Model of an Integrated Procurement-Production System for Food Products Incorporating Quality Loss during Storage Time

Transcription

1 Model of an Inegraed rocuremen-roducion Sysem for Food roducs Incorporaing Qualiy Loss during Sorage ime Gusi Fauza, Yousef Amer, and Sang-Heon Lee Absrac Research on procuremen-producion sysems for deerioraing iems has been done. he majoriy of sudies assume ha he perishable characerisics affec only he quaniy of invenoried iems. For fooroducs, however, heir quaniy remains consan during heir shelf life period, bu he qualiy deerioraes over ime. his paper proposes a new procuremen-producion model incorporaing his siuaion. he qualiy change behavior of fooroducs is approached differenly depending on heir forms eiher as raw maerials or finished goods. As raw maerials, he kineic model is used o represen he qualiy degradaion during sorage ime, while as finished goods he shelf-life dependen pricing is uilized o describe he value loss due o he qualiy percepion of cusomers. A mahemaical model represening he inegraed procuremen-producion of raw maerials and finished goods a a manufacurer is esablished in his research. he objecive is o maximize he oal profi per uni ime of he sysem by conrolling a number of variables, namely he producion cycle (), he number of raw maerials procuremen over one producion cycle (m) and he number of finished goods delivery over one producion cycle (n). Index erms Deerioraing iems, food invenory, procuremen-producion sysem, qualiy loss, value loss. I. INRODUCION Ever since EOQ (Economic of Quaniy) invenory conrol has been inroduced, many researchers sill develop i o solve various invenory problems. Convenionally, economic lo-size of raw maerials was decided separaely from finisheroduc and his may lead o sub-opimizaion. I is because demand for raw maerials depends on producion schedule of finisheroducs. Laer, Goyal [1] developed an inegraed invenory model for raw maerial and finished produc. his research gave he firs conribuion in he field of inegraerocuremen-producion (I) sysems. Recenly, research in he field of I sysem receives significan aenion from scholars and many invenory models has been developed o accommodae his issue [2]. Goyal and Deshmukh [3] developed a model for I sysems in jus in ime JI environmen o minimize se up ime. And laer, Lee [4] exend he I o an inegraed supply chain problem by inegraing he economic lo size of raw maerial, manufacuring se up and finisheroducs. However, hose sudies assume ha iems can be sored infiniely, while in Manuscrip received November 5, 212; revised January 1, 213. Gusi Fauza is wih he School of Engineering, Universiy of Souh Ausralia and Food Science and echnology Deparmen, Sebelas Mare Universiy, Indonesia ( faugy1@mymail.unisa.edu.au). Yousef Amer and Sang Heon Lee are wih he School of Engineering, Universiy of Souh Ausralia. fac, some iems have limied life ime. In realiy, i is ofen found ha some paricular iems deeriorae over he sorage period, for insance food producs. For such iems, he qualiy degradaion during he sorage ime can lead o a significan wase or loss. o illusrae, an FAO sudy repored ha every year 1.3 billion ones food are wased globally [5]. he major food losses occur in producer-reailer sage and he mismach beween producion and demand is idenified as he main cause. Noing his siuaion, i is crucial o incorporae he perishabiliy characerisics of he iems while managing he invenory. Acually, sudies on inegraed invenory models for perishable iems have been done [6]-[8]. However, hose models assume ha he deerioraion of he iems leads o he quaniy decrease, as observed in he invenory of gasoline, alcohol or radioacive maerials. Cerainly, hese assumpions are no suiable for fooroducs. he quaniy of food ypically remains he same during heir shelf-life, while heir qualiy, which can be represened by he freshness, obviously degrades. In addiion, i is also assumed in he previous models ha he deerioraion characerisics of he raw maerials and he finished goods are idenical. Bu food is a dynamic iem [9]. he perishable characerisics of food are no idenical and need o be approached differenly. herefore, he exising models are inadequae for represening he invenory sysems of fooroducs. his paper proposes a new model of food invenory in he I sysem incorporaing qualiy loss during sorage ime. Unlike he previous research in his field, he proposed model approaches deerioraing characerisics for raw maerials and finished goods in differen ways. he remaining secions of his paper are organized as follows: Secion 2 conains a review of exising invenory models for perishable iems, while Secion 3 discusses he modeling of qualiy degradaion of raw maerials. Moreover, Secion 4 presens model for he qualiy of finished goods, or called value loss model. he complee model of an inegraed procuremen-producion sysem for fooroducs is covered in Secion 5, while he las secion, Secion 6, summarizes his paper. II. LIERAURE REVIEW In his lieraure review, wo groups of sudies on he deerioraing invenory model are discussed. he firs group includes models ha address quaniy decay as he resul of sorage ime, while he second one covers models ha deal wih value or uiliy decrease. DOI: /IJMMM.213.V1.4 17

