The Design of a Forecasting Support Models on Demand of Durian for Export Markets by Time Series and ANNs

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1 AIJSTPME (20) 4(2): The Design of a Forecasing Suppor Models on Demand of Durian for Expor Mares by Time Series and ANNs Udomsri N. Deparmen of Indusrial Engineering, Faculy of Engineering, King Mongu s Universiy of Technology Norh Bango, Bango, Thailand Kengpol A. Deparmen of Indusrial Engineering, Faculy of Engineering, King Mongu s Universiy of Technology Norh Bango, Bango, Thailand Ishii K. Deparmen of Indusrial and Social Managemen Sysems, Kanazawa Insiue of Technology, Ishiawa, Japan Shimada Y. Deparmen of Indusrial and Social Managemen Sysems, Kanazawa Insiue of Technology, Ishiawa, Japan Absrac Nowadays, Durian is he mos imporan expored frui of Thailand. The expor value of durian is approximaely million USD per year and growing increasingly. The problem in his durian produc has been oversupply since he produc has been brough ou ino he mare simulaneously; causing durian growers sell heir produc lower han cos price. In order o avoid he problem of durian exceeds he needs of consumers. Therefore, he objecive of his research is o design he forecasing model of he demand of durian in expor mares. This research is o find for forecasing demand of four inds of durian: fresh durian, frozen durian, durian pase and durian chips in he nex year. Firsly, applying Oupu models he four Time Series by Moving Average, Deseasonalised, Exponenial Smoohing and Double Exponenial Smoohing, secondly, applying Inpu models: Regression model and Arificial Neural Newors (ANNs) model. The forecas model which has he leas value of Mean Absolue Percenage Error (MAPE) is he mos accurae forecas model. The resuls of Oupu models reveal ha he mos accurae forecas model is Deseasonalised model which gives he leas value of MAPE in hree inds of durian: ) durian pase a he percenage of 8.66, 2) frozen durian a he percenage of 9.78 and 3) fresh durian a he percenage of 9.24 while Inpu models reveal ha he mos accurae forecas model is Arificial Neural Newors (ANNs) model gives he leas value of MAPE of durian chips a he percenage of Afer aaining he accurae forecasing model, his is applied wih he Linear Programming (LP) model o assess he value of appropriae quaniy for domesic and expor mares of four inds of durian for he maximum profi in he following year. The maximum profi quaniy of each inds of durian able o helpful o he durian growers are able o sales planning and processed durian ha are he mos profiable. Keywords: Durian, Forecasing, Moving Average, Depersonalized, Exponenial Smoohing, Double Exponenial Smoohing, Arificial Neural Newors (ANNs) model and Linear Programming (LP) model 49

2 Inroducion A presen here are more han 290,000 acres growing durian in Thailand and 266,975 acres produced good producion. Two regions are of Thailand such as ) The Easern par of Thailand namely Chanaburi, Rayong and Trad 2) The Souhern par of Thailand namely Choomporn, Sura Thani, and Naorn Sri Thammara. Beside Thailand is he world bigges exporer of durian as fresh durian, frozen durian, durian pase and durian chips, as shown in he Figure. Percenage of quaniy demand of each ype of durian in expor mares in 2008, from The Cooperaion of he Office of Agriculural Economics and he cusoms year []. In 2008 he expor volume is 222,559 ons as he amoun of million USD and 2009 he expor volume is 272,200 ons as he amoun of million USD comparaively. The volume and value of expor of 2008 o 2009 are found ha he expor volumes in he expor mares are less han he domesic mare gradually. The expor value increased very few amoun ha from The Cooperaion of he Office of Agriculural Economics and he cusoms year []. The farmers ge he lower price a he increasing of cos of producion ha from he Office of Agriculural Economics [3] as shown in he Figure 3. Figure : Percenage of quaniy demand of each ype of durian in expor mares in 2008 The main expor mares of durian are he Republic of China, Hong Kong, Indonesia and oher, from he Office of Agriculural Economics [2] as shown in Figure 2. Figure 3: The comparison of domesic and expor sale volume of durian producion quaniy The Mares srucure of he sale of domesic and expor mares as shown in Figure 4. Figure 2: Percenage of durian expor for each counry Figure 4: The mareing sysem of he sale in he domesic and expor mares 50

3 The domesic and expor mareing sysems of durian in Thailand are sar from he durian growers harves durian and sell o he buyer group. Aferwards he buyer groups will sell he fresh durian and frozen durian for he domesic mare. Accordingly, he durian pase and durian chips are made by processing fresh durian from he facory. Finally he exporers will send he fresh durian, frozen durian, durian pase and durian chips o expor mares. The exporers mus conac o he Deparmen of cusoms for axaion and daa enry for each ype of durian before freighing or airways as shown in Figure 4. There are four ypes of durian o be expor such as fresh durian, frozen durian, durian pase and durian chips as shown in Figure 5. Fresh durian Durian pase Frozen durian Durian chips Figure 5: The inds of durian for domesic and expor mares As can be seen from he comparison of producion and domesic mare sale volume is higher han value o expor mares as shown in Figure 3. The reason of durian is he seasonal frui and usually concenrae especially from June o Augus. The durian of he Easern and he Souhern par of Thailand are promply sold o he mares ha cause excess supply and oher problems as follows:. Main problems of Producion and Mareing The main problems of producion and mareing for durian from he Agriculural Informaion Cener, he Office of Agriculural Economics [4]... Durian of he Eas and he Souh are ready o sell in June and Augus ha cause excess supply. The consumpion of domesic mare is less han he producion herefore; he durian growers sell durian a he low price coninuously...2 The expor mares on demand is durian farm guaranee for Good Agriculural Pracice (GAP) bu he durian growers had few planing areas cerified by GAP of Deparmen of Agriculure...3 The domesic mare managemen is inefficien because he imporan are as in he Eas and he Souh had problems of over-supply of durian producion ha causes he decreasing price of durian, he daa is from he Agriculural Informaion Cener, he Office of Agriculural Economics [4]...4 The expor durian in o he expor mares increased bu he decreasing price according o he siuaional problems of durian demand in domesic and expor mares, here are few researches in his field, he gap and problem of he research and are no solved efficienly so he research mehodology for an appropriae design of a forecasing suppor demand of durian for domesic and expor mares is necessary. The new mehodology able o help mareing sysem efficienly for forecasing a opimal demand durian in order ha durian in domesic and expor mares will no be over demand..2 The research quesions.2. Since previous ime unil presen, is have he forecasing models of durian demand been in domesic and expor mares..2.2 Wha is an appropriae model for forecasing on durian demand o conform o domesic and expor mares..3 Aims of he sudy.3. This research is designed for forecasing suppor models on demand of durian expor mares. 5

