Inernaonal Conference on Mechancal, Indusral and Maerals Engneerng 2015 (ICMIME2015) 11-13 December, 2015, RUET, Rajshah, Bangladesh. Paper ID: IE-44 Opmal procuremen sraegy for unceran demand suaon and mperfec qualy by genec algorhm Md. Sanowar Hossan*, Nur-E-Zanna*, Umme Afahaune Mohana* and Md. Mosharraf Hossan* *Deparmen of Indusral and Producon Engneerng Rajshah Unversy of Engneerng and Technology, Rajshah 6204, Bangladesh E-mal: sanowar_rue05@yahoo.com Absrac Ths paper deermnes an opmal procuremen sraegy as he demand over a fne plannng horzon s known. Ths sudy consders he scenaro of supply chan wh mulple producs and mulple supplers, all of whch have lmed capacy. I s assumed ha he receved ems from supplers are no of perfec qualy. Iems of mperfec qualy, no necessarly defecve, could be used n anoher nvenory suaon. Imperfec ems are sold as a sngle bach, pror o recevng he nex shpmen, a a dscouned prce. Some crcal parameers for deermnng opmal procuremen sraeges lke maxmum sorage space for he buyer, sandard devaon of demand durng lead me he correspondng produc dependen compensaon cos are also consdered here. The whole mahemacal model s srucured and represened as lnear programmng model and was solved by an effcen mea-heursc algorhm (Genec Algorhm). Some compuaonal sudes were also carred on o prove s accepance n he real world. Keywords: Supply Chan Managemen, Invenory conrol, Genec algorhm, Ineger lnear programmng, opmal procuremen sraegy, Suppler selecon. 1. Inroducon For a mul-objecve opmzaon problem, a complee opmal soluon seldom exss, and a Pareo-opmal soluon s usually used. A number of mehods, such as he weghng mehod, assgnng prores o he objecves and seng aspraon levels for he objecves are used o derve a compromsed soluon. In general, an nvenory model nvolves fuzzness snce shorage consran and demands are no always known exacly. Furhermore a DM ofen has vague goals such as Ths prof and ROII objecve funcons should be larger han or equal o a ceran value. For such cases, fuzzy se heory and fuzzy mahemacal programmng mehods should be used [16]. Agan some researcher proposed an neracve fuzzy mehod for mul-objecve nonconvex programmng problems usng genec algorhms. Classcal nvenory models generally deal wh a sngle-em. Bu n real world suaons, a sngle-em nvenory seldom occurs and mul-em nvenory s common. In a mul-em nvenory sysem, he companes or he realers are requred o maxmze/mnmze wo or more objecves smulaneously over a gven se of decson varables. Ths leads o he dea of a mul-objecve mahemacal programmng problem. Toroslu and Arslanoglu [14] researched a genec algorhm for he personnel assgnmen problem wh mulple objecves. Whle modelng an nvenory problem, nvenory coss, purchasng and sellng prces n he objecves and consrans are defned o be confrmed. However, s seldom so n he real-lfe. For example, holdng cos for an em s supposed o be dependen on he amoun pu n he sorage. Smlarly, se-up cos also depends upon he oal quany o be produced n a schedulng perod. Durng he las wo decades, many researchers have gven consderable aenon o he area of nvenory of deerorang/defecve/pershable ems, snce he lfe me of an em s no nfne whle s n sorage and/or all uns can be produced exacly as per he prescrbed specfcaons. Recenly, Goyal and Gr [7] have presened a revew arcle on he recen rends n modelng wh deerorang ems lsng all mporan publcaons n hs area. The applcaon of conrol heory n producon nvenory conrol analyss s now-adays gradually ncreasng due o s dynamc behavor. Many research papers [Bounkel e al. [4] Kleber e al. [9] ec.] have been publshed n hs regard. Laer many researchers ulzed opmal conrol heory o oban opmal producon polcy for producon nvenory sysems where ems are deerorang a a consan rae. Opmal conrol problems usually deal wh boh objecve funcon and he consrans. The objecve funcon
