A Hybrid Model for Forecasting Sales in Turkish Paint Industry

Transcription

1 Internatonal Journal of Computatonal Intellgence Systems, Vol.2, No. 3 (October, 2009), A Hybrd Model for Forecastng Sales n Turksh Pant Industry Alp Ustundag * Department of Industral Engneerng, Istanbul Techncal Unversty, Macka, Istanbul, 34367, Turkey Abstract Sales forecastng s mportant for facltatng effectve and effcent allocaton of scarce resources. However, how to best model and forecast sales has been a long-standng ssue. There s no best forecastng method that s applcable n all crcumstances. Therefore, confdence n the accuracy of sales forecasts s acheved by corroboratng the results usng two or more methods. Ths paper proposes a hybrd forecastng model that uses an artfcal ntellgence method (AI) wth multple lnear regresson (MLR) to predct product sales for the largest Turksh pant producer. In the hybrd model, three dfferent AI methods, fuzzy rule-based system (FRBS), artfcal neural network (ANN) and adaptve neuro fuzzy network (ANFIS), are used and compared to each other. The results ndcate that FRBS yelds better forecastng accuracy n terms of root mean squared error (RMSE) and mean absolute percentage error (MAPE). Keywords: Sales forecast, Hybrd model, Fuzzy rule based system, Multple lnear regresson and Pant ndustry. 1. Introducton The Turksh pant ndustry s the sxth-largest n Europe, wth a capacty of metrc tons annually. Pant s manufactured n the fve Turksh ctes wth the hghest populaton. The surge of new mmgrants nto these ctes has ncreased demand for new housng and wll be key to sustanng future growth n the pant market wth demand estmated at about metrc tons annually. Snce the ndustry s dependent upon mported raw materals, companes should ensure that they are properly postoned to meet future Turksh demand. Therefore, t s mportant for pant companes to have an effcent and accurate forecastng model to predct future monthly sales. A major requrement of successful marketng s accurately forecastng sales. Frst, market opportuntes are dentfed through marketng research. The sze, growth and proftablty of each market opportunty are then measured and/or forecasted. Sales forecasts are used by fnance dvsons to rase cash needed for nvestments and operatons, manufacturng dvsons to establsh capacty and output levels, purchasng dvsons to acqure the necessary supples, human resources dvsons to hre the necessary number of workers. Thus, an accurate sales forecast facltates effectve plannng. Over-estmates of demand can lead to several problems, such as occupancy of valuable shelf space and ncreased nventory carryng charges. On the other hand, under-estmates of demand can lead to stock depleton, lost sales, and expensve overtme producton to compensate for costumer demand. Gven the potentally negatve mpact of naccurate forecasts, marketers use a varety of technques to accurately forecast sales. Ths research focuses on monthly sales forecastng for the largest pant manufacturer n Turkey. A hybrd model that ntegrates AI and MLR methods s proposed * Istanbul Techncal Unversty, Department of Industral Engneerng, Macka Istanbul, Turkey, ustundaga@tu.edu.tr 277