4 .3.2 This research plans he selling appropriae fresh durian, frozen durian, durian pase and durian chips o conform o domesic and expor mares..3.3 This research is found he resul of forecasing durian demand in domesic and expor mares for he Office of Agriculural Economics and durian growers. 2 Lieraure Reviews There are several researches ha are relaed o apply he mahemaical models o consruc forecas models for many inds of wor. The deail of echniques using mahemaical models o forecas durian demands are consiss of wo ypes: he Oupu models are Time Series models and he Inpu models are he Regression model and Arificial Neural Newors (ANNs) model. The lieraure reviews are as follows: Par e al. [5] sudy he comparaive forecasing of hree mehods such as ANNs model, General Linear model and Regression rees model. The forecasing of he quaniy of corn producion from he differen growing is found ha he ANNs model is he mos accuracy forecasing model. Co and Bossarawongse [6] sudy abou he hree comparaive forecasing models such as he ANNs model, Exponenial Smoohing model and Auo Regressive Inegraed Moving Average (ARIMA) model o predic he quaniy of Thai rice expor and i is found ha he ANNs model is beer han oher model o predic he daa of he rend and he seasonal daa. In addiion o sudy of he Segura and Vecher [7] which apply he Hol-Winers rend and Seasonaliy mehod (HWS) model o predic he sale volume on he managemen able. I can be seen ha he HWS model provides he accuracy resuls of he shor-run. A par from he sudy of Alon e al. [8] predic ha he oal sale volume of he reailer by comparison he forecasing in advance for one ime uni and various ime uni beween he ANNs model and HWS model, Box-Jenins model and he Muliple Regression analysis. I can be seen ha during he recession he forecasing of he various ime uni provide he average error from he various forecasing models a lower rae han he one monhly forecasing model. The resul of he ANNs model produces he mos correcly forecasing. Linear Programming (LP) is firs used by Badri [9]. Linear Programming (LP) is a echnique ha achieves he opimal soluion. I can be hough of as an exension of Linear Programming (LP) ha normally has a conflic in he objecive funcion. In he LP, maximum or minimum objecive funcion is se for only one quaniy o manage on is opimal value. Chachiamjane and Kengpol [0] develop he mahemaic model in he form of Linear Programming for he producion planning o ge he maximize benefi and he limiaion of producion capaciy and invenory. The improvemen of producion planning increases he profi of an organizaion. Kengpol and Kaoien [] develop he Linear Programming model o calculae he appropriae level of invenory o increase he efficiency of purchasing power. The research is found ha he mahemaic model can be adjused for he planning of purchasing raw maerial and increasing he invenory policy a he level of 88.33%. Apar from revising he relaed research sudy of he forecasing demand of durian in he expor mares are forecased by Time Series for he Oupu models and Arificial Neural Newors (ANNs) for he Inpu models. The boh model o find he model of forecasing he demand for durian in each ype which is he bes ype for expor. Afer ha i will be processed by he Linear Programming models o calculae he demand for each ype of durian as he domesic and expor mares for he mareing sysem in Thailand o ge he maximize profi. 3 Research Mehodology The objecive of his sudy is o forecas he demand of each ype of durian in he expor mares. The mehodology of forecasing composes of wo models namely ) The Oupu models o forecas he expor volume and 2) The forecasing model o find he impac o expor volume by Inpu models. The forecasing models of demand durian finding he bes model relaed o MAPE accuracy. Afer using he Linear Programming models o calculae he opimal demand of each ype of durian as he domesic and expor demand for maximum profi by he sep of research ha resuls as shown in Figure 6. 52

5 Demand daa in he pas Ploed daa Idenificaion inpu variables Time Series models Moving Average Deseasonalised Exponenial Smoohing Double Exponenial Smoohing (Oupu models) Correlaion of inpu variables Affeced variables Bac-propagaion Neural Newors model and Regression model (Inpu models) Figure 7: A plo of durian consumer demand from he year in (ons) Demand forecasing Accuracy es The bes forecasing model The appropriae quaniy of durian for he maximize profi by Linear Programming Demand consrain of Forecasing demand for he oal quaniy for Fresh durian, Frozen durian, Durian pase and Durian chips for expor mares Figure 8: Forms of forecasing movemen from Bernard [2] Opimal demand for maximum profi of four durian ypes Figure 6: Seps of he research model 3. The seps of research model 3.. This forecasing research is carried ou by sudying he demand of four durian ypes: fresh durian, frozen durian, durian pase and durian chips beween 2002 and 2008, from he Office of Agriculural Economics, Minisry of Agriculure and Cooperaives in Thailand [] for forecas durian expor demand in The demand of he four ypes is similar, only he of fresh durian quaniy ha is used for forecasing are ploed graph as shown in Figure 7. Based on he daa gained in Figure 7 which illusraes durian consumer demand, when compared wih he forms of forecasing movemen from Bernard [2] ha are consis of four ypes, namely Trend, Cycle, Seasonal paern and Trend wih seasonal paern as shown in Figure 8 he forms of movemen in durian consumer demand are liely o be a Seasonal wih rend paern and Trend wih seasonal paern. Consequenly, he forecasing model suiable for he daa obained is Time Series. The forecas demand of durian in his sudy, he researchers employ wo models of forecasing: Oupu models and Inpu models. Oupu models mean he model ha used cusomer durian demand for forecasing demand in nex year ha is he Time Series models consiss of Moving Average, Deseasonalised, Exponenial Smoohing and Double Exponenial Smoohing. Inpu models are he model ha used durian demand affec variables for forecasing demand in nex year. The Inpu models are Regression and Arificial Neural Newors (ANNs) model. The 53

