Determination Forecasting Sporadic Demand in Supply Chain Management

Transcription

1 07 Published in 5h Inernaional Symposium on Innovaive Technologies in Engineering and Science 9-30 Sepember 07 (ISITES07 Baku - Azerbaijan Deerminaion Forecasing Sporadic Demand in Supply Chain Managemen * Mehme Gülşen and Kuner İpek, Başken Universiy, Faculy of Engineering, Ankara, Turkey Absrac: Wih increasing number of SKUs(sock keeping unis in he supply chain, demand daa for many producs have become more sporadic wih few nonzero observaions. Almos binary-like paern of he demand daa makes forecasing difficul. There are several esablished mehods such as Croson s exponenial smoohing or SBA wih limied general success. Mos of he ime forecasing of a sporadic demand requires modificaion of a sandard mehod o incorporae some domain specific informaion ino he forecasing model. In his research, we presen a demand forecasing approach for a local candy manufacurer. The company has a porfolio of producs wih highly sporadic demand. Our approach includes sandard mehods and an alernaive model ha is based on he dynamic aggregaion of he demand daa. Key words: forecasing, sporadic demand, croson. Inroducion In consumer driven marke economy of oday, he cusomer needs have become more sophisicaed. The produc life cycles are shorened while he variey of producs ges wider, and cusomers expec fas availabiliy of producs in he marke place. This pu pressure on all acors of he supply chain o procure and produce expanding variey of producs in a shor noice. The number of SKU s (sock keeping unis in he supply chain has increased significanly in recen years. According o FMI, average number of SKUs in a supermarke is 39,500[]. For big sores, he average moves up o 60,000 iems[]. The increasing number of SKU s brings several challenges o he managemen of supply chains. As more iems move inside he nework, he proper managemen ools need o be developed for demand forecasing and invenory managemen. Wih increasing number of producs, he daa becomes more granular and sparse. In a deparmen sore, a simple polo shir is caegorized according o color and size. There may be oher caegorizaion facors, such as: availabiliy of breas pocke, packaging, gender specific cuing and half sizes. The evenual produc variey will be deermined by he produc of hose caegories, and i may easily go up o several hundred wih he inclusion of oher caegories. The supply chain managemen sysem needs o generae demand forecas and develop sock keeping sraegies for each such sub-caegory. One challenging issue is he lower granulariy of daa a sub-caegory level. There may be periods wih no aciviy ha are regisered as zero demand/producion periods in hisorical records. The daa sream looks like a binary series wih zeros and low-valued posiive numbers. Such daa ses are called inermien or sporadic daa, and hey presen challenges when direcly used in many of he sandard forecasing ools. Based on he research and pracices in he real-life applicaions, several forecasing mehods are favored *Corresponding auhor: Address: Faculy of Engineering, Deparmen of Indusrial Engineering, Başken Universiy, Ankara, TURKE. address: mgulsen@basken.edu.r, Phone:

2 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 053 over ohers for inermien and sporadic daa[3]. The shor lis includes simple moving averages(sma, simple exponenial smoohing(ses and Croson s mehod. These ools have gained wide accepance of praciioners because of heir simpliciy, and hey can work wih daa ses ha include zero-valued observaions.. Lieraure Any ime series ype of forecasing mehod can be used for inermien daa. Some of he common approaches have gained populariy because of heir simpliciy and beer accuracy. The brief explanaion and review of hese mehods are given in his secion.. Simple Moving Average (SMA The underlying assumpion in simple moving average is ha he bes esimae for he fuure demand is he average of wha were observed recenly. In Simple Moving Average mehod, demand forecas for he nex period is given by:... m m The fuure value is based on he average of pas m observaion. Each observaion has an equal weigh of /m. One criical facor in simple moving average mehod is he lengh of hisory. If m is se o higher value, a longer hisory will be used. This will be more effecive in erms of filering noise, bu he model will be slow in responding o changes in daa rends. If m is smaller, he forecas model will be more responsive. However, ha will increase he risk ha he model is responding a noise, no an underlying rend change.. Simple Exponenial Smoohing (SES Mehod Exponenial smoohing mehod is similar o simple moving average as boh mehods aims o cach he underlying behavior of he pas daa based on he mean value of he pas observaions. The main difference beween wo mehods is in how hey calculae he hisorical mean. In simple moving average, each observaion has an equal weigh wheher he even occurred recenly or far in he pas. Every single observaion of hisory has equal impac on he fuure forecas. In exponenial smoohing he hisorical average is calculaed in a biased manner. A recen even is assumed o have more relevance as compared o somehing happened long ago. Thus, a higher weigh is given o a recen observaion when calculaing he mean. In SES approach, geomerically declining weighs are assigned o each hisorical daa poin, saring from he mos recen observaion o he oldes one. The exponenial smoohing is probably he mos common forecasing ool used in business applicaions. This primarily due o simpliciy of he mehod, and due o fac ha SES produces robus forecass under variey of condiions. In a business environmen, housands of forecas need o be generaed auomaically every single day. Under such circumsances, having a robus

