008) Simulation OUT ES Order variance,fill rate

2-Echelon Real data Impact of lead time, exponential smoothingfactor and safety stock on the bullwhip effect

Wright and Yuan(2008)

Simulation SmoothingOUT

MA, Holt’s andBrown’smethods

Order variance,root meansquare,inventory costs

4-Echelon Local trendsmodified by i.i.d

Impact of improved forecasting andinventory control parameters on thebullwhip effect and inventory costs

Ciancimino et al. (2012) Simulation SmoothingOUT

ES Order variance,inventoryvariance, fill rate

4-Echelon Step demand Impact of supply chain synchronization andorder smoothing on ordering and inventorystability

Hussain et al. (2012) Simulation OUT ES, MMSE Order variance,inventoryvariance

Singlesupplychain

AR Impact of ES and MMSE and lead time onorder and inventory variances

Bandyopadhyay andBhattacharya (2013)

Statistical OUT MMSE Order variance Singlesupplychain

ARMA The bullwhip effect for ARMA(p,q) undervarious ordering policies

Ma et al. (2013) Statistical OUT MA, ES, MMSE Order variance,inventoryvariance

Singlesupplychain

Price sensitivedemand withAR

Impact of MA, ES and MMSE on order andinventory variances

Costantino et al.(2013a)

Simulation OUT MA Order variance,inventoryvariance, fill rate

4-Echelon i.i.d, seasonaldemand

Exploring the bullwhip effect and inventoryvariance in a seasonal supply chain undervarious operational settings

Costantino et al.(2014d)

Simulation OUT MA Order variance,inventoryvariance, fill rate

4-Echelon i.i.d Impact of information sharing and inventorycontrol coordination on supply chainperformances

Jaipuria and Mahapatra(2014)

AI,simulation

OUT ARIMA, DWT-ANN

Mean squareerror, ordervariance,inventoryvariance

Singlesupplychain

Real data,literature data

Impact of forecasting with discrete wavelettransforms integrated with artificial neuralnetwork (DWT-ANN) on order and inventoryvariances

Costantino et al.(2014a), Costantinoet al. (2014b,Costantino et al.(2014e)

Simulation OUT,smoothing,SPC

MA, SPC-forecasting

Order variance,inventoryvariance, fill rate

4-Echelon i.i.d, AR,seasonaldemand

Developing inventory control systems basedon control charts to improve supply chaindynamics

Li et al. (2014) Controltheoretic

OUT MA, ES, Naïve,damped trendforecastingmethod

Order variance Singlesupplychain

Demandpatterns ofdifferentfrequencies,real data

Analyzing the bullwhip effect under dampedtrend forecasting method, and compared toother methods

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1775

with higher smoothing flexibility to allow controlling the sensitiv-ity to demand changes without affecting inventory performance.Motivated by that, we have chosen MA and ES for validating theeffectiveness of SPC-FS.

Simulation modeling is an appropriate tool to study the dynam-ics of complex systems like multi-echelon supply chains (Hussainet al., 2012; Wright & Yuan, 2008). Therefore, a simulation method-ology is adopted to evaluate the performance of SPC-FS in a four-

1776 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

echelon supply chain employs the order-up-to policy. A compari-son is conducted between SPC-FS, MA, and ES based on the bull-whip effect, inventory variance ratio and total stage variance,under various operational conditions in terms of demand processand lead-time. The results show that SPC-FS is superior to MAand ES in terms of ordering and inventory stability across the sup-ply chain, under a wide range of the autoregressive parameter. Thisconfirms the preliminary evaluation of Costantino et al. (2014b,2014e). SPC-FS has also shown a lower sensitivity to the lead-timein comparison to the other forecasting methods. The research pro-vides further contribution to the understanding of the impact ofMA and ES with OUT on the bullwhip effect and inventory variance.

The paper is organized as follows. The next section presents theformulation of the SPC control chart forecasting system. Section 3presents the supply chain model, order-up-to policy, traditionalforecasting models, the performance measures, and simulationmodel validation. Sections 4 presents simulation results and sensi-tivity analysis, and discussion and implications are presented in Sec-tion 5. The conclusions and future research are provided in Section 6.

2. SPC forecasting system

The SPC forecasting system, namely SPC-FS, is extracted fromthe inventory control model of Costantino et al. (2014b, 2014e) inwhich two control charts are integrated to a set of decision rulesto estimate the expected demand and control the inventoryposition, respectively. The first control chart, denoted as demandcontrol chart, is devoted to monitor the variation of the customerdemand/incoming order over time to make the proper changes indemand forecast whenever a considerable demand change has beendetected; without overreacting or underreacting to demand changes.In other words, if the customer demand is stable (i.e., in-control),then the expected demand should be the same as ever before andthus the target inventory level may be kept stable, otherwise, ifthe control chart alarms an out-of-control situation (i.e., demandchange), then the expected demand should be altered in order toaccount for the new situation. This control chart is integrated witha set of decision rules to decide about the out-of-control situationand the expected demand under different out-of-control situations.

A typical control chart consists: a centerline that representsthe average of the process variable, and lower and upper controllimits (Montgomery, 2008). If a process variable (e.g., customerdemand/incoming order) is in-control, then it is expected that99.73% of the demand data points will be within the lower andupper control limits, according to the normality assumption. Theindividual control chart in which the sample size is equal to oneis used to model the forecasting system (Montgomery, 2008).The control limits of the demand control chart for a normaldemand process can be calculated as follows in Eqs. (1)–(3)(Costantino et al., 2014a, 2014b, 2014e).

UCLid ¼ CLi

d þ 3r̂id ð1Þ

Xt

CLid ¼

1Tc s¼t�Tcþ1

Dis ð2Þ

i i i

LCLd ¼ CLd � 3r̂d ð3Þ

The CLid represents the grand mean of the demand process (cen-

terline of the demand control chart) at time t and is calculated basedon the average of the last consecutive Tc data points (t � Tc + 1, . . . , t)of the demand/incoming order data. The LCLi

d represents the lowercontrol limit at time t and equals the difference between CLi

d and3r̂i

d where r̂id stands for the estimated standard deviation of the

demand/incoming order over Tc. Similarly, the upper control limit(UCLi

d) at time t is equal to the sum of CLid and 3r̂i

d.

The demand decision rules are based on the status of the lastobservations of incoming order on the control chart as they arethe most important information for estimating the expecteddemand. In this approach, if the demand control chart signals thatthe customer demand is in-control and no change in the demandlevel, then the order quantity should be considered equal to theaverage value of the demand that is corresponding to the center-line of the demand control chart. Otherwise, if the demand isout-of-control, then the order quantity should be altered basedon the corresponding decision rules. This can be achieved throughestablishing a forecast smoothing zone around the centerline of thedemand control chart to control the forecasting sensitivity to fre-quent demand changes. The following decision rules are proposedbased on Costantino et al. (2014a, 2014b, 2014e) to control theexpected demand under various conditions.