2 A. Ustundag for predctng ths company s sales. The model s then appled to hstorcal sales data for ths specfc Turksh pant producer. Fuzzy rule based system (FRBS), artfcal neural network (ANN) and adaptve neuro fuzzy network (ANFIS) methods are used n the proposed hybrd model and ther relatve performances are compared to each other. The purpose of the study s to mprove forecastng accuracy and thus to help managers mprove ther decson makng. The remander of the paper s organzed as follows. Secton 2 summarzes the exstng lterature n related areas. Secton 3 descrbes the methodology used n ths study. In Secton 4, the proposed hybrd forecastng model and the FRBS, ANN and ANFIS methods are presented. The hybrd models usng dfferent AI methods are appled to sales data for the largest Turksh pant company, and the results are compared. In the fnal secton, conclusons are presented, and further research s proposed. 2. Background Multple lnear regresson (MLR) s commonly used for forecastng data wth several relevant ndependent varables. The technque has been used to make forecasts n a wde range of areas, ncludng toursm volume 1, ndustral electrcty consumpton 2, and retal sales. 3 MLR has often been utlzed to forecast demand based on known marketng varables and macroeconomc measures. 4 Although tradtonal sales forecastng methods have proven effectve, they stll have certan drawbacks. 5 As stated by Kuo and Cohen 6, newly developed artfcal ntellgence (AI) models have more flexblty and can be used to estmate non-lnear relatonshps, wthout the lmts of tradtonal models. As a result, an ncreased number of researchers are usng AI forecastng models to deal wth problems. Hruschka 7 studed the use of artfcal neural networks to predct market response usng consumer brand data and market response functons. Agrawal and Schorlng 8 compared the forecastng accuracy of artfcal neural networks wth multnomal logt models n the context of frequently purchased grocery products for a retaler. West et al. 9 demonstrated the approprateness of artfcal neural network modelng for predctng consumer choce based on product attrbutes and suggested ts potental for use n numerous other marketng applcatons. Alon et al. 10 addressed forecastng of U.S. aggregate retal sales, a tme-seres wth trend and seasonal patterns. In ths study, ANN s compared to the more tradtonal tmeseres forecastng methods, ncludng Wnters' exponental smoothng, autoregressve ntegrated movng average (ARIMA) modelng, and multple lnear regresson. The results ndcate that on average ANN s favorable, compared to the more tradtonal statstcal methods, followed by the Box-Jenkns model. Snce Zadeh 11 ntroduced the concept of fuzzy logc, fuzzy theory has been wdely appled n forecastng Fuzzy systems can handle the mprecson that s nherent n human reasonng, especally when dealng wth complex problems. Based on the concepts of fuzzy sets and fuzzy logc, fuzzy systems encode lngustc samples n a desgnated numercal matrx, whch lnks nput to output through fuzzy membershp functons and sets of fuzzy rules. Therefore, fuzzy rules are compact, effcent representatons of human knowledge. Thus, fuzzy rules provde a human-lke thnkng ablty whch allows expert knowledge to be ncorporated nto systems. 15 Tradtonally, these fuzzy rule bases (FRBs) are provded and extracted from doman experts. In recent years, many researchers have proposed methods for generatng FRBs from a set of sample data Adaptve neuro-fuzzy nference systems (ANFIS), whch ntegrate fuzzy logc and neural networks, s one of the most recently developed technques for forecastng. ANFIS has features of neural networks, such as learnng abltes, optmzaton abltes, and features of fuzzy nference systems, such as human-lke reasonng usng IF-THEN rules and ease of ncorporatng human expert knowledge. IF-THEN rules can be created (learned) and refned from preexstng data sets. Several attempts have been made to develop ANFIS-based systems to predct product demand. For example, Escoda et al. 18 examned the development and representaton of lngustc varables to qualfy the product demand usng ANN and ANFIS. By ntegratng ANN and ANFIS, Kuo and Xue 19, Kuo et al. 20 developed ntellgent sales forecastng systems that consder both quanttatve and qualtatve varables. Kuo 21 proposed an ANFIS-based decson support system for the stock market. Thomassey et al. 22 proposed a sales forecastng system for a French textle dstrbutor based on both fuzzy logc and ANN. Ths model s composed of several sub-models and forecasts for varous tme horzons and sales aggregaton levels. Efendgl et al. 23 proposed a new forecastng algorthm 278

