Robust planning model for logistics relief warehouses locating based on Monte Carlo simulation model

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1 2015, TexRoad Publcaon ISSN: Journal of Appled Envronmenal and Bologcal Scence Robu plannng model for logc relef warehoue locang baed on Mone Carlo mulaon model Farzaneh Mahdan 1, Meyam Feredun 2, Kamran Shahanagh 3 1 Suden, Deparmen of Indural Engneerng, Iran Unvery of Scence and Technology, 2 Maer of cence uden, Deparmen of Indural Engneerng, Iran Unvery of Scence and Technology, 3 Aan profeor, Deparmen of Indural Engneerng, Iran Unvery of Scence and Technology, ABSTRACT Receved: July24, 2015 Acceped: Sepember 31, 2015 Thouand loe her lve due o naural daer uch a flood and earhquae every year wh huge maeral co and moral damage nflced o many of he regon; o he preence of plan o repond uch even eem crucal. The curren paper repreen he ue of mahemacal modelng and robune approach n cr managemen. Moreover, he problem may be caued by he cr n he real world n relef offerng ha are evaluaed n he form of cenaro. Scenaro are produced and choen ung Mone Carlo mulaon robune logc ued for dealng wh he uncerany problem due o he unceran naure of cenaro. I ee o deermne he locaon of warehoue wh repec o he range of warehoue coverage baed on he vehcle. Gven he co of warehoue locang and drug ranporaon n relef newor, he problem ee o mnmze he co of warehoue eablhmen and ranporaon co n he regon.the reul of he model olvng ha been analyzed n he form of a numercal example, ndcang he mporance of locang problem. KEYWORDS: cr managemen, locang and allocaon, robu opmzaon, mahemacal programng, Mone Carlo mulaon 1. INTRODUCTION Accden and naural and unnaural daer caue lo of lfe and propery n he world, and our counry no excepon o h rule, bu he lo of lve ha are rreverble counry' man ae he wor par of he ragedy. The need for cr managemen n order o reduce he mpac of hee even and he managemen of cr uaon ncreangly ncreae. Cr an unable condon n need of rapd and mmedae relef. On he oher hand, cr managemen nclude all acve o preven and mgae he effec of he cr and he rapd reurn o normal condon. Rapd and mmedae relef afer a naural daer uch a an earhquae, flood or hurrcane o ave he lve of accden vcm one of he mo fundamenal addreed n he hadow of he rgh raegy elecon, mely decon and he ably o mplemen hee decon before, durng and afer he even, a a requremen and can reduce harmful and damagng effec of hee even o an opmal level. Accordng o ude, Iran one of he op 10 accden-prone counre of he world. Unforunaely Iran a hgh r of 31 ype of realzed daer n he world ou of he 40 one and pecfcally earhquae, flood and drough daer had nflced more damage no our counry. Accordng o Earhquae Engneerng Reearch Inue, nearly 83% of Iran populaon lvng n area wh hgh and very hgh earhquae r and 50% ae a flood r [1]. Therefore he need for appled reearch n he feld of relef logc managemen durng he cr o mnmze damage obvou. Obvouly, appled reearch on ue relaed o he relef logc n naural daer caue ncreae n nave n projec and fndng be polce and he mo effcen mehod and echnologe conderng he condon of he counry. So far, varou model were developed a ule n cr managemen decon-mang proce and locang problem one of hem. In fac, h ype of reearch am o provde a comprehenve model o locae he be relef po before and afer he cr, boh n erm of afey and effcency of performance and derable n erm of co, a well. Facle locang problem locae plehora of facle (reource) n order o mnmze he co o afy ome of he demand (from cuomer) gven he conran. Locang heory fr wa formally propoed n 1909, when Alfred Weber faced wh he problem of locaon a warehoue n order o mnmze he dance beween he ore and cuomer [2]. The curren arcle re o conrol he uaon and approprae decon mang n cr le he earhquae ung locang problem. A number of warehoue are conruced n h arcle each equpped wh four ype of dfferen equpmen and all hould compleely cover all demand pon and each pon drug demand hould be only and only afed by a Correpondng auhor: Farzaneh Mahdan, Suden, Deparmen of Indural Engneerng, Iran Unvery of Scence and Technology, Tehran, Iran farzane_mahdan73@yahoo.com 819