Rule 1. At echelon i, if q points of the last consecutive N data pointsof incoming order are above a controlled forecast smoothing zonebetween CLi

d � Cidr̂i

d and CLid þ Ci

dr̂id, then the expected demand

(bDit) should be estimated based the maximum of the average of the

last Ts data points of incoming order and CLid according to Eq. (4)

(Costantino et al., 2014b, 2014e).

bDit ¼ Max

1Ts

Xt

s¼t�Tsþ1

Dis;CLi

d

( )ð4Þ

Rule 2. At echelon i, if q points of the last consecutive N datapoints of incoming order are below the defined smoothing zone,then bDi

t should be set according to Eq. (5) (Costantino et al.,2014b, 2014e).

bDit ¼ Min

1Ts

Xt

s¼t�Tsþ1

Dis;CLi

d

( )ð5Þ

Rule 3. If the above condition is not satisfied, then bDit should be

equal to the centerline of the demand control chart as representedin Eq. (6) (Costantino et al., 2014b, 2014e).

bDit ¼ CLi

d ¼1Tc

Xt

s¼t�Tcþ1

Dis ð6Þ

3. Supply chain simulation modeling

Several modeling approaches have been adopted to study thebullwhip effect such as statistical modeling, control theoretic andsimulation (Chatfield, 2013; Chatfield, Kim, Harrison, & Hayya,2004; Costantino et al., 2014d). Among them, simulation modelingis an appropriate tool to study the dynamics of complex systemslike multi-echelon supply chains since it provides the ability to rep-resent a multi-echelon supply chain system in a single, connectedand cohesive model, so that the limitations of simple models in rep-resenting larger systems are avoided (Chatfield, 2013). Therefore,we believe that simulation modeling is the most appropriate meth-odology for this study as we model a four-echelon supply chain, andevaluate its dynamic response under different forecasting systems.In particular, a simulation model for a four-echelon supply chain isdeveloped and validated with previous research results.

3.1. Supply chain model

To evaluate the forecasting systems, we utilize a single productmulti-echelon supply chain, widely used for the bullwhip effectanalysis (Chatfield, 2013; Chen, Drezner, et al., 2000; Chen, Ryan,

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1777

et al., 2000; Ciancimino et al., 2012; Costantino, Di Gravio, Shaban,& Tronci 2014c, 2014a, 2014b; Dejonckheere et al., 2004), consist-ing of a customer, a retailer, a wholesaler, a distributor, and a fac-tory. Fig. 1 depicts a visual representation of the supply chainstructure in which the customer places orders with the retailer,the retailer places orders with the wholesaler, and so on up thesupply chain to the factory, which places its orders with an exter-nal supplier with unlimited capacity (Costantino et al., 2014a,2014b). Each echelon utilizes the incoming orders from his adja-cent downstream partner to make his forecasting and inventoryplanning, without knowing the actual customer demand.

In this model, the order-up-to inventory policy (OUT) isemployed at each echelon in the supply chain. The order-up-to isselected for this research because of its popularity in the literatureof the bullwhip effect and in practice since it is known to minimizeinventory costs (Chatfield, 2013; Disney & Lambrecht, 2008).Disney, Farasyn, Lambrecht, and Towill (2007) asserted that at leasttwo of the four largest UK grocery retailers use the OUT policy tomanage the flow of products in their supply chains. In this inven-tory policy, at the end of each review period (R), where R = 1 for thisresearch, a non-negative replenishment order Oi

t is placed when-ever the inventory position IPi

t is lower than a specific target levelSi

t . The IPit represents the sum of the inventory on hand (that is,

items immediately available to meet demand, Iit) and the inventory

in the supply line (that is, items ordered but not yet arrived due tothe lead time, SLi

t), minus the backlog (that is, demand that couldnot be fulfilled and still has to be delivered, Bi

t). The net inventorylevel of echelon i at time t (NIi

t) is calculated as the differencebetween Ii

t and Bit . The governing rules of the order-up-to policy

can be represented mathematically as follows in Eqs. (7)–(10).

Oit ¼ Max ðSi

t � IPitÞ;0

n oð7Þ

IPit ¼ Ii

t þ SLit � Bi

t ð8ÞSi

t ¼ LbDit þ SSi

t ð9Þ

The target inventory position Sit (see, Eq. (9)), known also as

order-up-to level, is calculated based on the expected demand overthe lead-time plus review period (L ¼ Li

d þ R), with a forecastingmethod that can be SPC-FS or any other, in addition to a safetystock component. Following the relevant literature (Costantinoet al., 2014d; Dejonckheere et al., 2004), we have considered thesafety stock that is required to account for demand variation byextending the lead-time by a safety stock factor denoted as ki,where ki P 0, as shown in Eq. (10).

Sit ¼ ðL

id þ Rþ kiÞbDi

t ð10Þ

Several forecasting systems can be employed to estimate thelead-time demand such as moving average (MA), exponentialsmoothing (ES), and Minimum Mean Square Error (MMSE). Mostof the previous studies have shown that MA and ES are the mostadopted in research and practice (Dejonckheere et al., 2004). Thepopularity of the MA and ES in practice is due to their ease ofuse, flexibility, and robustness in dealing with non-linear demandprocesses (Silver et al., 2000). Therefore, we select both MA and ESas benchmark to validate the effectiveness of the forecastingsystem (SPC-FS).

Retailer WholesaCustomer

Information flowProduct flow

Fig. 1. A multi-echelon supply cha

The demand forecast based on MA at time t is calculated basedon the following Eq. (11) (Dejonckheere et al., 2004):

bDit ¼

1Tm

Xt

s¼t�Tmþ1

Dis ð11Þ

where Tm stands for the moving average parameter, i.e., averageage of the forecast data, and Di

s is the incoming order/demand attime s where s = t � Tm + 1, . . . , t.

The demand forecast based on ES can be calculated based on thefollowing Eq. (12) (Dejonckheere et al., 2004):bDi

t ¼ aDit þ ð1� aÞbDi

t�1 ð12Þ

where a represents the exponential smoothing parameter where0 6 a 6 1. Larger values of a denote a greater weight placed onthe most recent demand observation while smaller a denote agreater weight assigned to demand history in estimating theexpected demand. According to Dejonckheere et al. (2004), thevalue of a can be linked to the average age of the data (Ta) in theforecast through a formula proposed by Makridakis, Wheelwright,and McGee (1978) (see, Eq. (13)).

a ¼ 1Taþ 1

ð13Þ

In order to make a fair comparison between exponentiallysmoothed forecasts and forecasts based on moving averages, thefollowing formula should be used: Tm = 2Ta + 1 (Dejonckheereet al., 2003, 2004). Based on this formula, the forecasts by bothMA and ES will be based on the same age of data and this approachhas been adopted in the literature for conducting consistent com-parisons between MA and ES (Chen, Ryan, et al., 2000;Dejonckheere et al., 2003, 2004).

3.2. Demand model

To evaluate the different forecasting methods, we assume thatthe customer demand is autoregressive demand process (AR) sothat using a forecasting method to estimate the future demandduring the lead-time is justified. This demand pattern has beenemployed widely in previous research as can be seen in Table 1.Furthermore, Lee, So, and Tang (2000) reported that the AR(1)demand process was found to match the sales patterns of 150 SKUsin a supermarket. The AR demand observations can be generatedfrom the following demand generator in Eq. (14) (Disney andGrubbström, 2004; Disney et al., 2006; Hussain et al., 2012):

D1AR¼ ld þ e1

DtAR¼ qðDðt�1ÞAR

� ldÞ þ et þ ld

ð14Þ

where ld stands for the mean of the demand process, which will beset arbitrarily high enough (relative to rd) to eliminate negativedemand (i.e., ld > 4rd) in order to satisfy the non-negativity condi-tion where negative replenishment orders or demand are notallowed in the considered supply chain model, et represents whitenoise following a normal distribution with le = 0 and r2

e , q is an auto-regressive coefficient, where�1 < q < 1, and DtAR is the AR demand attime t. The AR demand variance equals r2

d ¼ r2e=ð1� q2Þ, where

r2d ¼ r2

e when the demand process is identically and independently

ler Distributor Factory

in (Costantino et al., 2014d).