3 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 054 sysem has ulimae imporance, as here may be no chance for a manual inervenion. The SES model could be expressed in differen forms. One common way o define he forecased demand is o use inerpolaion beween he mos recen acual observaion and he mos recen forecas. ( where α is he smoohing consan beween 0 and. The SES is a dynamic and robus approach o forecasing. As soon as we have he firs acual observaion we can sar generaing forecass. Periodically he forecas is updaed as more acual daa become available. The alpha deermines he responsiveness of he model. If i is se o a lower value he changes in forecass from one period o anoher will be less volaile. This will smooh ou he noise effec in he daa, bu i will be slow down he model s abiliy o respond o rend changes in he daa se. The SES approach is based on he exponenially weighed average of pas observaions. To illusrae his poin, we can expand he equaion in ( o include all pas observaions ( Unlike SMA, he exponenial moving average use he enire hisory, and he weigh of an observaion is discouned by a facor of -α for each period of movemen on he ime frame..3 Croson s Mehod Croson s approach o forecasing can be considered as exension of he SES mehod[4]. The primary difference is in he daa handling. Croson divides he inpu daa ino wo sub-series. The firs se includes only non-zero observaions. The second se sores ime duraions beween he non-zero observaions. By using he radiional SES mehod wo ses of forecass are generaed: magniude of non-zero demand, ( ime inerval beween wo non-zero evens. The smoohing facor alpha is kep idenical in boh forecass. The final resuling forecas is he raio of non-zero demand forecas o ime inerval forecas. This number is no he forecas of he demand, bu a forecas for he demand rae[5][6]. In Croson s mehod he forecas is updaed only afer a posiive demand is observed. Oherwise i remains consan.

4 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 055 Z T original series non - zero demand series ime inernal series Z T (4 The mehod proposed by Croson s has been heavily researched and has been a subjec of some criicism. In 973, Rao published a correced version of Croson s mehod[7]. A modified version is developed o eliminae bias due o value of smoohing parameer. The original forecas of he Croson s is muliplied wih a de-biasing facor[8][9]. Z p T (5 3. Empirical Sudy The acual daa from a confecionary producer is used o evaluae he performance of he various forecasing approaches. The daa se include hisorical orders placed by local and inernaional cusomers. The hisory covers enire 06 and he firs four monhs of 07. In a period of 6 monhs he company received over wo housand orders for 7 differen confecionary iems. Alhough he company has a porfolio of over 300 hundred producs, he op 0 iems in he order hisory makes almos half of confecionary ordered by volume. On he oher end of he specrum, ou of 7 producs ordered wihin 6 monhs, 64 iems only ordered once. As i can be seen in Table, he order daa exhibi ypical characerisics of an inermien daa. Wihin he observaion period, here are 007 orders for 7 differen producs. The average ordering frequency is 007/7 = 9. The disribuion is highly skewed o he lower end. The median ordering frequency is hree. Table : Disribuion of ordering frequency for 7 producs Number of orders Frequency placed (oal To es he effeciveness of differen approaches, he daa se is divided ino wo secions. We remove he las 30 days of he hisory and keep i as holdou period. The original daa se minus las 30 days is used as raining daa. The forecasing model is developed on he runcaed daa.