s he cos funcon ha needs o be mnmzed wh respec o me, fuel, energy, ec. The consrans are usually he sysem dynamcs, he lms of he sysem saes and he conrol effor. The radonal economc order quany (EOQ) models canno be appled o solve hese ypes of producon problems. Wang e al. [13] dscussed an economc producon plan under chaoc demands o mnmze overall cos. There have been numerous publcaons on EOQ models wh fxed cos per un. Recenly, however, several papers relaxed he assumpon of he fxed cos per un for he EOQ models. Suppler selecon problem has ganed grea aenon n he busness managemen leraure and Under he busness envronmen of global sourcng, core-compeence ousourcng sraegy, supply base reducon, sraegc buyer suppler relaonshp, cross funconal purchasng program, Inerne and e-commerce and so forh, he suppler selecon decson s becomng ever mporan and complcaed decson. Basne and Leung [2] presened a model for opmal procuremen lo-szng wh suppler selecon. Mul-perod models also offer he opporuny o change supplers for a produc from one perod o he nex. Many suppler selecon models are sngle perod models. Benson [3] by nroducng capaces for he supplers, consdered a supply chan wh mulple supplers, all of whch have lmed capacy and deermned an opmal procuremen sraegy for hs mul-perod horzon. Rezae & Davood [11] provded a deermnsc mul-em nvenory model wh suppler selecon and mperfec qualy. O. Jadd e al [10] propose models he problem of suppler selecon as a mul-objecve opmzaon problem (MOOP) where mnmzaon of prce, rejecs and lead-me are consdered as hree objecves. In hs paper, a mul-em nvenory model s dscussed havng demand uncerany/lumpness as well as mperfec qualy ems. The demand uncerany s expressed n erms of he demand varaon n he lead me whch evenually causes he cos of compensaon for he organzaon concerned. Laer, a way for deermnng opmal procurng quanes from suppler along wh he selecon of supplers n a parcular perod s formulaed as an neger programmng model. Then he model s solved wh Genec Algorhm. 2. Problem formulaon The model whch s consdered here consss of mulple producs and mulple supplers havng capacy lmaon (fg.1). I s assumed ha he producs or maerals ha would be purchased from he suppler are all no of perfec qualy. Tha means some of hem may be of mperfec qualy, no necessarly defecve and would be used n anoher nvenory suaon. These mperfec qualy producs wll be sold as sngle bach a a dscouned prce pror o recevng he nex shpmen. In fg.1, s shown ha each of he supplers s provdng each of he producs. Afer recevng he producs, screenng akes place o sor ou he mperfec qualy ems. Then producon s carred ou and demand s fulflled wh he nvenores of currenly produced ones along wh he nvenores from he prevous perod. Imperfec qualy ems are also sold pror o he nex shpmen. Evenually, he unsold producs reman n he nvenory for use n nex perod. The demand over a fne plannng horzon s consdered o be known and wha needs o be deermned s he opmal procuremen sraegy for hs mul perod horzon. A suppler-dependen ransacon cos apples for each perod n whch an order s placed on a suppler. A produc-dependen holdng cos per perod apples for each produc n he nvenory ha s carred across a perod n he plannng horzon. A produc-dependen compensaon cos apples for each ype of produc due o he varaon of demand durng lead me. Also a maxmum sorage space for he buyer n each perod s consdered. In order o maxmze he oal prof, he decson maker, he buyer, needs o decde wha producs o order, n wha quanes, wh whch supplers, and n whch perods (x j). Snce mulple producs, mulple supplers, mulple perods are consdered; solvng such a large