2 Research in he firs group is based on he assumpion ha during he invenory period, he invenory level is depleed by demand and deerioraed iems. his deerioraing phenomenon was accommodaed ino an EOQ model by Ghare and Schrader [1] using a differenial equaion as can be seen from (1). di() d + I = D() (1) where I() refers o he invenory level, D() represens he demand rae a ime, and is he deerioraing rae of he iem. ark [6] exended he deerioraing models ino an inegraerocuremen-producion problem. He assumed ha only raw maerials decayed during he producion cycle. Laer, Raafa [11] developed i and used he more realisic assumpion ha he finished good deerioraed as well. Recenly, oher scholars [12] and [13] advanced he inegraed invenory model by implemening a mulishipmen policy in a muli-echelon sysem. While sudies in he perishable invenory model in he firs group were showing quaniy decrease as he resul of perishable iems, research in he second group was focusing on value and uiliy decay insead. Weiss [14] charged a non-linear holding cos on EOQ models. A few years laer, Ferguson, e al. [15] applied his model o manage perishable invenories. Similarly, Fujiwara and erera [16] viewed his problem from a uiliy perspecive. hey used boh linear and exponenial penaly cos charged for every perishable iem held in sorage as he usabiliy of he producs decayed over ime. Recenly, Blackburn and Scudder [17] developed a supply chain sraegy for perishable producs by considering fresh produce value decrease hrough a supply chain. Comparing models in hose wo groups, he approaches in second group are more suiable for fooroducs. However, hese models are sill insufficien o represen food invenory model in an inegraerocuremen-producion sysem. hey sill ignore he fac ha he raw maerials supplied for producion should no be procure separaely from finished goods producion planning. In addiion, he assumpion of an idenical deerioraing characerisic is sill used. herefore, here is a need o revisi hose models and revise hem ino a new model which is more appropriae in represening invenory model for fooroducs in he inegraed procuremen-producion sysem. q represens he qualiy facor measured depending food characerisics and is ime, which usually in monhs for more sable food and in days for more deerioraing food. Meanwhile, k is he rae of deerioraion depending on sorage environmen (e.g. emperaure, acivaion energy, gas consan) and n denoes a power facor or he reacion order [19]. he value of n influences he paern of he qualiy loss as described by Fig. 1. Fig. 1. Qualiy degradaion illusraion of fooroducs [18]. For n=, or called zero order reacion, he qualiy decreases linearly over ime as represened by line A in Fig.1. Alernaively, for n=1, or called firs-order reacion, he qualiy degrades exponenially as illusraed by line B a he same figure. Based on he phenomena in his figure, he invenory model of raw maerials accommodaing qualiy loss will be developed. a b c Invenory I Qualiy Δq r q max q q min r Cos because of qualiy loss d r C r III. MODELING HE QUALIY DEGRADAION OF RAW FOOD MAERIALS As explained in Secion 1, in his paper, he qualiy degradaion in raw maerials is approached differenly wih ha in finish goods. An ineresing approach on accommodaing qualiy degradaion in producion has been proposed by Rong, e al. [18]. hey employed qualiy loss funcion model o describe qualiy degradaion of food during disribuion ime. A quaniaive approach, called kineic model, is adoped o represen he qualiy loss of raw food maerials. In his model, he qualiy of he iems degrades depending on environmen and ime of sorage as illusraed by (2). dq d = kqn (2) Fig. 2. he relaion beween invenory, qualiy and cos of raw food maerials. Generally, he majoriy research in deerioraing invenory assumed ha during he shelf life period, he qualiy of he iems is consan. his assumpion, however, ignore he fac, which is shown in Fig. 1, ha he food qualiy degrades during sorage ime; he longer he iems are sored, he more heir qualiy degrade. his degradaion could affec he qualiy of final producs and could lead o a higher cos for mainaining produc qualiy. herefore, hese issues need o be addressed carefully in deerioraing invenory model o provide a more realisic model in presening food characerisic. he relaion beween qualiy, quaniy, ime 18