1778 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

distributed (i.i.d), i.e., the autocorrelation coefficient is equal q = 0.For �1 < q < 0, the process is negatively correlated and exhibits per-iod-to-period oscillatory behavior. For 0 < q < 1, the demand processis positively correlated which is reflected by a meandering sequenceof observations (Disney and Grubbström, 2004). This demand pro-cess is strictly stationary (hence its long run, unconditional, varianceand mean can be determined), but it does exhibit some non-station-ary characteristics that justify the use of a forecasting mechanism(Disney and Grubbström, 2004).

3.3. Performance measurement system

This research is mainly focused on evaluating the bullwhipeffect under different forecasting methods. Therefore, the orderingbehavior under the different forecasting systems can be evaluatedby estimating the total variance amplification (TVAi) or bullwhipeffect which is used to quantify the demand variance amplificationthroughout the supply chain (Chatfield, 2013; Chatfield et al.,2004). The TVAi, as shown in Eq. (15), is estimated in terms ofthe ratio of orders variance divided by the respective orders aver-age at echelon i relative to the customer demand variance (r2

D)divided by the average demand (Chen, Drezner, et al., 2000;Costantino et al., 2014d; Dejonckheere et al., 2004; Disney &Lambrecht 2008).

TVAi ¼r2

Oi=lOi

r2D=lD

ð15Þ

Similar to the bullwhip effect measure, the inventory perfor-mance and its stability can be evaluated by measuring the inven-tory variance ratio (see, Eq. (16)) which represents the ratio ofthe net inventor variance (r2

NIi) to the customer demand variance

(Costantino, Di Gravio, Shaban, & Tronci, 2013a; Costantino, DiGravio, Shaban, & Tronci, 2013b; Disney & Towill 2003).

InvRi ¼r2

NIi

r2D

ð16Þ

The bullwhip effect tends to increase the cost at the upstreamechelons while the inventory variance ratio expresses the localinventory performance that affects the inventory costs (holdingand shortage). Therefore, it is worth comparing the sum of TVAi

and InvRi (which is called Total Stage Variance, TSVi) under the dif-ferent forecasting methods (Costantino et al., 2014e; Disney et al.,2006). By adding up TVAi and InvRi, it is thus assumed that both fac-tors are equally important at each echelon in the supply chain (see,Eq. (17)). The minimization of this measure reflects improved sup-ply chain performance in terms of ordering and inventory stability.

TSVi ¼ TVAi þ InvRi ð17Þ

Table 2Bullwhip effect closed form expressions for MA and ES.

Forecasting system Bullwhip effect expression

Moving average (MA) – Chen,Drezner, et al. (2000)

r2Oi

r2D

PQm

i¼1 1þ 2LiTmþ

2L2i

Tm2

� �8i

(18)

Exponential smoothing (ES) –Chen, Ryan, et al. (2000)

r2Oi

r2D

PQm

i¼1 1þ 2Liai þ2L2

i a2i

2�ai

� �� �8i

(19)

3.4. Simulation and validation

A general simulation model has been built for the supply chainmodel described above, using SIMUL8 simulation package. To eval-uate the forecasting systems, the simulation model is run for 10replications of 2400 periods each (Costantino et al., 2014a,2014b, 2014e). Each simulation run consists of four stages, the firststage is a warm-up period for the order-up-to with a traditionalforecasting system (MA or ES), and the second stage is the effectivesimulation run, then, another warm-period for the order-up-towith SPC-FS is considered, followed by an effective simulationrun. Both warm-up periods have the same length of 200 periods,and both effective simulation runs are set to be of the same lengthof 1000 periods. These simulation settings are considered for allthe following simulation experiments unless something else ismentioned.

We validate our simulation model by comparing the observedbullwhip effect ratio generated by the simulation model for differ-ent forecasting methods to those from the analytical work of Chen,Drezner, et al. (2000) and Chen, Ryan, et al. (2000), the controlengineering work of Dejonckheere et al. (2004) and the simulationwork of Chatfield et al. (2004). Chen, Drezner, et al. (2000) andChen, Ryan, et al. (2000) derived closed-form expressions for thetotal variance amplification in a two-stage supply chain undermoving average and exponential smoothing forecasting methods,respectively, which can also be generalized to multi-echelonsystems through multiple applications (i.e., a product of severalindividual stage amplification values) as shown in Table 2. Chen,Drezner, et al. (2000) and Chen, Ryan, et al. (2000) are widelyperceived as a benchmark for bullwhip quantification (Chatfield,2013; Dejonckheere et al., 2004).

To conduct the validation test, the simulation settings areselected to be the same as those ones used by both Dejonckheereet al. (2004) and Chatfield et al. (2004) in order to make directcomparisons with them. Therefore, for each forecasting system,the simulation model was run for 20 replications of a replicationlength of 5200 periods each and with a warm-up period of 200periods (effective simulation run of 5000 periods), consideringthe above simulation setup. The demand pattern was consideredto follow the normal distribution with ld = 100, r2

d ¼ 102, andq = 0. The parameters of MA and ES were set to Tm = 19 andTa = 9 (respectively), "i, and the safety stock parameter was setto ki = 2, "i, i.e., the value of Li

d þ Rþ ki ¼ 5; 8i where Lid ¼ 2; 8i

and R = 1. For the simulation validation, the SPC-FS parametersare set to turn SPC-FS forecasting system to behave as MA as fol-lows: Ts = Tm, Ts = Tc and Ci

d P 0. We applied these values in Eqs.(18) and (19) to get the bullwhip effect ratio at each echelon ibased on Chen, Drezner, et al. (2000) and Chen, Ryan, et al.(2000) under MA and ES, respectively, where i = 1, . . . ,m (echelonindex) and m = 4, and Li ¼ Li

d þ Rþ ki in which the safety stockparameter is included.

The comparison results are depicted in Table 3 and show thatour simulation model is working as intended where there is a verysmall difference between the bullwhip effect estimated by the sim-ulation model for the different forecasting systems and the otherresults from previous leading research. The results also indicatethat both MA and SPC-FS that achieve the same bullwhip effecthave a superior performance compared to ES although the param-eters of the different forecasting methods are tuned to achieve thesame forecasting accuracy (i.e., Ts = Tm = 19 and Ta = 9).

4. Simulation results analysis

4.1. Preliminary evaluation

A preliminary comparison has been conducted among the threeforecasting systems (with setting their average age of the data tobe equal) under different values of the demand parameter, rangesbetween q = �0.5 and q = 0.5. The other parameter of the demandprocess are fixed for all the following simulation experiments withld = 30 and r2

e ¼ 32. The parameters of both MA and ES areselected to have the same average age of data in the forecast with

Table 3Simulation model validation with previous research results.