6 forecasing models of durian demand beween he Oupu models and he Inpu models as appropriae o compare wih he Mean Absolue Percenage Error (MAPE) as he mos accurae. Is model is used o forecas he demand of durian in he expor mares Oupu models are a Time Series Analysis conaining ) Moving Average 2) Deseasonalised, 3) Exponenial Smoohing and 4) Double Exponenial Smoohing. Time Series models are based on he assumpion ha he fuure is a funcion of he pas. In oher word, hey loo a wha has happened over a period of he ime and use a series of pas daa o mae a forecasing.. Moving Average model forecas uses a number of hisorical acual daa values o generae a forecas from Bernard [2]. This research designs for forecasing he Moving Average saring from 2, 3, 4, 6, 8, 9 and 2 monhs. 2. Deseasonalised model refers o he influence of seasonal variaion ha affecs Time Series daa which can be separaed by seasonal index: weely, monhly and quarerly from Heizer and Render [3]. This research designs for forecasing he Deseasonlised model saring from 3, 6, and 2 monhs is calculaed and he resuls of he calculaion are compared o find ou he leas MAPE. 3. Exponenial Smoohing model is a sophisicaed weighed Moving Average forecasing mehod ha is fairly easy o use from Heizer and Render [3]. This model employs smoohing consan 0 saring from 0. 0 o. 0. The resuls of he calculaion are compared o find ou he leas MAPE. 4. Double Exponenial Smoohing denoes esimaes for boh he average and he rend ha are smoohed. These procedures require wo smoohing consans, for he average and for he rend. The model employs smoohing consan 0 saring from 0.0 o. 0 where as smoohing consan 0 saring from 0. 0 o. 0 and he resuls of he calculaion are compared o find ou he leas MAPE Inpu models are derived from he analysis of he four forecas variables by using Regression and ANNs model. These variables are gained from hree resources.. Inerviews expers in he field of agriculural economics woring a he Office of Agriculural Economics, Minisry of Agriculure and Cooperaive and hose in he Deparmen of Expor Promoion, Minisry of Commerce in Thailand. 2. Sudy previous models. 3. Sudy relaed researches. ) Regression model is a forecasing echnique ha measures he relaionship of one variable o one or more oher variables. This model is designed by using he demand of each of he four durian ypes beween 2002 and 2007 in Thailand as a raining daa used for forecasing he durian demand in ) Arificial Neural Newors (ANNs) model is a forecasing echnique consising of hree seps: inpu layer, hidden layer and oupu layer of which each sep is deermined by he researchers. Laer, he daa of durian demand beween 2002 and 2007 are used as raining daa in ANNs programme for forecasing he demand of durian in nex year o The demand of each inds of durian from each model are o found he error of Mean Absolue Percenage Error (MAPE). The leas MAPE model is he good model for each inds of durian Linear Programming is used in maximum profi of fresh durian, frozen durian, durian pase and durian chips appropriae for domesic and expor mares o suppor he mare sysem in Thailand and he informaion for durian demand o be disribuing o durian growers Conclusion of he sudy and recommendaions of he forecasing models of durian demand. 4 Modelling Forecas of Time Series for Oupu models The researchers employ wo models of forecasing: Oupu models and Inpu models. The Oupu models are Moving Average, Deseasonalised, Exponenial Smoohing and Double Exponenial Smoohing. This forecasing is brough he resul of demand of durian in he expor mares in he following year o apply for i. 4. Moving Average model The forecasing by Moving Average model is found he average of durian demand in he pas for a monh and a year in advance ha he imporan facor is index n from Bernard [2] and Heizer and Render [3].We can calculae by equaion. 54

7 m A m n MA( n) F () n MA( n) F = Moving Average of n forecased demand in period = The monh of forecas m = The las monh in ha period use for calculaing = The firs monh in ha period a sar for calculaing n = Number of monh in Moving Average a from 2, 3, 4, 6, 8, 9 and 2 monhs = Kind of durian if = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips A = Acual demand in period 4.2 Desesonalised model The forecasing by Desesonalised model o find he demand conforming o seasonal changes and differences each monh and each year from Bernard [2] and Heizer and Render [3]. We can calculae by equaion 2 5. D MA D MA m A mn ( n) p (2) n ( n) p = Deseasonalised Moving Average of n for i in period p p = The period of forecas for Moving Average p = a sar for calculaing from he firs monh o las monh of number Moving average A If m n p = 2a sar for calculaing from he second monh o las monh of number Moving Average = The las monh in ha period use for calculaing = The firs monh in ha period a sar for calculaing = Number of monh in Moving Average a from 3, 6 and 2 monhs = Kind of durian if = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips = Acual demand in period A RcD (3) n RcD = Raio canered Deseasonalised nm RcD Si (4) ma Si = Seasonal index ma = Toal of monhly average n m = Number of monhly A DF (5) Si DF = Deseasonalised forecasing 4.3 Exponenial Smoohing model The forecasing by Exponenial Smoohing model which smoohed wih he moving daa and he counerbalance using he efficiency of smoohing o smooh he gained average he accurae forecas from Bernard [2] and Heizer and Render [3]. We can calculae by equaion 6. 55