opmal problem usng convenonal mehods s que mpossble. In order o oban a populaon of soluons a GA approach s proposed o solve he problem. Assumpons & noaons Some assumpons & noaons are adoped o develop he model- O j Transacon cos for suppler j does no depend on he varey and quany of producs nvolved H Holdng cos of produc per perod s produc-dependen D Demand of produc n perod s known over a plannng horzon P j Each lo of produc receved from suppler j conans an average percenage of defecve ems b j Purchasng prce of produc from suppler j S g Good-qualy ems have a sellng prce per un S d Dscouned prce of defecve ems are sold as a sngle bach v screenng cos of produc I, W Avalable oal sorage space w Produc needs a sorage space L Sandard devaon of demand durng lead me Correspondng compensaon cos for hs varaon s consdered o be of produc C 2
New Global Tex Zhejang Zhongha Suzhou Tanyuan Tex Maranne Jackes Honey Trousers Helsnk Shrs Good ems from Perod -1 Sale Good ems Sale mperfec ems Good ems o Perod +1 Fg. 1: Behavor of he model n perod The assumpons are 100% screenng process of he lo s conduced. Iems receved, are no of perfec qualy, no necessarly defecve, kep n sock and sold pror o he nex perod as a sngle bach. Each suppler has a lmed capacy. All requremens mus be fulflled n he perod n whch hey occur: shorage or backorderng s no allowed. Also S g>s d Now, he revenue & cos erms of he model can be saed as below- Toal revenue (TR) = revenue of sellng good qualy producs + revenue of sellng mperfec qualy producs. TR = ( 1 P ) S P S......( 1) j j g j j Toal cos (TC) = purchase cos of producs + ransacon cos for he supplers + screenng coss of he producs + holdng cos for remanng nvenory n each perod + compensaon cos TC= + j b j j O jy j d + jv H ( j (1 Pj ) Dk j LC k1 k1 So, Prof, (π) = TR TC = ( 1 P ) S j j g j P S j d {......(2) + j b j jv + H j (1 Pj ) Dk ) k 1 k 1 j j L O j Y j ( C }...(3) The problem s o fnd he number of produc ordered from suppler j n perod so as o maxmze he oal prof funcon subjec o resrcons and boundary condons. Objecve funcon: Max(π)=Max[ j ( 1 Pj ) S g jpjsd jb j + O jy j { + H ( (1 P ) D ) C }]......(4) j j k k1 k1 j L j j V 3
Subjec o: k1 k 1 D w Y jk 1 P ) j ( for all, (5) k1 D k \ 0 ( 1 P ) for all, j,... (6) k \ j j j 0 1 P ) jk j k 1 j k 1 ( for all (7) D k W 0 j for all, j,..(8) The consrans (5) ndcae ha all requremens mus be fulflled n he perod n whch hey occur and shorage or backorderng s no allowed. The consrans (6) represens ha each Supplers have lmed capaces. The consran (7) represens ha he avalable oal sorage space s lmed. 3. Resuls and dscussons To solve he model and o observe how prof s maxmzed, daa are colleced from one of he repued garmen ndusres n Bangladesh namely Talsman Ld. whch s a sub-company of FCI group and s a UK-based company. Garmens of dfferen syles are usually produced by Talsman Ld. each year. Bu consderng all he syles wll make he maxmzaon problem more cumbersome and also he collecon of such a huge daa s que arduous. Thus hree parcular syles namely Maranne jackes, Honey rousers and Helsnk shrs are aken no consderaon. These producs are suppled from each of he hree supplers.e. New Global Tex, Zhejang Zhongha Prnng & Dyeng Co. Ld. and Suzhou Tanyuan. In hs paper, resul s acually represenng wha producs o order, n wha quanes, wh whch supplers and n whch perods. Tha means he resul s assocaed wh he varables j and Y j. Thus for he wo varables a nearly opmal oucome s reached such ha maxmzes he prof. The MATLAB R2012a s used wh genec algorhm beng he solver o solve he maxmzaon problem. The opons and codes ha are used for runnng he problem are menoned n appendx along wh he oher used & requred deals. Table 1: Demand n peces of hree