TVAi SIM. – SPC-FS

Moving average Exponential smoothing

SIM. –MA

Dejonckheere et al.(2004)

Chatfield et al.(2004)

Chen, Drezner, et al.(2000)

SIM. –ES

Dejonckheere et al.(2004)

Chen, Ryan, et al.(2000)

Retailer 1.67 1.67 1.67 1.67 1.67 2.27 2.26 2.26Wholesaler 3.00 3.00 2.99 2.99 2.77 5.18 5.16 5.06Distributor 5.74 5.74 5.72 5.72 4.61 11.83 11.84 11.39Factory 11.45 11.45 11.43 11.43 7.68 25.96 27.22 25.63

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1779

Tm = 15 and Ta = 7. Also, the values of the SPC-FS parameters areset to be consistent with the selected parameters for the bench-mark forecasting systems with Ts = 15 (i.e., Ts = Tm) and the otherparameters are set to Tc = 50, Ci

d ¼ 1, q = 5 and N = 7 where the val-ues of Tc, q and N are fixed in all the following simulation experi-ments. The results of sample simulation runs are presented inFigs. 2 and 3 in which the ordering and inventory performance ofthe factory under SPC-FS compared to MA and ES, respectively,over the last 200 periods of the effective simulation run in eachcase are plotted. We selected the factory since it is the highest ech-elon level in the supply chain and thus the most exposed to thebullwhip effect (Chatfield et al., 2004; Costantino et al., 2014b).The factory orders are compared to the customer demand whereasthe factory inventory is compared to the distributor order. The SPC-FS shows a higher ordering and inventory stability than MA. Theseresults are discussed in details in the following results that arebased on 10 simulation runs.

01020304050607080

1 21 41 61 81 101 121 141 161 181

Ord

er q

uant

ity

MA (Tm=15)

-40-20020406080100

1 21 41 61 81 101 121 141 161 181

Inve

ntor

y le

vel

MA (Tm=15)

Fig. 2. The performance of the factory unde

01020304050607080

1 21 41 61 81 101 121 141 161 181

Ord

er q

uant

ity

ES (Ta=7)

-60-40-20020406080100

1 21 41 61 81 101 121 141 161 181

Inve

ntor

y le

vel

ES (Ta=7)

Fig. 3. The performance of the factory und

The bullwhip effect results depicted in Fig. 4a (based on theaverage of the simulation runs) show that SPC-FS achieves the low-est bullwhip effect across the supply chain compared to MA and ES,regardless of the autoregressive parameter value. For example,when q = 0, the bullwhip effect increases form 1.70 at the retailerto 12.05 at the factory under MA, increases from 2.30 to 26.67under ES, and increases from 1.21 to 2.20 under SPC-FS. This meansthat the ordering stability across the supply chain is higher whenSPC-FS is employed, confirming the previous results byCostantino et al. (2014b, 2014e). The results also show that thebullwhip effect across the supply chain under MA is lower thanthe bullwhip effect under ES regardless of the value of q. Thesefindings also confirm the previous results that have shown thatMA will achieve a better performance in supply chain than ES interms of the bullwhip measure (Dejonckheere et al., 2003, 2004).

The previous studies on the impact of the forecasting methodson the bullwhip effect have always been considering the bullwhip

1 21 41 61 81 101 121 141 161 181

Customer Demand Factory Order

SPC-FS (Cd=1, Ts=15)

1 21 41 61 81 101 121 141 161 181

Distributor Order Factory Inventory

SPC-FS (Cd=1, Ts=15)

r SPC-FS compared to MA when q = 0.

1 21 41 61 81 101 121 141 161 181

Customer Demand Factory Order

SPC-FS (Cd=1, Ts=15)

1 21 41 61 81 101 121 141 161 181

Distributor Order Factory Inventory

SPC-FS (Cd=1, Ts=15)

er SPC-FS compared to ES when q = 0.

1.68 1.70 1.70 2.34 2.30 2.16 1.19 1.21 1.36

11.72 12.05 11.94

25.4626.67

22.88

2.08 2.20 2.96

0.0

5.0

10.0

15.0

20.0

25.0

30.0

rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5

MA(15) ES(7) SPC-FS(Cd=1, Tc=50, Ts=15)

TVA

Forecasting System

(a) Total Variance Amplification

Retailer

Wholesaler

Distributor

Factory

1.96 3.937.50

2.14 3.966.76

1.61 3.236.13

13.36

27.40

52.48

24.28

44.34

67.97

2.765.69

12.92

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5

MA(15) ES(7) SPC-FS(Cd=1, Tc=50, Ts=15)

InvR

Forecasting System

(b) Inventory Variance Ratio

Retailer

Wholesaler

Distributor

Factory

3.64 5.639.20

4.47 6.26 8.922.80 4.44 7.49

25.09

39.44

64.41

49.73

71.02

90.85

4.84 7.8915.87

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5 rho=-0.5 rho=0 rho=0.5

MA(15) ES(7) SPC-FS(Cd=1, Tc=50, Ts=15)

TSV

Forecasting System

(c) Total Stage Variance

Retailer

Wholesaler

Distributor

Factory

Fig. 4. Supply chain performance under the different forecasting systems.

1780 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

effect ratio without considering the other side of the problemwhich is the inventory variance ratio. This research has focusedon both the measures TVAi and InvRi. Specifically, the inventoryvariance ratio results are depicted in Fig. 4b and show thatSPC-FS achieves the highest inventory stability (lowest InvRi)across the supply chain compared to MA and ES. The results alsoreveal that MA can achieve a higher inventory stability across thesupply chain than ES. However, another important result can beseen in Fig. 4b where the inventory variance ratio increases as qincreases regardless of the selected forecasting method but thesensitivity of InvRi to q is higher under both MA and ES comparedto SPC-FS. For instance, as the autoregressive parameter increasesfrom q = �0.5 to q = 0.5, the InvRi increases from 1.96 to 7.5 atthe retailer and from 13.36 to 52.48 at the factory under MA;increases from 2.14 to 6.76 at the retailer and from 24.28 to67.97 at the factor under ES; and increases from 1.61 to 6.13 atthe retailer and from 2.76 to 12.92 at the factory under SPC-FS. This

means that SPC-FS is successful to achieve both ordering andinventory stability in comparison to other widely applied forecast-ing systems and this can also be shown in Fig. 4c that summarizethe total stage variance across the supply chain under the differentforecasting systems. The performance of SPC-FS is consistentalong a wide range of the parameter of the considered demandprocess.