8 A ( ESF (6) ESF ) ESF = Exponenial Smoohing forecas of nex monh in ha in period ESF = Exponenial Smoohing forecas demand he each of in period = Presen ime when he forecasing ofi value is calculaed -, -2 and -3 are he pas, +, +2, +3,,n are he fuure o = Smoohing consan an opimal of ind of durian = Kind of durian if = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips = Smoohing consan when 0 A = Acual demand in period o = An opimal of for Exponenial Smoohing 4.4 Double Exponenial Smoohing model The forecasing by Double Exponenial Smoohing mode which counerbalanced he daa by using he efficiency of smoohing and o find more accurae forecas of rend and season from Bernard [2] and Heizer and Render [3].We can calculae by equaion 7-9. DESF ES T (7) DESF = Double Exponenial Smoohing for nex monh in ha period A ( ESF (8) ESF ) ( F F ) ( T T ) (9) ESF = Forecasing for nex monh in ha period for Exponenial Smoohing T = rend facor for nex monh in ha period for Exponenial Smoohing F = Forecas demand of in period A = Acual demand in period = Kind of durian if = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips o = Smoohing consan an opimal of ind of durian o = Smoohing consan for rend an opimal of ind of durian T o = Exponenial smoohed rend facor in period = Opimal of and for Double Exponenial Smoohing = Smoohing consan when 0 = Smoohing consan for rend when 0 5 Modelling Forecas for he Inpu models The Inpu models are Regression and Arificial Neural Newors (ANNs). Is is o forecas he relaed facors o forecas he expor volume for he demand of durian in he expor mares of he following year such as: ) Expor price Free On Board (FOB) 2) Consumer price index 3) Average Gross Domesic Produc (GDP) and 4) Average exchange rae of Thai money and USD as follows: These variables are gained from hree resources: ) Inerviews expers in he field of agriculural economics woring a he Office of Agriculural Economics, Minisry of Agriculure and Cooperaive and hose in The Deparmen of Expor Promoion, Minisry of Commerce in Thailand 2) Sudy previous models and 3) Sudy relaed researches. In summary, variables peraining o he forecas of durian demand in expor mares comprise he following of his research sar from 9 inpu variables as follows: 56

9 . Durian fresh, Durian frozen, Durian pase and Durian chips expor price Free On Board (FOB) 2. Pacaging cos 3. Carrying cos 4. Farm price 5. Consumer price index 6. Average Gross Domesic Produc (GDP) 7. Oil price 8. Transporaion cos 9. Average exchange rae of Thai money and USD Afer geing he inpu variables o ge he correlaion all of four variables. ) Variable : Durian fresh, Durian frozen, Durian pase and Durian chips expor price Free On Board (FOB) of each ype of durians in each monh of he year 2) Variable 2: Consumer price index of Thailand in each monh of he year 3) Variable 3: Average Gross Domesic Produc (GDP) of he world in each year 4) Variable 4: Average exchange rae of Thai money and USD of each year There are four variables as shown in Table which are colleced during he period of Regression model A Regression model aemps o represen he relaionship beween a se of a dependen variable and independen variables using a mulivariae mahemaical funcion in his sudy, he Regression model from Maridais e al. [4] and Spyros e al. [5]. We can calculae by equaion 0. = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips A = Acual demand in period A, = Expor price Free On Board (FOB) in period 2 = Consumer price index in period A, A, 3 = Average Gross Domesic Produc (GDP) for expor mares in period A, 4 = Average exchange rae of Thai money and USD period 5.2 Arificial Neural Newors (ANNs) model The model of Arificial Neural Newors (ANNs) as he ype of Bac Propagaion Neural Newors (BPN) is he model of he relaionship beween he independen variables and dependen variable for he gradually sudy consising of he processing uni or Neural which composing of hree layers such as he inpu layer, he hidden layer and he oupu layer which are fully conneced feed forward. Each neural layer lined o every neural in he nex layer o send he signal each oher. In each lining line will be included he weigh. The sudy of newors is he adjusmen and finding he appropriae weigh o forecas he lowes error and accuracy resuls, from Zhang and Qi [6]. 0 A, A A 2 2, 3 3, 4 4 RF A, (0) 0 = The consan,..., 4 = Parameers represening conribuions of he independen variables RF F = Forecasing demand in Regression in period = Forecas demand of in period = Kind of durian if Figure : Srucure of Arificial Neural Newors as he ype of Bac Propagaion Neural Newors 57

10 The archiecure of Arificial Neural Newors model in his sudy is fully conneced, feed-forward and a muliple layer percepion neural newors. I consiss of hree layers: an inpu layer, a hidden layer, and an oupu layer. Each of hese layers conains neurons. In addiion, he bac propagaion paradigm has become he mos popular for demand forecasing. Figure shows he opology of he neural newors used in his paper. The independen variables V, V2, V3, V4,..., Vn are designed as inpu daa for ind of durian and Fm, as demand forecasing for inds of durian. All inpu daa are insered o each neuron a an inpu layer. The neurons a an inpu layer are conneced o every hidden neuron and every hidden neuron is conneced o he oupu neuron. Connecions beween neurons have numerical weighs and hese are adjused in raining process. Each neuron has wo main funcions: he firs funcion is he summaion funcion. The second funcion is he acivaion funcion. The value for a neuron in he hidden or oupu layers is ypically he sum of each incoming acivaion level imes is respecive connecion weigh. Each neuron in he hidden layer calculaes m when j, 2,..., n from Marin e al. [7]. We can calculae by equaion. m j n i i v w ji j () w = weigh which becomes o a mahemaical value for he relaive srengh of connecions o ransfer daa from one layer o anoher layer j is number of neural in he hidden layer and i is he number of inpu layer. Also, a sigmoid funcion mt in he following form is used o ransform he oupu so ha i falls ino an accepable range. This ransformaion is done before he oupu reaches he nex level. The purpose of a sigmoid funcion is o preven he oupu value from being oo large, as he value of m T mus fall beween 0 and. We can calculae by equaion 2. mt (2) m e Fm Finally,, in neuron of he oupu layer in Figure. We can calculae by equaion 3. n m, i F m w (3) n Ti i = he amoun of neuron in he hidden layer is w which is weigh reurns a mahemaical value for he relaive srengh of connecions o ransfer daa from one layer o anoher layer and i is number of inpu layer. The ANNs modelling for demand forecasing for each ind of durian is developed by using MATLAB. The daa is applied wih he Arificial Neural Newors model. Inpu variables for Arificial Neural Newors model are: V = Fresh durian, Frozen durian, Durian pase and Durian chips expor price Free On Board (FOB) (A he ime -) V 2 = Consumer price index (A he ime -) V 3 = Average Gross Domesic Produc (GDP) (A he ime -) V 4 = Average exchange rae of Thai money and USD (A he ime -) as shown in Table for example. = Kind of durian if = ; Fresh durian = 2; Frozen durian = 3; Durian pase = 4; Durian chips Oupu variable for Arificial Neural Newors model is: m F = Forecas durian demand quaniy of year (A he ime ) 58