3 Hybrd Model for Forecastng Sales that uses artfcal ntellgence technques and compares ANN and ANFIS to manage the fuzzy demand wth ncomplete data. Ths algorthm was appled to data from a company that s actve n a Turksh durable consumer goods ndustry. Balan et al. 24 tuned a fuzzy logc controller usng an adaptve neuro-fuzzy nference system (ANFIS) to forecast demand wth less dstorton, thus mprovng supply chan effectveness. Wang and Chen 25 (2008) proposed an ANFIS model to predct rush orders and regulate the capacty reservaton mechansm n advance. Yng and Pan 26 appled ANFIS to forecast the regonal electrcty demand n Tawan and demonstrated ths method s effectveness n forecastng performance. In ths study, a hybrd forecastng model s proposed, whch uses an AI method wth multple lnear regresson (MLR). In the proposed model, annual product sales are estmated for a Turksh pant company usng MLR n the frst phase. And n the second phase, an AI method s used to estmate the monthly product sales as a percentage of the estmated annual sales. The overall motvaton s to develop an ntellgent forecastng method usng artfcal ntellgence (AI) methods wth MLR and to help pant companes accurately forecast monthly sales. The hybrd models usng fuzzy rule base (FRBS), artfcal neural network (ANN) and adaptve neuro fuzzy network (ANFIS) methods are compared to each other. 3. Methodology Ths study s conducted usng data from the largest Turksh pant company, wth a 25% market share of the Turksh pant ndustry. Before determnng the best forecastng model, the man product groups were classfed. The ndependent varables nfluencng product sales were then determned. The forecastng results of the proposed hybrd models usng FRBS, ANN, and ANFIS methods were compared n terms of root mean squared error (RMSE) and mean absolute percentage error (MAPE). Actual value and forecast value are denoted as A and F respectvely n Eqs. (1) and (2). 2 A t Ft RMSE n 1 (1) MAPE A F t t 100 At n The gven company has three man product groups: nteror pants, exteror pants and solvent-based pants. After several ntervews and meetngs wth experts n the pant ndustry, fve ndependent varables were selected for use n the forecastng models accordng to ther correlaton wth sales data: probablty of spendng for housng repars and renovatons n the next 6 months, monthly constructon expenses, consumer trust ndex, prce dscount rate and campagn type. The frst two varables are used n the MLR method to estmate the annual cumulatve sales rate of change n the frst phase of the hybrd model. And n the second phase, the last three varables are used n the AI methods to estmate the monthly sales. The model tranng and forecasts were performed usng actual monthly data of a fve-year perod (January December 2008) (Fg 1). In the frst phase, the cumulatve yearly sales data from 2004 to 2007 was (2) Fg. 1. Actual monthly product sales. 279

4 A. Ustundag used to estmate the cumulatve sales rate of change n In the second phase, the frst 48-month data set was used to tran the models of ANN and ANFIS. In FRBS method, the experts create the rule base analyzng the frst 48 month data and usng ther experence. The performances of the three models were tested and compared through the last 12 months of data. Monthly data for the frst two ndependent varables were obtaned from the Turksh Statstcal Insttute, and data for the other ndependent varables were obtaned from sales and marketng experts n the company. 4. Applcaton In ths secton, the proposed hybrd forecastng model and the FRBS, ANN, and ANFIS methods that are used n ths hybrd model are presented. The models are then appled to the actual sales data. Fnally, RMSE and MAPE values are calculated for the last 12 months of data, and the models are compared The proposed hybrd forecastng model The proposed hybrd forecastng model has a top-down approach consstng of two phases. In the frst phase, the annual cumulatve sales rate of change s forecasted for each product group usng MLR. In the second phase, the monthly sales of each product group are estmated as a percentage of the annual cumulatve sales forecast on the bass of the prce dscount rate, the consumer trust ndex and campagn type usng an AI method (Fg. 2). Multple lnear regresson (MLR) attempts to model the relatonshp between two or more explanatory varables and a response varable by fttng a lnear relatonshp to observed data. MLR s a statstcal method that models the relatonshp between a dependent varable Y, ndependent varables X, ( = 1,..., p) and a random term. In the proposed model, the monthly product sales are estmated as a percentage of the annual cumulatve sales forecast. Before determnng the monthly percentages the expected annual sales volume of the product s forecasted usng a MLR. The probablty of spendng for housng repar/renovaton n the next 6 months and the monthly constructon expenses were used as the ndependent varables n the MLR. Thus, the MLR model can be wrtten as n Eq. 3: Y = X X 2 (3) In ths study, the expected annual cumulatve sales rate of change of each product group was forecasted for the year 2008 usng the company sales data between 2003 and As shown n Table 1, the expected market growth of nteror pants, exteror pants and solventbased pants s 1.15%, 15.89% and 12.88%, respectvely. Table 1. Cumulatve sales forecast for Forecast for cumulatve sales rate of change Interor pants Exteror pants Solventbased pants 1.15% 15.89% 12.88% Actual sales n Sales forecast for In the second phase of the hybrd model, three alternatve AI methods, FRBS, ANN and ANFIS, are used and compared to each other Fuzzy Rule Based System (FRBS) A fuzzy rule-based system (FRBS) s a systematc reasonng methodology that can capture the contextual judgment of experts by usng fuzzy set theory. There are two man types of fuzzy modelng schemes: Takag Sugeno models and Mamdan models. The Takag Sugeno modelng s a data drven approach n whch membershp functons and rules are developed usng a tranng data set. The parameters for the membershp functons and rules are subsequently optmzed to reduce tranng error. 27 The Mamdan modelng structure s constructed manually on the bass of expert knowledge, and the fnal model s nether traned nor optmzed. Both model types are smlar and consder fuzzy nputs; however, whle Mamdan models return fuzzy outputs, Takag Sugeno models return crsp outputs (lnear combnaton of the nputs) Snce the Mamdan approach s not exclusvely relant on a data set, wth suffcent expertse regardng the nvolved system, a generalzed model can be obtaned for effectve forecastng. 30 Utlzng a completely lngustc form of rule set, Mamdan models have advantages n representng expert knowledge and lngustcally nterpretng dependences. 280