3 and cos is illusraed by Fig. 2. In Fig. 2a, invenory (I) is depleed only by demand (d r ). Moreover, all invenoried iems are in heir maximum qualiy (q max ) a he beginning of he procuremen cycle (=). However, by he ime, as can be seen from Fig. 2b, he qualiy of raw maerial linearly degrades during he period, +d r, called q(). Every single iem which suffers from he qualiy loss will be charged by qualiy cos C which linearly increases over ime (Fig. 2c). I means ha, he longer iems sored in he sorage, he higher cos of qualiy. hus, adaping Fujiwara and erera [16] approach, he cos of he raw maerial qualiy loss (L) during one replenishmen cycle ( r ) can be represened by (3). L = r Cd r q() d IV. MODELING VALUE DEERIORAION OF FINISHED FOOD RODUCS Generally, in realiy, cusomers realize ha he qualiy of fooroducs deerioraes over ime. Alhough cusomers may no have direc access o examine he qualiy of food producs, hey can judge hem from he producs remaining lifeime by seeing he producs bes before dae (BBF). In his siuaion, cusomer prefer o buy producs wih longer remaining lifeime or laer BBF which are judged as fresher [2]. siros and Heilman [21] repored ha cusomers willingness o pay (W) decrease as he produc s lifeime ges closer o is BBF. I means ha even hough a produc is sill in is shelf-life period, he value of he produc could loss. his value loss needs o be handleroperly as i can influence companies sales benefi. he relaion beween benefi and remaining lifeime is illusraed by Figure 3. In Fig. 3, benefi b is a linear funcion of remaining lifeime. In his case, is come from shelf life SL minus sorage ime S. If is equal o SL, which means here is no S or S =, hen manufacurer will ge maximum benefi (). Oherwise, if is equal o cusomers minimum requiremen of produc s remaining life ime min, manufacurer will gain no benefi. B() Benefi (3) A = subsiuing (5) o (4) leads o (6). b() =. min (5). SL SL min S () (6) min Equaion (6) shows ha since he SL and min are fixed and given, he lengh of sorage ime or S becomes he only facor which reduces benefi b. In oher words, he longer he iems are sored in he sorage, he more hey will lessen he benefi. V. HE ROOSED MODEL FOR QUALIY AND VALUE DEGRADAION IN AN INEGRAED ROCUREMEN-RODUCION SYSEM In his secion, he qualiy loss of raw maerial and he value degradaion of finished goods will be inegraed ino an inegraerocuremen-producion sysem. he ineracion beween boh deerioraion ypes will affec he invenory policy, namely, he producion cycle, raw maerial ordering and frequency of he delivery of finished goods. he bes value of hose decision variables will lead o he companies maximum profi. his proposed model will use he following noaions and assumpions Noaion d r : Raw maerials demand rae (d r = ) : Finished goods demand rae ( > ) : roducion rae m : Raw maerials ordering frequency n : Finished goods delivery frequency o : Ordering cos s : Se up cos a : Delivery cos h r : Raw maerials holding cos h p : Finished goods holding cos C : Cos of qualiy loss r : Raw maerials replenishmen cycle p : roducion run lengh : roducion cycle ime S : Sorage ime SL : roduc shelf life min : Cusomers requiremen of minimum d : Delivery cycle of finished good : roduc remaining shelf life where = SL - S : Company s maximum benefi when = SL or S = b() : Company s benefi depending B(,m, : Company s oal profi n) min =SL-S SL Remainning shelf life () Fig. 3. he relaion beween shelf life, remaining shelf life and sales benefi [adaped from 2]. Equaion (4) shows he linear correlaion beween benefi b and remaining life ime. b() =. + A (4) If is equal o min, hen b( min ) will be equivalen o zero. Consequenly, he value of A (consan) will be equal o (5). Assumpions 1) he rae of demand anroducion is consan during cycle ime where > 2) he qualiy degradaion of he raw food maerial is consans (n=) 3) he deerioraion of he value of he finished goods during sorage ime ( S ) is consan 4) he shelf life of raw maerials is se o be longer han he replenishmen cycle ( qmin sl ) 5) No shorage or backlog is allowed he characerisic of his sysem is illusraed by Fig