11 Table : The daa of durian demand for fresh durian o inpu variables in year 2002 Table 2: MAPE calculaed by Arificial Neural Newors forecas model for durian chips Monh Expor Price (USD/ons) Comsumer Price Index Average GDP of he wolrd Average of Exchange Rae of Thai money and USD Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec In his research, he daa is divided o be wo series which are he raining series conaining 72 daa sequences and he esing series conaining 2 daa sequences. The infrasrucure consised of four inpus variables, one hidden layer, changing unil 0 hidden nodes and he parameer of learning. The error goals are 0., 0.2, 0.3, 0.4, 0.5, 0.6, 07, 0.8, 0.9 and.0. The resuls of Arificial Neural Newors forecas model for durian chips and he forecas error by comparing MAPE as shown in Table 2 for example. Error goal Hidden Node Comparison of model efficiency The forecas model efficiency compares he forecas error by comparing Mean Absolue Percenage Error (MAPE) resuling from forecas models from Zhang e al. [8]. We can be calculaed by equaion 4. n A F MAPE 00 (4) n A F = Forecased of durian demand quaniy in period A = Acual of durian demand quaniy in Period = Period a consider n = Toal number of periods 59

12 In general, he seleced models are no very accurae in he mos of he measuring dimension. The classified forecass wih MAPE values of less han 0% as high accurae for forecasing, beween 0% and 20% as good forecasing, beween 20% and 50% as reasonable, and forecasing, larger han 50% as inaccurae forecasing from Frechling [9]. 7 Research resuls of forecasing models The research resul of forecasing using Moving Average model, he mean of forecasing used are 2, 3, 4, 6, 8, 9 and 2 monhs, respecively. When n is 3 monhs a frozen durian he lowes MAPE is 64.4%, durian pase is 85.36% and fresh durian is 6.26%. When n is 6 monhs a durian chips, he lowes MAPE is 86.02%, respecively. The resul of forecasing using Desesonalized model, he mean of forecasing used is 3, 6 and 2 monhs, respecively. When monh is 3 monhs a frozen durian he lowes MAPE is 9.78%, fresh durian is 9.24%, and when he imes is 6 monhs a durian pase he lowes MAPE is 8.66%, durian chips is 34.47%, respecively. The resul of forecasing using Exponenial Smoohing model he mean of forecasing used is beween 0.0 unil.0, respecively. When is 0.9 a frozen durian lowes MAPE is 43.66%, durian pase is 67.54%, and fresh durian is 85.23%, and when 0. a durian chips he lowes MAPE is 8.3%, respecively. The resul of forecasing by using Double Exponenial Smoohing model, he mean of forecasing used is and beween 0.0 unil.0, respecively. When 0.5, 0.9 is frozen durian he lowes MAPE is 43.9%, when 0.5, 0. 9 durian pase is 67.04% and durian fresh is 82.85% and when 0., 0.a durian chips lowes MAPE is 68.46%, respecively. The resul of forecasing by using Regression model is forecased as follows. When MAPE a durian pase he lowes MAPE is 55.73%, frozen durian is 82.26% durian chips is 95.74% and fresh durian is 200.9%, respecively. The resul of forecasing using Arificial Neural Newors model, he mean of forecasing used is Arificial Neural Newors (ANNs) as he ype of Bac Propagaion Neural Newors (BPN) model uses four inpus respecively. When we compare hidden layer and error goal, he mean of inpu four variables, hidden layer since o, 2, 3,..., 0 and error goal variables since o 0. o.0 is forecased as follows. When inpu four variables, hidden layer is 6 and error goal is 0. a frozen durian he lowes MAPE is 2.6%, when inpu four variables, hidden layer is 4 and error goal is 0.8 a fresh durian he lowes MAPE is 25.35%, when inpu four variables, hidden layer is 6 and error goal is 0. a durian chips he lowes MAPE is 29.76%, and when inpu four variables, hidden layer is 9 and error goal is 0.3 a durian pase he lowes MAPE is 48.7%, respecively. When we compare forecasing models he mean of model an opimal is Deseasonlised model as follows. A durian pase he lowes MAPE is 8.66%, frozen durian is 9.78%, fresh durian is 9.24%, and Arificial Neural Newors (ANNs) model an opimal a durian chips he lowes MAPE is 2.76%, as shown in Figure 2 and Table 3. Figure 2: The resul of six models comparing of MAPE and he inds of durian Table 3: The resul of models comparing MAPE for inds of durian Model. Moving Average Fresh Durian Type of durian Frozen Durian Durian Pase Durian Chips MAPE MAPE MAPE MAPE 3 monh 3 monh 3 monh 6 monh Deseasonalised 3 monh 3 monh 6 monh 3 monh 3. Exponenial Smoohing 4. Double Exponenial Smoohing = 0.9 = 0.9 = 0.9 = =0.6 = 0.9 = 0.5 = 0.9 = 0.5 = 0.9 = 0. = Regression ANNs