5 Hybrd Model for Forecastng Sales Fg. 2. The proposed hybrd forecastng method The structure of the Mamdan-type fuzzy logc rule s expressed as follows: 28 IF x 1 s A 1 AND x 2 s A 2 AND... AND x n s A n, THEN y s B, where x ( = 1, 2,..., n) are nput varables and y s the output varable. A 1, A 2,..., A n and B are the lngustc terms (L-Low; M-Medum; H-Hgh) used for the fuzzy subsets (membershp functon dstrbutons) of the correspondng nput and output varables, respectvely. The output of a fuzzy rule-based model whose rule base s constructed usng Mamdantype fuzzy logc rules s obtaned as follows (the centrod method s consdered for defuzzfcaton): 1 R r A C r r1 A Y 1 R r A r1 (4) where A r s the area of the fuzzy subset of output varables, covered by a membershp value α that s obtaned by the r th rule after the fuzzy nference method; C A r s the center dstance of the area A r, and n Mn v 1 (5) where 1 v n s the number of nput varables that appear n the rule premse, and n s the total number of nputs. R l (R l R) s the number of rules fred out of a total of R rules present n the rule base for a set of nput values. v (x v ) s the value of the membershp functon for the x v nput varable. In ths study, the pant company arranges a marketng campagn for ts dealers two tmes a year. The campagns last three months and begn n March and August. The company apples two types of campagns: (a) descendng dscount rate, (b) constant dscount rate. In the frst type, the company decreases the prce dscount rate for the next month of the campagn. Thus, 281

6 A. Ustundag the dealer tends to place the order wth the pant company n the begnnng of the campagn. In the second type of campagn, the prce dscount rates do not change durng the campagn, and the dealers have the same advantage for all months of the campagn. In order to estmate the monthly percentages of sales, marketng and sales experts of the company created a rule base usng the prce dscount rate and the consumer trust ndex (Table 2-3). Accordng to ther opnon, the consumer trust ndex s an ndcator for economc uncertanty, and the prce dscount rate s an ndcator for the campagn value. For Months: 1;2;6;7;11;12 Campagn Type: No campagn Consumer Trust IF Index Hgh Medum Low THEN Table 3. Fuzzy rule base for no campagn status Sales (%) Hgh Hgh Medum Table 2. Fuzzy rule base for descendng rate and constant rate campagns For Months: 3;4;5;8;9;10 Campagn Type: Descendng / Constant Dscount Rate IF Prce Dscount Rate AND Consumer Trust Index THEN Sales (%) Hgh Hgh Hgh Hgh Medum Hgh Hgh Low Medum Medum Hgh Hgh Medum Medum Medum Medum Low Low Low Hgh Medum Low Medum Low Low Low Low As shown n Tables 2 and 3, twelve rules were determned for the hybrd forecastng model n ths study. As there s no campagn n months 1, 2, 6, 7, 11 and 12, the consumer trust ndex s the determnng varable for forecastng the sales percentages (s ) n these months. In the rule base, trangular and trapezodal fuzzy numbers are used to develop the membershp functons of the prce dscount rate, the consumer trust ndex and the monthly sales percentages. The same prce-dscount-rate and consumer-trustndex membershp functons are used for each month. Alternatvely, dfferent sales percentage membershp functons are determned for each month dependng on the product and campagn type. The max-mn method s used for the aggregaton mechansm, and the centrod method s used for defuzzfcaton of the fuzzy outputs. Snce the sum of the monthly sales percentages must be 100% for a year, the defuzzfed forecasted values (s ) are adjusted usng Eq. (6) to remove small devatons. ' s s 12 s (6) The membershp functons for the prce dscount rate and the consumer trust ndex are shown n Fgs. 3 and 4, respectvely. The membershp functons for the sales percentage change for each month dependng on the product and campagn type. The membershp functon for the nteror pant product s shown n Fg. 5 for the month of March and a decreasng dscount rate campagn type. 282