4.2. The impact of the forecasting parameters

The above results have shown that MA can achieve a higher sta-bility in the supply chain, in terms of TVAi and InvRi, than ES. There-fore, MA is selected to conduct further extensive comparisons withSPC-FS under other operational conditions. In this section, a com-parison is conducted between MA and SPC-FS across a wide rangeof the demand parameter q, under different levels of forecastingsensitivity to demand changes. The sensitivity of MA to demand

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1781

changes can be controlled through only changing the value of Tmwhile the sensitivity of SPC-FS can be controlled through manyvariables (dimensions) such as Tc, Ci

d, Ts, q and N. Three sensitivitylevels are proposed for this comparison: high (Tm = Ts = 7), med-ium (Tm = Ts = 15), and low (Tm = Ts = 30). For all the sensitivitylevels, the SPC-FS is evaluated under different values of Ci

d rangesbetween Ci

d ¼ 0:5 and Cid ¼ 1:5 in order to investigate the impact

of this control parameter on the performance measures. Theparameter Ci

d can be considered as another dimension for moreforecast smoothing without the need for increasing the level ofaverage age of data (Ts). Thus, SPC-FS can be protected from

2.86 1.28 1.19 1.18 1.68 1.21

70.65

2.87 2.08 2.07

11.72

2.30.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

TVA

Forecast

(a) rho

2.83 1.74 1.24 1.20 1.70 1.36

92.11

6.632.33 2.13

12.053.8

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

TVA

Forecast

(b) rho=0

2.81 2.73 1.78 1.22 1.70 1.71

88.72

15.65

3.80 2.18

11.947.44

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC-

High Sensitivity Medium

TVA

Forecasti

(c) rho

Fig. 5. The bullwhip effect sensitivit

frequent reaction to demand noise that drives the bullwhip effect,without affecting its responsiveness to serious demand changesthat should be incorporated in inventory planning to keep a desir-able service level. The comparisons are conducted under three lev-els of the demand parameter so that the interaction between aforecasting parameter and the demand pattern parameter can beunderstood. The other parameters are set as follows: ki = 1,Li

d ¼ 2, and Tc = 50.It can be observed from the comparisons in Fig. 5 that decreas-

ing the forecasting sensitivity to demand changes leads to decreasethe bullwhip regardless of the value of the demand parameter.

1.19 1.18 1.32 1.19 1.19 1.183 2.08 2.07 3.36 2.16 2.07 2.07

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

=-0.5Retailer

Wholesaler

Distributor

Factory

1.21 1.20 1.33 1.24 1.20 1.201 2.20 2.13 3.44 2.53 2.15 2.13

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

Retailer

Wholesaler

Distributor

Factory

1.36 1.20 1.33 1.32 1.22 1.192.96 2.12 3.48 3.49 2.34 2.09

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ng System

=0.5

Retailer

Wholesaler

Distributor

Factory

y to the forecasting parameters.

1782 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

Most importantly, it can be further seen that SPC-FS achieves alower bullwhip effect than MA for all comparisons and that byincreasing the level of Ci

d further order smoothing and thus lowerbullwhip effect could be achieved. However, when demand ishighly positively correlated, both MA and SPC-FS achieve a compa-rable TVAi to each other especially at the most downstream eche-lons while the bullwhip effect propagation at the upstreamechelons is restricted under SPC-FS especially when higher levelis selected for Ci

d. Therefore, improved forecasting systems areessential to improve ordering stability at higher levels in supplychains (see, Figs. 5).

2.65 1.65 1.61 1.61 1.96 1.62

106.66

3.63 2.77 2.76

13.363.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

InvR

Forecast

(a) rho

5.55 3.68 3.24 3.23 3.93 3.31

238.71

14.36 5.82 5.6027.40

8.30.0

50.0

100.0

150.0

200.0

250.0

300.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

InvR

Forecast

(b) rho=0

16.59 8.45 6.37 6.10 7.50 6.32

422.33

55.10

14.55 10.78

52.4826.2

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC-

High Sensitivity Medium

InvR

Forecasti

(c) rho

Fig. 6. The inventory variance ratio sensi

The results in Fig. 6 show also that decreasing the forecastingsensitivity to demand changes leads to improved inventory stability(smaller inventory variance) across the supply chain regardless ofthe value of the demand parameter. Increasing the level of Tmimproves the inventory stability across the supply chain underMA but much more inventory stability can be obtained underSPC-FS even when Ts = Tm and that by increasing the level of Ci

d

leads to higher inventory stability. The results show that SPC-FS issuperior to MA under all sensitivity levels regardless of the valueof q. The results of the total stage variance (see, Fig. 7) also confirmthis conclusion. Although MA seems to achieve a comparable

1.61 1.61 1.71 1.61 1.61 1.614 2.76 2.76 4.36 2.84 2.76 2.76

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

=-0.5

Retailer

Wholesaler

Distributor

Factory

3.23 3.23 3.43 3.25 3.23 3.231 5.69 5.60 8.96 6.28 5.63 5.60

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

Retailer

Wholesaler

Distributor

Factory

6.13 6.09 6.49 6.07 6.08 6.081 12.92 10.57 17.30 14.15 11.13 10.52

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ng System

=0.5

Retailer

Wholesaler

Distributor

Factory

tivity to the forecasting parameters.

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1783

bullwhip effect to SPC-FS when the demand is highly positively cor-related, the SPC-FS achieves a corresponding TSVi lower than MAsince the measure is compensated with the lower InvRi under SPC-FS (see, Fig. 6c).

4.3. The impact of lead-time

The lead-time is a main factor in the inventory control problemwhich contributes significantly to the bullwhip effect in supply

5.51 2.93 2.80 2.80 3.64 2.83

177.31

6.50 4.86 4.84

25.09

5.30.020.040.060.080.0100.0120.0140.0160.0180.0200.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

TSV

Forecast

(a) rho

8.38 5.42 4.48 4.43 5.63 4.67

330.82

20.998.15 7.73

39.4412.1

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC

High Sensitivity Medium

TSV

Forecast

(b) rho

19.40 11.18 8.15 7.31 9.20 8.02

511.05

70.74

18.34 12.9664.41

33.6

0.0

100.0

200.0

300.0

400.0

500.0

600.0

Cd=0.5 Cd=1.0 Cd=1.5 Cd=0.5

MA(7) SPC-FS(Tc=50, Ts=7) MA(15) SPC-

High Sensitivity Medium

TSV

Forecasti

(c) rho

Fig. 7. The total stage variance sensitiv

chains (Chen, Drezner, et al., 2000; Chen, Ryan, et al., 2000; Leeet al., 1997a, 1997b; Zhang, 2004). Although it is known that longerlead-time increases the bullwhip effect when forecasting isemployed to predict future lead-time demand (Chen, Drezner,et al., 2000; Chen, Ryan, et al., 2000), in this analysis, we aim atinvestigating and comparing the sensitivity of the studied forecast-ing systems to the lead-time factor in terms of TVAi, InvRi and TSVi.The three forecasting systems have been evaluated under two lev-els of sensitivity to demand changes in order to understand the

2.80 2.80 3.03 2.81 2.80 2.807 4.84 4.84 7.72 5.00 4.84 4.84

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

=-0.5

Retailer

Wholesaler

Distributor

Factory

4.44 4.43 4.76 4.49 4.43 4.432 7.89 7.73 12.40 8.81 7.78 7.73

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

-FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ing System

=0

Retailer

Wholesaler

Distributor

Factory

7.49 7.28 7.82 7.39 7.30 7.285 15.87 12.69 20.78 17.64 13.46 12.61

Cd=1.0 Cd=1.5 Cd=0.5 Cd=1.0 Cd=1.5

FS(Tc=50, Ts=15) MA(30) SPC-FS(Tc=50, Ts=30)

Sensitivity Low Sensitivity

ng System

=0.5

Retailer

Wholesaler

Distributor

Factory

ity to the forecasting parameters.