13 The conclusion of he research, o sudy of he forecas of durian demand in he expor mares of four durian ypes; here are six forecasing models ha used wo forecasing ypes as follows.. The daa of durian demand aen from he Office of Agriculural Economics are analysed by means of he four models: Moving Average, Deseasonlised, Exponenial Smoohing, and Double Exponenial Smoohing. The resuls gained from each of he four models analysis are compared o find ou error rae of MAPE. I is revealed ha Deseasonlised model has he bes resul since i has he leas MAPE. This means ha he model has he mos accuracy of all he oher five models used o forecas demand of four durian ypes: fresh durian, frozen durian, durian pase and durian chips. The firs hree durian ypes have he leas MAPE (he mos accuracy) while he las durian ype has he leas accuracy. 2. The variables influencing he forecas are analysed by Regression model and ANNs model. The resuls are hen applied o forecas he demand of durian by using inpu models ype. The resuls gained from each of he wo models analysis are compared o find ou error rae of MAPE. I is revealed ha, in conras o he above forecas ype, he mos accuracy of he MAPE s error rae is gained from he calculaion of durian chips. Boh of he wo forecas models, Oupu and Inpu models have differen advanages which will be presened in deail below. According o he Oupu models ype which has four models: Moving Average, Deseasonlised, Exponenial Smoohing and Double Exponenial Smoohing, Deseasonlised model is he bes forecas model due o he fac ha durian produc has yielded ino expor mares in season. On he oher hand, he remaining models which are no he Deseasonalised model have he leas accuracy. The Inpu models ype which has wo models: Regression and ANNs, he laer is he bes forecas model of expor durian demand. The disadvanage of inpu models is ha if here is no relaionship among he variables influencing he forecas, he forecas will give he leas accuracy. Wih respec o he findings of he appropriae durian demand, his sudy apply he Linear Programming for calculaing he amoun of he demand for fresh durian, frozen durian, durian pase and durian chips in domesic and expor mares for he maximum profi for he durian growers. The resuls of he findings benefi durian growers in ha hey are possibly able o mae he mos profi of durian produc. Moreover, he findings also suppor he forward expor planning devised by he Minisry of Agriculure and Cooperaive, paricularly he Office of Agriculural Economics including en official areas locaed in differen pars of Thailand. 8 Maximum Profi of Durian Produc As can be seen he appropriae forecasing models of durian demand of each ype of durian o ge each ype of durian demand o forecas he producion of durian. The profi per on of each ype of durian from he governmen agencies such as ) Office of Agriculural Economics 2) Bureau of Agriculural Economic Research 3) Garden plan research division and 4) Deparmen of Expor Promoion by applying he Linear Programming o calculae he appropriae quaniy of durian o ge he maximize profi and offer each ype of durian boh domesic and expor mares under he limiaion and sending he informaion of durian demand o he Office of Agriculural Economics, he Office of Agriculural Economics of each area and durian growers. The Linear Programming model is he echnique which developed from he problem of he resource allocaion. The objecive of he program is o gain he opimal benefi by minimizing cos of maximum profi by he condiion of he limiaion of he relaionship of linear program of various resource by composing he opimize problem which composing four pars such as form Taha [20]. There are wo sysem of selling durian in Thailand namely ) he domesic mare 2) he expor mare. Therefore he quaniy of selling durian of boh sysems will ge he whole quaniies of durian. As we expec o sell durians in he expor mare and he forecasing durian quaniy afer exporing hen here will be consume in he domesic mare.. Objecive Funcion in he form of Max or Min: f X, X,..., X ) form Ragsdale [2] ( 2 n 2. Consrain Funcion 3. Decision Variables in he equaion and he limiaion of he linear program. There are wrien by X X,..., X, 2 n 4. Decision Variables more han zero value This research is relaed o he facors and mahemaic model by he argeed equaion wih he maximize profi. 6