producs over four perods Producs Plannng horzon (perods n four quarers of a year) 1 s 2 nd 3 rd 4 h Maranne jackes 330 1594 357 1461 Honey rousers 320 1977 1886 426 Helsnk shrs 405 1925 2712 653 For ha, he requred daa nclude demand, purchase prce, ransacon cos, average percenage of defecve ems, sellng prce of boh he good & defecve ems, holdng cos, screenng cos, compensaon cos for a varaon n demand durng lead me and warehouse space. Daa of hree producs.e. jackes, rousers, shrs are colleced over a plannng horzon of four perods. In hs paper, daa for only fabrcs are consdered snce ncurs 95 % of he oal cos. Demand n peces of hree producs over four perods (Table 1). Table 2: S g, S d, C, H, V, L, w for hree producs parameer Producs 1 2 3 S g $ 16.15 $ 12.5 $ 10 S d $ 9.5 $ 6.8 $ 5.75 C $ 0.80 $ 0.30 $ 0.10 H $ 2.75 $ 2 $ 2.5 V $ 0.20 $.15 $.18 L 5 pcs 5 pcs 5 pcs w 28.14 m 2 16 m 2 20.6 m 2 There are hree supplers and her prces and ransacon cos and average percenage of he defecve ems are shown n Tables 2 and 3, respecvely. In Table 4, sellng prce of good produc (S g), sellng prce of defecve produc (S d), sorage space of produc (W ), holdng cos of produc per perod (H ) and screenng cos of produc (v ) are shown. 4
Table 3: Average percenage of defecve ems for hree supplers Average percenage of defecve ems Producs 1 2 3 Maranne jackes 13 15 16 Honey rousers 12 11 14 Helsnk shrs 14 13 10 Toal sorage space, W = 3521.03 m 2 In hs secon he numercal example of he above model s solved by usng a Real Parameer Genec Algorhm. So, afer runnng he problem n MATLAB sofware, he magnudes of he varables j & Y j are obaned. The nearly opmal values of orderng frequency ( j) of he hree producs.e. jackes (Table 4), rousers (Table 5) & shrs (Table6) from each of he hree supplers a each quarer of a year s summarzed. As he model has been formulaed wh vague parameers, he decson maker may choose ha soluon whch sus hm bes wh respec o resources. A he same me he sandard devaon of lead me demand and he percenage of defecve em suppled by suppler s consdered. Table 4: Orderng quanes for Maranne jackes Jackes Perods () (=1) Supple rs (j) Table 5: Orderng quanes for Honey rousers Trousers (=2) Suppl ers (j) Table 6: Orderng quanes for Helsnk shrs Shrs (=3) Supplers (j) 1 9688 55 9 55 2 13 151 29 20 3 9935 181 8 23 Perods () 1 27 108 100 70 2 323 1576 25 9597 3 21 6498 337 9930 Perods () 1 93 10001 139 9516 2 122 9848 50 8169 3 145 171 9963 24 Here uncerany s ncorporae o he analyss by he sandard devaon of demand durng lead me.e. L. For 5% sandard devaon of demand durng lead me.e. L he correspondng resul s obaned he genec algorhm. Snce he supplers have lmed capaces, hus he quanes ha he suppler can provde are also resraned. Dependng on ha resrcon, he decson of whch suppler s seleced (Y j) n whch quarer of a year ha summarzed n (Table 7). Also mperfec qualy and compensaon cos ncorporaed o he model o fnd he acual scenaro of nvenory conrol sysem. In he able, he bnary values represen yes/no decsons. 1 for yes and 0 for no.e. 1 means o selec he suppler where 0 ndcaes hose supplers ha should no be seleced for parcular perod of a year. Thus order should be receved from suppler 1 n perods 2 and 4, from suppler 2 n perods 1 and 3, from suppler 3 n perods 1 and 2. The objecve funcon value for he concerned problem s 282518.85, whch acually ndcaes he magnude of annual prof of he concerned company. Thus he prof s deermned o be $ 282518.85. Table 7: Decson for he selecon of supplers Perods suppler 1 0 1 0 1 2 1 0 1 0 3 1 1 0 0 5