7 Hybrd Model for Forecastng Sales By mplementng the nput data for 2008 nto the model, the FRBS sales percentage outputs were determned, shown n Table Artfcal Neural Networks Fg. 3 Membershp functon for prce dscount rate. Fg. 4. Membershp functon for consumer trust ndex. Fg. 5 Membershp functon for sales percentage n March for a decreasng dscount rate campagn type and the nteror pant product. There are many types and structures of neural networks. The type of ANN used n ths study s a standard feedforward multlayer network. A feed-forward multlayer network conssts of dfferent layers of unts that are nterconnected by a set of weghted connectons. Sgnals can be propagated n two drectons: functon sgnals are propagated forwards, and error sgnals are propagated backwards. The back-propagaton algorthm s used to adjust the weghts of the connectons and s the ANN algorthm that s most frequently compared to models derved from multvarable regresson analyses. 31 The output pattern produced by the network usng the nput s compared wth the deal target pattern, and the error s propagated back through the network. The tranng process s repeated wth many examples untl the error s below some tolerance. In ths study, the ANN model was desgned usng the Matlab Neural Network Tool. The proposed feedforward, multlayer ANN model has three layers: nput, hdden and output. The two model nputs are the consumer trust ndex and the prce dscount for decreasng/constant rate campagn type. And, the prce dscount s the sngle model nput for no campagn status. For the hdden layers, varous layer structures wth varous numbers of neurons were tested n the ANN model. The best product group forecasts for decreasng/constant rate campagn type were obtaned Month Prce Dscount Rate Table 4. Adjusted FRBS outputs for 2008 Consumer Trust Index Campagn Type Interor pants Exteror pants Solvent-based pants Jan % 2.00% 0.95% Feb % 5.00% 5.14% Mar-08 15% 132 Decreasng 20.00% 12.00% 8.80% Apr-08 12% 130 Decreasng 18.30% 15.00% 10.27% May-08 10% 130 Decreasng 4.00% 7.50% 4.40% Jun % 11.50% 10.79% Jul % 10.00% 19.49% Aug-08 12% 125 Constant 8.00% 10.50% 7.33% Sep-08 12% 120 Constant 8.00% 10.00% 4.40% Oct-08 12% 105 Constant 7.00% 7.50% 6.60% Nov % 5.50% 7.30% Dec % 3.50% 14.53% Total 100% 100% 100% 283