14 X = Quaniy fresh durian for expor, ons X = Quaniy frozen durian for expor, ons 2 X = Quaniy durian pase for expor, ons 3 X = Quaniy durian chips for expor, ons 4 X = Fresh durian for domesic, ons 5 X = Frozen durian for domesic, ons 6 X = Durian pase for domesic, ons 7 X = Durian chips for domesic, ons 8 a j = Profi coefficien of four durian ypes in domesic and expor mares, USD per ons Max Z a X a X a Subjec o 5 X 5 2 a 6 2 X a X 6 3 a 7 3 X a 7 4 X 8 4 a X 8 (5) X X 2 X 3 X 4 X 5 X 6 X7 X 8 Toal supply X X X Supply for expor 2 3 X 4 X X X Supply for expor 2 3 X 4 X X X Supply for domesic X 8 X X 5 The oal quaniy of fresh durian X 2 X 6 The oal quaniy of frozen durian X 3 X 7 The oal quaniy of durian pase X 4 X 8 The oal quaniy of durian chips X 0 j, 2, 3,..., 8 j The Linear Programming is he mahemaics model ha is applied o survey he durian demand quaniy in ons, of four durian ypes: fresh durian, frozen durian, durian pase and durian chips by using he forecasing daa of demand and he Linear Programming is he mahemaics model ha is applied o survey he durian demand quaniy in ons, of four ypes such as fresh durian, frozen durian, durian pase and durian chips by using he forecasing daa of demand by Linear Programming ha is he ool for calculaing he demand of durian in each ype as appropriae quaniies o ge he maximize profi. The oal of durian producion in 2008 from forecasing resul durian supply is 693,640 ons. The durian demand of domesic mare is 467,953 ons and 209,487 ons for expor mares. As he limiaion of he quaniy demand of durian for domesic and expor mares. The quaniy demand of durian for domesic and expor mares are as follows: ) here are 632,992 ons of fresh durian from he oal quaniy of fresh durian sold from he oal volume of 90,554 ons for expor mares (forecasing resul from Deseasonalised model) and he res of he 442,437 ons for he domesic mares. 2) There are 35,40 ons of frozen durian from he oal quaniy of frozen durian sold from he oal volume of 5,955 ons for expor mares (forecasing resul from Deseasonalised model) and he res of he 9,85 ons for he domesic mares. 3) The oal volume of durian pase is 8,448 ons from he oal quaniy of durian pase ha will be sold for he expor mare a 2,647 ons (forecasing resul of Deseasonalised model) and he res of he 5,80 ons for he domesic mares. 4) There are 858 ons of durian chips from he oal quaniy of durian chips ha for exporing a 329 ons (forecasing resul from he Arificial Neural Newors model) and he res of 529 ons for he domesic mare. The profi per on of selling durian for domesic and expor mares are as follows: ) The profi of fresh durian for he domesic mare is 49 USD per on and 57 USD per on for expor mares 2) The profi of frozen durian for domesic mare is 59 USD per on and 67 USD per on for expor mares 3) The profi of durian pase for domesic mare is 69 USD per on and 77 USD per on and 4) The profi of durian chips for he domesic mare is 80 USD per on and 86 USD per on for expor mares. As can be seen ha his limiaion can be calculaed for he appropriae quaniy of each ype of durian for he maximize profi in 2009 he Office of Agriculural Economics receives he informaion of he appropriae quaniies of domesic and expor demand for durian hen he farmers will ge o now abou his informaion hrough he Regional Office of Agriculural Economics for sales planning and processed durian by Linear Programming. We can calculae wih he equaion 5. The purpose of he Linear Programming model is o find he appropriae quaniy by each inds of durian in order o achieve a suiable price for he durian. The maximized profi canno be less han he demand cos, a forecasing of four durian ypes: fresh durian, frozen durian, durian pase and durian chips of quaniy in he demand-side and he resul of durian demand of four durian ypes o ge he less han profi a 65 USD per on which is 62

15 he good price for durian growers o ge he maximum opimal profi. The oal durian demand for domesic and expor mares able no be more han 693,640 ons. The quaniy of durian demand par for domesic and expor mares able o as follows: Fresh durian in domesic mare = 442,437 ons Frozen durian in domesic mare = 9,85 ons Durian pase in domesic mare = 5,80 ons Durian chips in domesic mare = 529 ons Fresh durian in expor mares Frozen durian in expor mares = 90,555 ons = 5,955 ons Durian pase in expor mares = 2,648 ons Durian chips in expor mares = 329 ons The ne profi is equal o 50 million USD relaed o he real value of profi from selling durian in 2009 is 58 million USD. The increasing of profi by he counry's oal is 8 million USD and equivalen o 6 %. 9 Summary and Recommendaions The objecive of his research is o design forecasing on demand of durian for expor mares. The value of his research is in mehodology for forecasing durian demand in monhly of fresh durian, frozen durian, durian pase and durian chips. Which can be implemened forecasing demand durian in expor mares and he mehodology of his research is apply by forecasing mehod. Then he resuls from he analysis of he wo models ypes are compared o find ou he error rae of MAPE.. The Oupu models are he forecasing of previous year expor volume o apply. The models are calculaed by Moving Average, Deseasonalised Exponenial Smoohing and Double Exponenial Smoohing o compare each variable by he las arge of forecasing he demand of durian. The resul of Mean Absolue Percenage Error (MAPE) mus be less error by forecasing he expor demand of durian such as fresh durian, frozen durian, durian pase and durian chips. The objecive of his research is find he bes model o compare wih he accurae of he minimum MAPE of Oupu models ype which consis of he Deseasonalised model. ) The findings are found ha he durian pase has he leas error a he percenage of 8.66 and giving he high accuracy 2) The frozen durian has he error a he percenage of ) The fresh durian has he error a he percenage of The good poin of he Deseasonalised model is he qualificaion of he seasonal forecasing which is consisen o he durian producion as he seasonal fruis o domesic and expor mares in one year. The analysis of he seasonal aleraion by he seasonal index from Vichaisin and Chaweesu [22]. Therefore he Deseasonalised model is o forecasing he fresh durian, frozen durian and durian pase which are more accuracy han oher mehods. As he reason of he agriculural producs are influenial by he season which can be measured from Vichaisin and Chaweesu [22]. 2. Inpu models are he forecasing model o find he affec o expor volume nex year. The Inpu models are Regression and Arificial Neural Newors (ANNs) o forecasing demand of durian of each inds of durian such as fresh durian, frozen durian, durian pase and durian chips o ge he bes model. The comparison of he minimum value of MAPE is Arificial Neural Newors (ANNs) model ha found ha he durian chips have he leas error a he percenage of 29.76% and giving he high accuracy. The good poin of he forecasing by Arificial Neural Newors is o find ou he shor run and long run of he forecasing daa. Besides he ANNs can ge he righ value in he many forms which is beer han oher models from Siripanich e al. [23]. Especially he durian chips are differen from he fresh durian, frozen durian and durian pase. This preservaion can sore durian for long ime. The expor produc has relaed by many facors. In conclusion hese wo models can forecas he expor demand of durian. The difference beween wo models is as follows; he Oupu models ype can forecas he expor volume of nex year s producion. However he Inpu models are he forecasing models which find ou he impaced facors o he expor volume and o forecas he expor volume nex year. The Oupu models ype can forecas he expor volume of nex year s producion which is good for forecasing he appropriae demand in expor mare. I is he Deseasonlised model. The forecasing of he appropriae demand of durian from 3 ypes of durians such as fresh durian, frozen durian and durian pase. The informaion of he daa in 2008 for he forecasing of demand for durian in However he Inpu models are he 63