1784 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

interaction between forecasting and lead-time. The followingparameters settings have been used to conduct this analysis:q = 0, ki = 1, Tc = 50, and Ci

d ¼ 1.The bullwhip effect results are depicted in Table 4 and show

that longer lead-time leads to higher bullwhip effect regardlessof the forecasting method. This means that all studied forecastingmethods are sensitive to the lead-time. However, it can beobserved that SPC-FS has the lowest sensitivity to the lead-timeamong others. For example, as the lead-time increases fromLi

d ¼ 1 to Lid ¼ 5, the bullwhip effect increases from 1.50 to 2.39

at the retailer and from 6.48 to 53.50 at the factory underMA(15), increases from 1.94 to 3.61 at the retailer and from13.86 to 106.91 at the factory under ES(7), increases from 1.16 to1.37 at the retailer and from 1.83 to 3.85 at the factory underSPC-FS. It can also be observed that the effect of the lead-timeunder MA is lower than when ES is employed and that MA has alower sensitivity to the lead-time than ES. Furthermore, decreasingthe sensitivity of the forecasting system to demand changes(increasing Tm for MA, Ta for ES, and Ts and Ci

d for SPC-FS) leadsto decrease the sensitivity of the forecasting system to the lead-time and contribute to mitigate the contribution of the lead-timelevel to the bullwhip effect.

The inventory variance ratio results are summarized in Table 5and show a similar behavior to the bullwhip effect results in Table 4where the lead-time contributes largely to the inventory stabilityregardless of the forecasting systems. The SPC-FS achieves againthe highest inventory stability in comparison to MA and ES underthe studied lead-time range. Thus, SPC-FS outperforms both MAand ES in terms of TVAi and InvRi across the lead-time range andthis can also be observed in Table 6 that presents the total stagevariance. Furthermore, it can be observed that decreasing theforecasting sensitivity to demand changes not only reduces the

Table 4The bullwhip effect sensitivity to lead-time under the different forecasting systems.

TVAi Forecasting system

MA ES

Ld = 1 Ld = 3 Ld = 5 Ld = 1

1 – Tm = 15, Ta = 7, Ts = 15Retailer 1.50 1.90 2.39 1.94Wholesaler 2.35 4.00 6.61 3.74Distributor 3.84 9.05 19.71 7.22Factory 6.48 21.08 53.50 13.86

2 – Tm = 30, Ta = 14.5, Ts = 30Retailer 1.24 1.41 1.59 1.45Wholesaler 1.56 2.05 2.68 2.10Distributor 1.97 3.06 4.74 3.01Factory 2.53 4.71 8.70 4.32

Table 5The inventory variance ratio sensitivity to lead-time under the different forecasting system

InvRi Forecasting System

MA ES

Ld = 1 Ld = 3 Ld = 5 Ld = 1

1 – Tm = 15, Ta = 7, Ts = 15Retailer 2.54 5.40 10.58 2.57Wholesaler 3.95 11.53 33.50 4.87Distributor 6.42 27.48 96.24 9.30Factory 10.80 60.10 227.99 17.80

2 – Tm = 30, Ta = 14.5, Ts = 30Retailer 2.25 4.67 7.30 2.27Wholesaler 2.81 6.80 12.53 3.25Distributor 3.56 10.23 23.22 4.64Factory 4.56 15.77 41.69 6.62

bullwhip effect throughout the supply chain but also reduces theinventory variance ratio and thus the total stage variance isimproved as shown in Table 6. In general, selecting the proper fore-casting methods and their parameters would definitely lead to abetter performance in the supply chain.

5. Discussion and implications

Although forecasting is an essential component in the inventorymanagement of supply chains, it has been recognized as a majorcause of ordering and inventory instability in supply chains. There-fore, several researchers have been attempting to investigate theimpact of the different available forecasting methods on supplychain performance, with focusing mainly on the bullwhip effectproblem. The main target of these studies is to give useful manage-rial insights on how to select the proper forecasting systems aswell as their parameters under various operational conditions. Fol-lowing this research stream, we have attempted to present andevaluate a forecasting system that relies on a control chartapproach designed mainly to overcome the problem of traditionalforecasting methods in terms of their high sensitivity to demandchanges that is the main driver for the bullwhip effect and othersources of instability in supply chains. The main target is to evalu-ate a forecasting system known as SPC-FS that can avoid the fre-quent reaction to demand changes without affecting theinventory performance.

The forecasting system (SPC-FS) uses the control chart in orderto monitor the incoming orders/demand, to control the sensitivityof the forecasting to demand changes, and to estimate the expecteddemand. It has been evaluated in a four-echelon supply chainemploys the standard order-up-to inventory policy since it is

SPC-FS

Ld = 3 Ld = 5 Ld = 1 Ld = 3 Ld = 5

2.70 3.61 1.16 1.26 1.377.34 13.04 1.33 1.60 1.88

19.44 41.50 1.56 2.03 2.6745.86 106.91 1.83 2.61 3.85

1.78 2.15 1.15 1.25 1.343.16 4.58 1.33 1.56 1.855.58 9.76 1.54 1.98 2.599.86 20.25 1.80 2.54 3.71

s.

SPC-FS

Ld = 3 Ld = 5 Ld = 1 Ld = 3 Ld = 5

5.47 9.18 2.14 4.34 6.6314.12 30.52 2.46 5.44 9.0736.64 93.00 2.84 6.88 12.6892.44 288.44 3.29 8.81 18.19

4.66 7.25 2.14 4.34 6.638.06 14.87 2.45 5.41 9.03

13.96 30.94 2.82 6.81 12.6124.35 62.77 3.27 8.71 18.00

Table 6The total stage variance sensitivity to lead-time under the different forecasting systems.

TSVi Forecasting system

MA ES SPC-FS

Ld = 1 Ld = 3 Ld = 5 Ld = 1 Ld = 3 Ld = 5 Ld = 1 Ld = 3 Ld = 5

1 – Tm = 15, Ta = 7, Ts = 15Retailer 4.04 7.30 12.98 4.50 8.17 12.79 3.30 5.60 8.00Wholesaler 6.30 15.53 40.11 8.61 21.46 43.56 3.79 7.04 10.95Distributor 10.26 36.53 115.95 16.52 56.08 134.50 4.39 8.92 15.34Factory 17.29 81.18 281.48 31.66 138.30 395.34 5.12 11.43 22.05

2 – Tm = 30, Ta = 14.5, Ts = 30Retailer 3.49 6.08 8.89 3.72 6.44 9.40 3.29 5.58 7.98Wholesaler 4.37 8.85 15.22 5.35 11.22 19.46 3.77 6.97 10.88Distributor 5.53 13.29 27.96 7.65 19.55 40.71 4.36 8.79 15.21Factory 7.09 20.48 50.39 10.94 34.21 83.02 5.07 11.25 21.72

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1785

commonly used in research and practice. In order to validate theeffectiveness of SPC-FS, an extensive comparison has beenconducted with moving average and exponential smoothing thatare commonly used in practice and bullwhip effect research.A simulation approach has been adopted to evaluate SPC-FS andto conduct the various comparisons.

The results have shown that SPC-FS is superior to MA and ES interms of the bullwhip effect and inventory stability throughout thesupply chain under various operational conditions. Furthermore,the results confirm the previous studies that MA can achieve alower bullwhip effect than ES even if both are tuned to achievethe same forecasting accuracy. We further extended this conclu-sion to the inventory stability where the results have shown thatMA can achieve a higher inventory stability (i.e., lower inventoryvariance) than ES. The above results holds for the experimentalconditions used in this research where we evaluated the differentforecasting systems under the autoregressive and i.i.d demand pro-cesses with autoregressive parameter ranges between q = �0.5 andq = 0.5 to avoid negative demand values which is a major assump-tion in this study. Therefore, the conclusions concerning SPC-FSforecasting model should be restricted for these assumptionsalthough it could be extended for a wider range based on the cur-rent results.