5 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 056 Once he model is ready, a 30-day projecion of demand is generaed and compared wih he holdou daa. Figure shows he hisory and forecas for he mos frequenly order iem (produc id: 5 0 in he produc porfolio. The black and blue lines represen raining and holdou porions of he original daa se. The green line represens he back-fiing of he model. The red line shows he 30-day projecion. The forecasing performance of each model is measured over he holdou period. Figure : Order hisory and forecas for he mos frequenly ordered iem One challenging area for sporadic daa is he selecion of proper error merics. For comparison purposes, scale-free merics such as MAPE (mean absolue percen error are frequenly used in evaluaing forecas performance of differen daa series. However, MAPE is based on percenage error, 00 e /, requires division o, which is commonly equal o zero in sporadic daa ses. Several alernaives merics are proposed in he lieraure[0][]. The MASE, mean absolue scaled error, an alernaive error merics used frequenly in evaluaing forecas performance in sporadic daa models. In MASE, he performance of he proposed mehod is evaluaed wih respec o he performance of a simple benchmark. Le s assume ha a naïve forecas is compleely based on he las observed value ( is used as benchmark. Then he scaled error will be:

6 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 057 q e n n i The mean absolue scale error is calculaed by averaging he absolue values of q s. A value greaer indicaes ha he performance is worse han he performance of a naïve forecasing mehod. 3. Resuls Three differen forecasing mehods are used in his sudy. Firs one is a simple average which is based on hisorical average demand. The calculaed average value is used as a saic projecion of he fuure demand. The oher wo approaches used in his sudy, exponenial smoohing and Croson are dynamic mehods which means forecass are updaed wih each new observaion. The simple average is he wors performing mehod as compared o oher wo. This is probably due o saic naure of he approach. Table shows performance of each approach on 0 differen daa ses. These are he mos frequenly ordered producs wihin he las 6 monhs. The able includes one more iem, , which is he aggregae of previous 0 iems. The forecas performance for he aggregaed daa is relaively beer han individual producs. Considering ha lo of iems in he daa ses are ordered jus once or wice a year, aggregaion could be reasonable approach. Similar producs wih exremely sporadic demand could be pooled ogeher o form a single produc. Table : Forecas comparison for 0 producs Produc ID Simple Average Exponenial Smoohing Croson Conclusion and fuure work Among he hree alernaives used in his sudy, only wo, exponenial smoohing and Croson s mehods look like reasonable approaches. They do beer han he benchmark (i.e., naïve on

7 M. GULSEN e al./ ISITES07 Baku - Azerbaijan 058 average. We are planning o exend his sudy o include mehodology o pick up he bes forecasing model. For ha purpose, he daa should be esed for in-sample (i.e., raining and ou-sample(i.e., holdou daa. Based on he performance on he raining daa a proper model should be seleced for he holdou period. References [] FMI: Food Markeing Insiue, indusry group for food reailers. hps:// Accessed on 03-July-07 [] hp:// Accessed on 03-July-07 [3] Peropoulos, F., Kourenzes, N., Nikolopoulos, K., Anoher look a esimaors for inermien demand. Inernaional Journal of Producion Research: 06; 8, p [4] Croson, J.D. Forecasing and sock conrol for inermien demands. Operaional Research Quarerly: 97; 3(3, p [5] Kourenas, N. Inermien demand forecass wih neural neworks. Inernaional Journal of Producion Economics: 03; 43, p [6] Peropoulos, F., Kourenzes, N. Forecas combinaions for inermien demand. Journal of Operaions Research Sociey: 05; 66, p [7] Rao, A. V. A commen on: Forecasing and sock conrol for inermien demands. Operaional Research Quarerly: 973; 4(4, p [8] Syneos, A. A., Boylan, J.E. On he bias of inermien demand esimaes. Inernaional Journal of Producion Economics: 00; 7, p [9] Syneos, A. A., Boylan, J.E. The accuracy of inermien demand esimaes. Inernaional Journal of Forecasing: 005; (, p [0] Makridakis, S. & Hibon, M., 000; The M3-compeiion: Resuls, conclusions and implicaions, Inernaional Journal of Forecasing, 6, []Hyndman, R. J. & Koehler, A. B., 006; Anoher look a measures of forecas accuracy, Inernaional Journal of Forecasing.