4 Fig. 4a shows ha he raw maerial fulfills he producion demand d r in baches m during he producion run ime p. he oal cos per uni ime for raw maerials C r consiss of ordering cos, holding cos and cos of qualiy loss which are hen divided by producion cycle. he shaded area of he riangle figure represens he oal invenory of raw maerials during, which is equal o ½q r p. Since q r is idenical o /m and p is he same wih /, as a resul he oal invenory of raw maerial is equivalen wih mp. Adjusing Eq. 3 and combining i ino ordering cos and holding cos is equivalen o he oal cos of raw maerials per uni ime (7). C r (, m) = 1 +Cd r om + h r 2 dp mp 2 m q r d (7) b = Sn = n 1 + (2 n) (9) n Max B. n SL min n 1 N n n=1 (1) (2 n) + n Finally, he manufacurer s oal profi, B(, m, n), which is equal o oal benefi b minus boh oal cos of raw maerials C r and finished goods C p is represened by (11). B, m, n = 1 SL min. N n=1 om + h r 2 SL min n 1 n + n 2 m + mcd r mp q r d 2 n Qp Finished roducs nqp an +s + h p 2n 2 n + n 1 (11) b 3qp Sn Equaion 11 shows ha inegraing he resul of deerioraion of raw maerials and finished goods affecs he value of he invenory policy (, m, n). herefore, ignoring hese deerioraing characerisics may lead o less han bes decision in managing perishable iems such as fooroducs. 2qp S3 a qr 1qp S1=q/p 2q/p d r r = p/m S2=d=/n 3q/p Raw maerials p=dp./ Fig. 4. he behavior of he I sysem. On he oher hand, finisheroducs figure (Fig.4b) shows ha he producion rae is higher han cusomers demand rae and causes invenory of finished goods (represened by shaded area). In addiion, he finished goods deliver o reailer using muli-shipmen delivery policy[18]. Hence, he oal cos of finished goods (8) is composed by delivery cos per uni ime, se up cos and holding cos per uni ime. C p (, n) = an +s + h p 2n 2 n + n 1 (8) In addiion, as menioned before in Secion VI, he sales benefi depends on he produc s remaining shelf life (6). In his case, is equal o produc shelf life SL minus sorage ime S (Fig.4b). S is defined as compleion ime of he produc (in bach) minus he ime when he produc sar o be produced. For firs bach or n=1, S is equal o q p /p and for n=2, S is equal o d or /n. he mahemaical funcion o express he sorage ime for n bach is represened by (9). Subsiuing his funcion o (6), leads o oal benefi b (1) VI. CONCLUSION A new model for I sysem has been developed in his paper. he model is more appropriae for fooroducs for several reasons. Qualiy degradaion and value loss, which are he main characerisics of perishable food, have been addressed in he model. he differen qualiy degradaion impacs on he invenory of wo perishable iems, eiher raw food maerials or finished fooroducs, have been considered. herefore, his model is more realisic in represening he food invenory in I sysem. In addiion, he mahemaical model of he objecive funcion (he company s oal profi) has been developed o examine he observed sysem. hree decision variables, namely, he producion cycle (), raw maerials ordering frequency (m) and he finisheroduc delivery number (n) are idenified and need o be opimized for he I s maximum profi. However, here are some limiaions in his research waiing for he fuure research. Firs, he proposed model only considers food invenory problems a manufacuring level or known as a single-sage perspecive, while managing food is very complex and need o be viewed from an inegraed supply chain or muli sage perspecive. Second, in fooreservaion heory, he qualiy loss acually can be conrolled by adjusing he emperaure, so his is anoher imporan facor o be considered. Finally, a consan qualiy degradaion (n=) has been assumed in he model, while in fac, some food has an exponenial qualiy degradaion or n=1 [9]. herefore, for fuure developmen, i is expeced o be able o revise hese limiaions o a more represenaive food invenory model. 2

5 ACKNOWLEDGMEN his work was suppored by he Ausralian Governmen Overseas Aid rogram (AusAid). REFERENCES [1] S. K. Goyal, "An inegraed invenory model for a single produc sysem," Operaional Research Quarerly ( ), vol. 28, pp , [2] S. K. Goyal and S. Deshmukh, "Inegraerocuremen-producion sysems: Areview," European journal of operaional research, vol. 62, pp. 1-1, [3] S. Goyal and S. Deshmukh, "Inegraerocuremen-producion sysem in a jus-in-ime environmen-modelling and analysis," roducion lanning and Conrol, vol. 8, pp , [4] W. Lee, "A join economic lo size model for raw maerial ordering, manufacuring seup, and finished goods delivering," Omega, vol. 33, pp , 25. [5] J. Gusavsson, C. Cederberg, U. Sonesson, R. van Oerdijk, and A. Meybeck, "Global food losses and food wase," Food and Agriculure Organizaion of he Unied Naions, Rom, 211. [6] K. S. ark, "An inegraeroducion-invenory model for decaying raw maerials," Inernaional