The impact of the forecasting parameters on the different per-formances measures have shown that decreasing the level of fore-casting sensitivity to demand changes leads to decrease thebullwhip effect whilst improving inventory stability. The tradi-tional forecasting systems have only a single dimension to controlthis sensitivity whereas SPC-FS has many dimensions to controlthe forecasting sensitivity to demand changes such as Tc, Ts andCi

d as well as the out-of-control rule. Specifically, we have focusedon the impact of both Ts and Ci

d as two important dimension forcontrolling the SPC-FS performance. We have found that increasingthe level of Ts combined with increased level of Ci

d leads to higherordering and inventory stability in the supply chain. Although thisresearch does not aim at proposing optimum parameters for theforecasting, the results show that setting Ci

d ¼ 1 combined withappropriate values for Ts and Tc (with Tc > Ts) can achieve a stableperformance across the considered demand range under differentlevels of the lead-time, compared to the other traditional forecast-ing systems (e.g., MA(Tm = Ts) or ES((Ts � 1)/2)). These parameterssettings can be recommended for the real applications of the SPC-FS forecasting systems for the considered environmentalconditions.

The strength of SPC-FS forecasting system emerges from itsflexible structure where it has multiple parameters to regulatethe reaction to demand changes without affecting its responsive-ness to serious demand changes that should be considered in theinventory planning for keeping acceptable service level. The

SPC-FS can be considered a modified version of the moving averagemethod, with increased level of flexibility to tune the forecastingsensitivity to demand changes. For example, setting Tc = Ts com-bined with any value for the other parameters of SPC-FS turns itinto a moving average method with Tm = Tc = Ts. This has alreadybeen confirmed in the simulation model validation section. There-fore, SPC-FS has also the advantages of MA and ES in terms of itsease of use, flexibility, and robustness in dealing with non-lineardemand processes but in a controlled manner. The evaluation ofSPC-FS has shown a superior performance to MA and ES under var-ious operational conditions. A possible weakness of the proposedresearch method is that we evaluated SPC-FS only under autore-gressive demand covering a specific range of q and that SPC-FShas many parameters to set compared to MA and ES.

6. Conclusions

Forecasting has been recognized as a major cause of the bull-whip effect and inventory instability in supply chains. Therefore,several studies have attempted to evaluate the impact of availableforecasting methods on the bullwhip effect under various opera-tional conditions. However, limited research has been devoted todevelop novel forecasting systems to counteract the bullwhipeffect. This paper has evaluated a novel forecasting system, namelySPC-FS, that relies on a control chart approach to estimate theexpected demand without under/over-reacting to demandchanges. It is designed to counteract the bullwhip effect whilstkeeping acceptable inventory performance. A simulation analysishas been conducted to evaluate and compare SPC-FS with movingaverage and exponential smoothing in a four-echelon supply chainemploys the order-up-to inventory policy. The customer demandwas assumed to follow AR(1) demand process. The simulationresults showed that SPC-FS is superior to the traditional forecastingmethods in terms of bullwhip effect and inventory variance underdifferent operational settings, confirming the preliminary evalua-tion of Costantino et al. (2014b, 2014e). The results have also con-firmed and extended the previous researches that the movingaverage achieves lower bullwhip effect and higher inventory sta-bility than the exponential smoothing method. The sensitivity ofboth MA and ES to the lead-time has been found to be higher thanthe sensitivity of SPC-FS to the lead-time. It has also been foundthat decreasing the forecasting sensitivity to demand changesleads to improve ordering and inventory stability especially whenthe demand is normal.

This research contributes towards the development of theknowledge in the areas of forecasting and provides ideas andinsights that should be valuable for practitioners. This researchhas presented a novel forecasting system based on control charts

1786 F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787

that can balance the ordering and inventory stability, compared toother common methods. The previous researches have been focus-ing on the impact of the forecasting methods on the bullwhip effectwithout investigating the corresponding inventory variance thataffects inventory costs. This study has considered both measuresproving that the proper selection of forecasting methods and itsparameters can help improving both ordering and inventory stabil-ity in supply chains. The results have further confirmed the signif-icant contribution of lead-time to the bullwhip effect. We haveextended these conclusions to the inventory variance showing thatimproved forecasting with controlled sensitivity to demandchanges can reduce the contribution of longer lead-times to boththe bullwhip effect and the inventory variance.

The above conclusion and implications have been obtainedbased on a simulation study. However, in order to ensure the effec-tiveness of SPC-FS, it should be tested in real applications or withreal data from industry but this is not always convenient. In gen-eral, the previous bullwhip effect researches can be categorizedinto theoretical and empirical research and both have been utilizedto get useful insight for controlling the bullwhip effect in supplychains. This study follows the first category which has already beenemployed to get useful managerial insight for controlling bullwhipeffect and specifically for investigating the impact of the availableforecasting systems on the bullwhip effect (Hussain et al., 2012;Jaipuria & Mahapatra, 2014; Wright & Yuan, 2008). The simulationmodel used for the analysis has been validated with previous lead-ing research in the literature and thus the obtained conclusions canbe useful for both academics and practitioners. This is a first test ona simulation model and as performances are promising, we plan toextend it in practice to validate the theoretical results.

This research can be extended in many directions. The forecast-ing system has been compared only with simple two forecastingmechanisms under autoregressive demand. Therefore, futureresearch should consider other advanced forecasting methods thatare suitable with this type of demand pattern. Further evaluationof the SPC-FS should consider other demand patterns. Most impor-tantly, the decision rules used in this model based on Costantinoet al. (2014a, 2014b, 2014e) allows the construction of a singleforecast smoothing zone but it can be revised to allow gradual sen-sitivity to demand changes with multiple smoothing zones. Finally,the application of other types of control charts such as ARMA andEWMA control charts can be used to replace the individual controlchart especially when demand is not stationary as Cheng and Chou(2008) proposed.

References

Babai, M. Z., Ali, M. M., Boylan, J. E., & Syntetos, A. A. (2013). Forecasting andinventory performance in a two-stage supply chain with ARIMA (0,1,1)demand: Theory and empirical analysis. International Journal of ProductionEconomics, 143(2), 463–471.

Bandyopadhyay, S., & Bhattacharya, R. (2013). A generalized measure of bullwhipeffect in supply chain with ARMA demand process under various replenishmentpolicies. International Journal of Advance Manufacturing Technology, 68, 963–979.

Bayraktar, E., Lenny Koh, S. C., Gunasekaran, A., Sari, K., & Tatoglu, E. (2008). The roleof forecasting on bullwhip effect for E-SCM applications. International Journal ofProduction Economics, 113(1), 193–204.

Campuzano-Bolarín, F., Mula, J., & Peidro, D. (2013). An extension to fuzzyestimations and system dynamics for improving supply chains. InternationalJournal of Production Research, 51(10), 3156–3166.

Chandra, C., & Grabis, J. (2005). Application of multi-steps forecasting for restrainingthe bullwhip effect and improving inventory performance under autoregressivedemand. European Journal of Operational Research, 166(2), 337–350.