8 A. Ustundag usng four hdden layers consstng of 2, 5, 3 and 2 neurons, respectvely. And for no campagn status, four hdden layers were used consstng of 1, 5,3 and 2. A log-sgmod transfer functon was appled for the actvaton functon that calculates the output neurons Adaptve Fuzzy Neural Networks ANFIS are a class of adaptve networks that are functonally equvalent to fuzzy nference systems. 32 It s assumed that the fuzzy nference system has two nputs x and y and one output z. A frst-order Takag and Sugeno fuzzy model has the followng rules: 29 RULE 1: If x s A 1 and y s B 1, then f 1 = p 1 x + q 1 y + r 1 RULE 2: If x s A 2 and y s B 2, then f 2 = p 2 x + q 2 y + r 2 In ANFIS archtecture, the node functons n the same layer belong to the functon famles descrbed below: Layer 1: Every node n ths layer s an adaptve node wth a node functon 1 Q ( x) (7) A where the I s the nput node and A s the lngustc label assocated wth ths node functon. Gaussan functons are commonly used membershp functons n ANFIS, such as the followng: 2 x c A ( x) exp (8) 2 2 where c and are the centers and wdths of the functons, respectvely, and are referred to as the antecedent parameters for the membershp functon. Layer 2: Every node n ths layer s a crcle node labeled, whch multples the ncomng sgnal and outputs the product. Layer 3: Layer 3 s the normalzaton layer where the rule strength s normalzed as follows: w w (9) w where w s the frng strength of the th rule. The number of nodes n ths layer s the same as n the last layer. Ths layer computes each rule s frng strength to the sum of all the rules frng strengths. Layer 4: Every node n ths adaptve layer s a lnear functon, and the coeffcents of the functon are adapted through a combnaton of least squares approxmaton and back propagaton. w f w c c x c x... c x ) (10) ( n n Layer 5: It s the output layer. The result of ths layer s obtaned as a summaton of the outputs of the nodes n the prevous layer as follows: w f w f (11) w where w f s the output of node from the prevous layer. In ths study, the Matlab ANFIS tool was used to tran the zero-order Sugeno model (p=q=0) wth the two nput varables for decreasng/constant rate campagn and sngle nput for no campagn status as n the ANN model. The Gaussan membershp functons are traned by the hybrd optmzaton method consstng of backpropagaton for the parameters assocated wth the nput membershp functons, and least squares estmaton for the parameters assocated wth the output membershp functons. In ths model, 9 rules were created for decreasng/constant rate campagn and 3 rules for no campagn status Comparson of the results In our study, two phases of the proposed hybrd forecastng model are conducted. In the frst phase, the annual cumulatve sales rate of change s forecasted for each product group usng MLR. As the varables of the probablty of spendng for housng repar/renovaton n the next 6 months and the monthly constructon expenses nfluence the total market growth of the pant ndustry accordng to the sales and marketng experts of the company, they are used as the ndependent varables n the MLR to estmate the annual cumulatve sales. And then n the second phase, the monthly sales of each product group are estmated as a percentage of the estmated annual cumulatve sales forecast on the bass of the prce dscount rate, the consumer trust ndex and campagn type usng an AI method. Three dfferent AI methods, FRBS, ANN and ANFIS, are used n the hybrd model and compared to each other n terms of RMSE and MAPE. As shown n Table 5, usng fuzzy rule base methods, FRBS and ANFIS, n the hybrd model, gve better sales forecasts for each product group 284

9 Hybrd Model for Forecastng Sales Fg. 7. Forecast generated by the proposed hybrd FRBS model for the year Therefore, t can be stated that the rule base s more sutable to forecast the sales of the Turksh pant producer. Table 5 suggests that the FRBS s superor to the ANFIS and ANN wth respect to MAPE and RMSE. Hence, t ndcates that the rule base created by the sales and marketng experts of the company has a better outcome than the rule base created by ANFIS. The actual and forecasted data generated from the proposed hybrd model used wth FRBS are shown n Fg. 7. Table 5. Comparson of the dfferent methods used n the hybrd model Product Interor Pants Exteror Pants Solvent- Based Pants Forecast Error Hybrd Model FRBS ANN ANFIS RMSE MAPE RMSE MAPE RMSE MAPE Concluson To enhance commercal compettve advantage n a constantly fluctuatng sales envronment, an organzaton's management must make the approprate decsons based on the avalable nformaton. An effcent forecastng system can mprove machne utlzaton, reduce nventores, acheve greater flexblty to changes and ultmately ncrease profts. In partcular, sales forecastng s very mportant, as ts outcome s used by many functons n the organzaton. 4 In ths paper, a hybrd forecastng model s presented to help pant companes forecast monthly sales. The purpose of the study was to develop an ntellgent forecastng method that ntegrates tradtonal and well-known artfcal ntellgence (AI) forecastng methods. Usng a combnaton of MLR and AI technques, the proposed hybrd forecastng method s easy applcable. It has a top-down approach consstng of two phases. In the frst phase, MLR method s used to forecast annual cumulatve sales. And n the second phase, three dfferent AI methods are used to estmate the monthly sales percentages and compared to each other. In ths study, FRBS, ANN and ANFIS are used n the hybrd model and compared to each other. Accordng to the results, n the hybrd model, the use of fuzzy rule base created by the experts provdes hgh precson and strong forecastng ablty of monthly 285

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