For sensvy analyss, he man parameer o be consdered n hs paper s he sandard devaon of demand durng lead me.e. L whch s he ndcaor of unceran demand. So, by boh ncreasng and decreasng he values of L wll show how has affeced he resul. For ncreased value of L ( L=10 pcs) s seen ha he orderng quanes of each produc has changed a lo. No only ha bu also he suppler selecon suaon has also changed. The prof has decreased remendously. For decreased value of L ( L=1 pcs) s seen ha he orderng quanes of each produc reman he same so do he suppler selecon suaon. The prof here has ncreased approxmaely by 42%. So, comparng he prof ndcaes ha a lle larger value of L can cause a grea loss o he concerned organzaon whle keepng as lower as possble can enlarge he prof. 4. Conclusons A mulple-producon-nvenory model wh mulple supplers s consdered n hs paper. The curren paper ams a provdng a bass of plannng and conrollng he nvenory n supply chan and unfyng he selecon of suppler for mul-producs, perod, and supplers Backloggng compensaon s one of he major consderaons of hs paper. They also face a grea problem o decde approprae supplers from mulple supplers wha producs o order, n wha quanes, and n whch perods. Bu can be possble for he decson maker (DM) o apply hs process o come o an overall verdc wh fewer hurdles. Genec Algorhm s used o solve he problem bu Fuzzy Logc solver or oher heursc approaches can also be used o solve he problem. Ths sudy consders fabrc cos of hree producs. So n fuure one may also consder accessores cos for as hgh number of producs as possble. References [1] A.B. Smh, C.D. Jones, and E.F. Robers, Arcle Tle, Journal, Vol.1, No.2, pp. 1-10, 2012. [2] Basne, C 2005, Invenory lo-szng wh suppler selecon, Compuer Operaon Research, vol.32, pp.1 14. [3] Benson, HY 2005, Opmal prcng and procuremen sraeges n a supply chan wh mulple capacaed supplers, Compuer Operaon Research, vol.32, no.1, pp.1 14. [4] Bounkel, M. 2004, Opmal conrol of a producon sysem wh nvenory-level-dependen demand, Appled Mah E- Noes, vol.5, pp.36 43. [5] Degraeve, EL 2001, The evaluaon of vendor selecon models from a oal cos of ownershp perspecve, European Journal of Operaonal Research, vol-125, pp.34 58. [6] G Kesmuller, S.M, R.K. 2000, Opmal conrol of a one produc recovery sysem wh backloggng, IMA Journal of Mahemacs Appled n Busness and Indusry, vol.11, pp.189 207. [7] Goyal, S.K. 2001, Recen rends modelng of deerorang nvenory, European Journal of Operaonal Research, vol.134, pp.1 16. [8] Jola,F.,Yazdan,S.A.,Shahanagh,K.,Khojaseh,M.A.,2011.Inegrang fuzzy TOPSIS and mul-perod goal programmng for purchasng mulple producs from mulple supplers.j. Purchasng Supply Manage.17(1),42 53. [9] Kleber, R. 2002, A connuous me nvenory model for a produc recovery sysem wh mulple opons, Inernaonal Journal of Producon Economy, vol.79, pp. 121 141. [10] O. Jadd a, S.Zolfaghar b,n, S.Cavaler (2014). A new normalzed goal programmng model for mul-objecve problems: A case of suppler selecon and order allocaon. In. J.ProduconEconomcs148(2014)158 165 [11] Rezae, Jafar & Davood, Mansoor 2008, A deermnsc mul-em nvenory model wh suppler selecon and mperfec qualy, Appled Mahemacal Modellng, vol.32, pp.2106-2116. [12] S. Blanchn, S.M, R.P, P.R. 2001, Conrol polces for mul-nvenory sysems wh unceran demand, IEEE Conference on Decson and Conrol, Orlando, FL, USA. [13] Wang, K-J, Wee, H-M, Gao, S-F & Chung, S-L 2005, Producon and nvenory conrol wh chaoc demands The Inernaonal Journal of Managemen Scence, vol.33, pp.97-106. [14] Toroslu, Y.A. 2007, Genec Algorhm for he personnel Assgnmen problem wh mulple objecves, Informaon Scence, vol.177, pp. 786-803. [15] T.Y. Wang, Y.H. Yang, A fuzzy model for suppler selecon n quany dscoun envronmens, Exper Sys. Appl. 36 (10) (2009) 12179 12187. [16] Zmmermann, H.J. 1978, Fuzzy programmng and lnear programmng wh several objecve funcons, Fuzzy Ses and Sysems, vol. 1, pp.45 5 6