Chatfield, D. C. (2013). Underestimating the bullwhip effect: A simulation study ofthe decomposability assumption. International Journal of Production Research,51(1), 230–244.

Chatfield, D. C., Kim, J. G., Harrison, T. P., & Hayya, J. C. (2004). The bullwhip effect—impact of stochastic lead time, information quality, and information sharing: Asimulation study. Production and Operations Management, 13(4), 340–353.

Chen, F., Drezner, Z., Ryan, J. K., & Simchi-Levi, D. (2000). Quantifying the bullwhipeffect in a simple supply chain: The impact of forecasting, lead times, andinformation. Management Science, 46(3), 436–443.

Chen, F., Ryan, J. K., & Simchi-Levi, D. (2000). The impact of exponential smoothingforecasts on the bullwhip effect. Naval Research Logistics, 47(4), 269–286.

Cheng, J. C., & Chou, C. Y. (2008). A real-time inventory decision system usingwestern electric run rules and ARMA control chart. Expert Systems withApplications, 35(3), 755–761.

Cho, D. W., & Lee, Y. H. (2013). The value of information sharing in a supply chainwith a seasonal demand process. Computers and Industrial Engineering, 65(1),97–108.

Ciancimino, E., Cannella, S., Bruccoleri, M., & Framinan, J. M. (2012). On the bullwhipavoidance phase: The synchronised supply chain. European Journal ofOperational Research, 221(1), 49–63.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2013a). Exploring the bullwhipeffect and inventory stability in a seasonal supply chain. International Journal ofEngineering Business Management, 5, 1–12.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2013b). Information sharingpolicies based on tokens to improve supply chain performances. InternationalJournal of Logistics Systems and Management, 14(2), 133–160.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2014a). SPC-based inventorycontrol policy to improve supply chain dynamics. International Journal ofEngineering & Technology, 6(1), 418–426.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2014b). Inventory controlsystem based on control charts to improve supply chain performances.International Journal of Simulation Modelling, 13(3), 263–275.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2014c). Replenishment policybased on information sharing to mitigate the severity of supply chain disruption.International Journal of Logistics Systems and Management, 18(1), 3–23.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2014d). The impact ofinformation sharing and inventory control coordination on supply chainperformances. Computers and Industrial Engineering, 76, 292–306.

Costantino, F., Di Gravio, G., Shaban, A., & Tronci, M. (2014e). A real-time SPCinventory replenishment system to improve supply chain performances. ExpertSystems with Applications, 42(3), 1665–1683.

Dejonckheere, J., Disney, S. M., Lambrecht, M. R., & Towill, D. R. (2003). Measuringand avoiding the bullwhip effect: A control theoretic approach. European Journalof Operational Research, 147(3), 567–590.

Dejonckheere, J., Disney, S. M., Lambrecht, M. R., & Towill, D. R. (2004). The impactof information enrichment on the bullwhip effect in supply chains: A controlengineering perspective. European Journal of Operational Research, 153(3),727–750.

Disney, S. M., Farasyn, I., Lambrecht, M. R., & Towill, D. R. (2007). Controllingbullwhip and inventory variability with the golden smoothing rule. EuropeanJournal of Industrial Engineering, 1(3), 241–265.

Disney, S. M., Farasyn, I., Lambrecht, M., Towill, D. R., & de Velde, W. V. (2006).Taming the bullwhip effect whilst watching customer service in a single supplychain echelon. European Journal of Operational Research, 173(1), 151–172.

Disney, S. M., & Grubbström, R. W. (2004). Economic consequences of a productionand inventory control policy. International Journal of Production Research, 42(17),3419–3431.

Disney, S. M., & Lambrecht, M. R. (2008). On replenishment rules, forecasting, andthe bullwhip effect in supply chains. Foundation and Trends in Technology,Information and Operations Management, 2(1), 1–80.

Disney, S. M., & Towill, D. R. (2003). On the bullwhip and inventory varianceproduced by an ordering policy. Omega-The International Journal of ManagementScience, 31(3), 157–167.

Hussain, M., Shome, A., & Lee, D. M. (2012). Impact of forecasting methods onvariance ratio in order-up-to level policy. The International Journal of AdvancedManufacturing Technology, 59(1–4), 413–420.

Jaipuria, S., & Mahapatra, S. S. (2014). An improved demand forecasting method toreduce bullwhip effect in supply chains. Expert Systems with Applications, 41(5),2395–2408.

Kelepouris, T., Miliotis, P., & Pramatari, K. (2008). The impact of replenishmentparameters and information sharing on the Bullwhip effect: A computationalstudy. Computers and Operations Research, 35(11), 3657–3670.

Klug, F. (2013). The internal bullwhip effect in car manufacturing. InternationalJournal of Production Research, 51(1), 303–322.

Kurano, T., McKay, K., & Black, G. (2014). Proactive inventory policy intervention tomitigate risk within cooperative supply chains. International Journal of IndustrialEngineering Computations, 5(2), 249–264.

Lee, H. L., Padmanabhan, V., & Whang, S. (1997a). The bullwhip effect in supplychains. Sloan Management Review, 38(3), 93–102.

Lee, H. L., Padmanabhan, V., & Whang, S. (1997b). Information distortion in a supplychain: The bullwhip effect. Management Science, 43(4), 546–558.

Lee, H. L., So, K. C., & Tang, C. S. (2000). The value of information sharing in a two-level supply chain. Management Science, 46(5), 626–643.

Lee, H. T., & Wu, J. C. (2006). A study on inventory replenishment policies in a two-echelon supply chain system. Computers and Industrial Engineering, 51(2),257–263.

Li, Q., Disney, S. M., & Gaalman, G. (2014). Avoiding the bullwhip effect usingdamped trend forecasting and the order-up-to replenishment policy.International Journal of Production Economics, 149, 3–16.

Ma, Y., Wang, N., Che, A., Huang, Y., & Xu, J. (2013). The bullwhip effect on productorders and inventory: A perspective of demand forecasting techniques.International Journal of Production Research, 51(1), 281–302.

Makridakis, S., Andersen, A., Carbone, R., Fildes, R., Hibon, M., Lewandowski, R., et al.(1982). The accuracy of extrapolation (time series) methods: Results of aforecasting competition. Journal of Forecasting, 1(2), 111–153.

F. Costantino et al. / Expert Systems with Applications 42 (2015) 1773–1787 1787

Makridakis, S., Wheelwright, S. C., & McGee, V. E. (1978). Forecasting: Methods andapplications. John Wiley & Sons.

Montgomery, D. C. (2008). Introduction to statistical quality control. New York:Wiley.

Pfohl, H. C., Cullmann, O., & Stölzle, W. (1999). Inventory management withstatistical process control: Simulation and evaluation. Journal of BusinessLogistics, 20(1), 101–120.

Silver, E., Peterson, R., & Pyke, D. F. (2000). Decision systems for inventorymanagement and production. New York: Willey.

Wright, D., & Yuan, X. (2008). Mitigating the bullwhip effect by ordering policiesand forecasting methods. International Journal of Production Economics, 113(2),587–597.

Zhang, X. L. (2004). The impact of forecasting methods on the bullwhip effect.International Journal of Production Economics, 88(1), 15–27.

Zotteri, G. (2012). An empirical investigation on causes and effects of the bullwhipeffect: Evidence from the personal care sector. International Journal of ProductionEconomics, 143(2), 489–498.