16 forecasing models which find ou he affec facors o he expor volume and o forecas he expor volume nex year. The Inpu model namely he Arificial Neural Newors Model is he suiable model o forecas he appropriae demand in expor mare. I is good for forecasing he demand for durian chips in he year 2008 which is he daa for forecasing he demand for durian in The forecasing mehod of oupu model and inpu model are good and suiable model. However he volume of expor demand from he forecasing does no ge he maximize profi bu i sill need he Linear Programming o find he sale volume of each ype of durian in domesic and expor mare. The resul of his forecasing is applying for he durian growers, domesic and expor merchans. The Office of Agriculural Economics has nown he demand for durian in he following year relae o presen year. How much demand for durian a he same ime he Office of Agriculural Economics, Minisry of Agriculure and Cooperaives can selec he forecasing model he demand for durian easily. The comparison of six forecasing models of he demand of durian can be seen ha he model of he less error and more accuracy is he model of Deseasonilsed model and Arificial Neural Newors model as shown in Table 3. Moreover, he researchers have consruced he Linear Programming model o find he appropriae demand of each ype of durian for he domesic and expor mares o suppor he mare sysem in Thailand for maximizing profi. This research is beneficial o he relaed people lie durian growers, reailers, wholesalers, food processors, he relaed business and governmen agencies such as he Office of Agriculural Economics, he Minisry of Agriculure and Co-operaive, he Minisry of Commerce and he Minisry of Indusry ec. The resul from he forecasing model able o applied for oher fruis in Thailand and expor mares. Furher, he nex sep of he research able o produce a compuer sofware pacage for calculaing he forecasing of demand for each of he ypes of durian in he following year ha able inpu he selling price or he domesic price, he expor price or he exchange rae ino he programme for calculaing he resuls of quaniy demand of each ypes of durian. These daa will help o mae a decision o expor durian a he appropriae volume and he good price for maximize profi. 0 Acnowledgemens The research is suppored he daa from he Office Agriculural Economics, he Agriculural Informaion Cener of Thailand during 2002 o The auhors also able o lie o han very much he members of McGill Universiy in Canada and Kanazawa Insiue of Technology in Japan research newors for heir suggesion and cooperaion in his research projec. References [] The Cooperaion of he Office of Agriculural Economics and he cusoms year. The Agriculure saisics of Thailand and Basic Agriculural Economy, [Source: hp:// March, 2009]. [2] The Office of Agriculural Economics, Basic Agriculural Economical, Daa, Aroonprining, Bango. decisioneering, Inc. [3] The Office of Agriculural Economics. The Area of Planing and Produc, Available. [Source: hp:// March, 2008]. [4] The Agriculural Informaion Cener, he Office of Agriculural Economics. Main Problem of Producion and Mareing, [Source: hp:// March, 2008]. [5] Par S.J., Hwang C.S. and Vle P.L.G., Comparison of Adapive Techniques o Predic Crop Yield Response under Varying Soil and Land Managemen Condiions, Journal of Agriculural Sysems, [6] Co H.C. and Boosarawongse R., Forecasing Thailand s Rice Expor: Saisical Techniques vs Arificial Neural Newor, Compuers & Indusrial Engineering, [7] Segura J.V. and Vercher E., 200. A Spreadshee Modelling Approach o The Hol- Winers Opimal Forecasing, European Journal of Operaion Research, [8] Alon I., Oi M. and Sadowsi R.J., 200, Forecasing Aggregae Reail Sales: a Comparison of Arificial Neural Newor and Tradiional Mehod, Journal of Reailing and Consumer Services, [9] Badri M.A., 999. Combining he Analyic Hierarchy Process and Goal Programming for Global Faciliy Locaion-Allocaion Problem. 64

17 Inernaional Journal of Producion Economics, 62: [0] Chachiamjane T. and Kengpol A., Suiable Producion Quaniy Evaluaion Using Mahemaical Models: A Company Case Sudy of Producion Planning, in Paper Indusry Conference, Bango, Thailand. [] Kengpol A. and Kaoien P., A Procuremen Planning Improvemen by Using Linear Programming and Forecasing Model, Faculy of Engineering, King Mongu s Insiue of Technology Norh Bango, Thailand. [2] Bernard W.T III., 2006 Inroducion o Managemen Science, 9h Ediion, Prenice Hall, New Jersey America. [3] Heizer J. and Render B., Operaion Managemen. 8h Ediion, Prenice Hall, Upper Saddle River. New Jersey America. [4] Maridais S., Seven C.W. and Vicor E.M., 983. Forecasing: Mehods and Applicaions, 2nd Ediion, John Wiley & Sons. New Yor America. [5] Spyros M., Seven C. and Rob J.H., 998. Forecasing Mehods and Applicaions. Third Ediion, John Wiley & Sons, Inc. New Yor America. [6] Zhang G.P. and Qi M., Neural Newor Forecasing for Seasonal and Trend Time Series. European Journal of Operaional Research (60): [7] Marin T.H., Howard. D. and Mar B., Neural Newor Design. Cengage Learning in India. [8] Zhang G., Pauwo B.E. and Hu M.Y., 998. Forecasing wih Arificial Neural Newors: The Sae of The Ar. Inernaional Journal of Forecasing (4): [9] Frechling D.C., 200. Forecasing Tourism Demand: Mehods and Sraegies. Buerworh- Heinem ANNs. [20] Taha H.A., Operaions Research an Inroducion, 8h Ediion, Singapore: Pearson Educaion. [2] Ragsdale C.T., Spreadshee Modelling & Decision Analysis, 4h Ediion, Thomson. [22] Vichaisin S. and Chaweesu R., Techniques Time Series Analysis for Forecasing Quaniy of Fruis and Vegeables, in Paper Logisic and Supply Chain Conference, Bango, Thailand. [23] Siripanich P., Ninorn P. and Traganalerngsa S., Time Series Forecasing using a combined ARIMA and Arificial Neural Newor Model, in Paper Operaion Research Conference, Bango, Thailand. 65

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