Journal of Sysems Science, vol. 14, pp , [7] F. Raafa, "Invenory sysems of age-independen perishable iems subjec o on-going deerioraion," Oklahoma Sae Universiy, [8] H. Rau, M. Y. Wu, and H. M. Wee, "Inegraed invenory model for deerioraing iems under a muli-echelon supply chain environmen," Inernaional Journal of roducion Economics, vol. 86, pp , 23. [9] D. R. Heldman, "2 - Kineic models for food sysems," in Food reservaion rocess Design, ed San Diego: Academic ress, 211, pp [1]. Ghare and G. Schrader, "A model for exponenially decaying invenory," Journal of Indusrial Engineering, vol. 14, pp , [11] F. Raafa, "Invenory model for a sysem wih monoonically increasing decay of raw maerials and a decaying single finished produc," Inernaional Journal of Sysems Science, vol. 19, pp , [12] J. F. Jong and H. M. Wee, "A near opimal soluion for inegraed producion invenory supplier-buyer deerioraing model considering JI delivery bach," Inernaional Journal of Compuer Inegraed Manufacuring, vol. 21, pp , 28. [13]. C. Yang and H. M. Wee, "An inegraed muli-lo-size producion invenory model for deerioraing iem," Compuers and amp; Operaions Research, vol. 3, pp , 23. [14] H. J. Weiss, "Economic order quaniy models wih nonlinear holding coss," European Journal of Operaional Research, vol. 9, pp. 56-6, [15] M. Ferguson, V. Jayaraman, and G. C. Souza, "Noe: An applicaion of he EOQ model wih nonlinear holding cos o invenory managemen of perishables," European Journal of Operaional Research, vol. 18, pp , 27. [16] O. Fujiwara and U. L. J. S. R. erera, "EOQ models for coninuously deerioraing producs using linear and exponenial penaly coss," European Journal of Operaional Research, vol. 7, pp , [17] J. Blackburn and G. Scudder, "Supply chain sraegies for perishable producs: he case of fresh produce," roducion and Operaions Managemen, vol. 18, pp , 29. [18] A. Rong, R. Akkerman, and M. Grunow, "An opimizaion approach for managing fresh food qualiy hroughou he supply chain," Inernaional Journal of roducion Economics, vol. 131, pp , 211. [19] A. Kramer, F. E. Bender, and S. Sirivichaya, "A generalized heory on rae of qualiy loss in foods," Inernaional Journal of Refrigeraion, vol. 3, pp , 198. [2] M. L. Enrup, H. O. Günher,. Van Beek, M. Grunow, and. Seiler, "Mixed-Ineger Linear rogramming approaches o shelf-life-inegraelanning and scheduling in yoghur producion," Inernaional Journal of roducion Research, vol. 43, pp , 25. [21] M. siros and C. M. Heilman, "he effec of expiraion daes and perceived risk on purchasing behavior in grocery sore perishable caegories," Journal of Markeing, pp , 25. Gusi Fauza received he bachelor and maser degree in indusrial engineering from Andalas Universiy and Insiue echnology of Bandung Indonesia. Currenly, she is a h.d. suden of he School of Engineering in Universiy of Souh Ausralia. Research in supply chain managemen, specifically invenory models, is her main ineres. Now, she is working in invenory models for perishable iems, especially food, from supply chain managemen perspecive. Yousef Amer holds a h.d. in mechanical and manufacuring engineering from he School of Engineering, Universiy of Souh Ausralia. Currenly he is a rogram Direcor in he School of Engineering Universiy of Souh Ausralia. He has 18 years experience in auomaion, manufacuring, operaions, logisics and supply chain managemen in various firms in Adelaide, boh global and local. His research ineress include simulaion-based Lean Six-Sigma and Design for Six-Sigma, Arificial Inelligence, Manufacuring Sraegy and echnology, Susainabiliy in roduc and Service developmen, Lean and Green Supply Chain Modelling, Opimisaion and Simulaion and Susainable Nano-manufacuring. He aims o develop links and collaboraion wih indusry o foser relevan and innovae research. He has published books and many papers in academic journals, including Inernaional Journal of roducion Economic and Inernaional Journal of roducion Research, Journal ribology Inernaional, and Inernaional Journal of Roboics and Compuer Inegraed Manufacuring. Sang Heon Lee received he h.d. degree in Sysem Engineering from Ausralian Naional Universiy. He is a senior lecurer in he School of Engineering, Universiy of Souh Ausralia. His main research ineress are in he area of Close-loop supply chain, discree-even sysem and fuzzy logic conrol and neural neworks. He has published many papers in academic journals, including Inernaional Journal of roducion Economic, Inernaional Journal of roducion Research, Journal ribology Inernaional and Inernaional Journal of Roboics and Compuer Inegraed Manufacuring. 21