2 Mahdan e al.,2015 warehoue and equpmen whch ervce may be on land or ar. The curren paper, ung Mone Carlo mulaon framewor and cenaro defnon aume ha poble ha ome of he land roue face wh damage durng accden wh rouble n ranporaon hu nended o defne he cenaro model o ge cloer o he real world condon. 2- LITERATURE REVIEW Evdence ndcae ha he number of accden and naural daer occurrng annually around he world n need of effcen plan and managemen o reduce he damage. Accordng o ude conduced by he Aocaon of IFRC, world have wneed 7184 ncden from 2000 and 2009, among hem are aac on he World Trade Cener n 2001, he unam n Indonea n 2004, Karna Hurrcane n 2005, he earhquae n Ha n The IFRC emaed economc loe caued by hee even equal o mllon dollar a well a lve loe of 1,105,352 people and wh 2,550,272,267 njured. Alo, accordng o Mon Cher ncden n 2010 caued more han deah and economc loe of more han 130 bllon. Thee ac reflec he hgh probably of cr and he need o develop beer raege o reduce uch loe [2]. Torga ude conduced n 1971 among he fr acve o locae emergency equpmen n whch he coverage wa modeled and a mehod of lnear programmng wa developed for olvng [3]. Many ude on he relef logc n he cr (emergency chan) are focued on he mplemenaon of logc acve wh he am of opmzng nvenory hrough he exng drbuon newor. For example, Kno (1987) propoed a lnear model conderng food ranporaon problem wh he am of mnmzng ranporaon co and he maxmum amoun of food delvery o he affeced area [4]. He, n he ubequen nvegaon n 1988 propoed a lnear model of plannng for vehcle wh he am o maxmze he delvery of food a a cr managemen problem [5]. However, ranpor loe and her reamen compared o relef good have been le of concern and focu. Brocorne e al (2003) and propoed clafed locang of emergency vehcle n he form of dynamc and queung model. Ahal (2006) uded warehoue opmal locaon for placng fr ad before he cr [6]. Sepanov (2007) propoed a defne mul objecve model for he drbuon n demand pon wh repec o co, repone me and coverage. The arcle dcued decon mang on where o evacuae vcm and provde relef [7]. Many ude, uch a Fedrch e al. (2000) and Saabara e al.(2004) are conduced n he drbuon of relef aance hrough plannng a o mnmze repone me and maxmze coverage [8,9]. In mo ude deal goal programmng, uch a mnmzng repone me and maxmzng coverage ued. Plannng for he managemen of relef n cr uaon ofen faced wh many uncerane. In he overall clafcaon, he uncerane are of wo nd: 1) uncerany n plannng for he fuure and 2) uncerane relang o he amoun of npu parameer of he problem. Deal of he caegore are led below. Table 1. Uncerany clafcaon n cr plannng [1] Uncerany n plannng for relef managemen Deal Uncerany aocaed wh he npu parameer Uncerany n plannng for fuure need Uncerany of Even Dfferen effec n dfferen regon Cr dfferen characerc (ype, locaon, me, ze) Uncerany aocaed wh he npu parameer Uncerany of provder The lac of defnve roue Logn uncerany parameer n mahemacal model a follow: 1- Draw r and poble value 2- Facle drbuon and uncerany plannng 3- Robu opmzaon 4- The mulaed model 5- Fuzzy e Crp programmng mehod ceranly beer han ceran echnque bu becaue of ncomplee and unceran daa are ofen wh dfferen approach. Many cen have done reearche baed on he cr by mean robu opmzaon. More arcle on he problem of he cr are focued on he flow of good or he vcm and furher ude are avalable baed on boh aumpon nended. Barbarooglu & Arda (2004) developed a randomzed wo-ep framewor for ranporaon plannng n repondng phae on cr uaon under uncerany. In h udy, he reearcher developed a model preened n he paper by (Oh and Haghan, 1996) a a defnve, mul-produc and mul-ype ranpor flee. h udy 820

3 nvegaed, uncerany n he emaon of reource needed for relef good, vulnerably and poenal upply ource a well a roue reance [10]. Ja e al. (2007) propoed a ngle-purpoe facly locang model whou lmed capacy for large emergency ervce uch a ambulance or fre aon. The pobly of damage o facle wa condered zero and one.the model doe no conder nvenory level n he preparaon phae and lmed capacy of facle [11]. Chang e al. (2007) uded more logc plannng for emergency preparedne n flood condon. In h udy, flood emergency logc problem modeled a a random plannng under demand uncerany. So ha four ype of acve nended o uppor and all pon on he newor dvded no fve group.the fve group are: he recue cener bae n charge of recue operaon n he all affeced area and regonal recue cener are ub ha are developed o operae recue on her execuve auhory and uppor of demand pon n oher regon. The hrd are local recue group e ha are reponble for her mplemenaon n he regon. Two random plannng model are propoed o deermne he orage cener and he amoun of equpmen needed n he recue and recue equpmen drbuon o help governmen agence ave reource o ha he fr model o mnmze he dance from he recue equpmen and he econd model alo am o mnmze he deploymen co and mean co of recue equpmen [12]. Mee and Zabny(2009) propoed a randomzed opmzaon model for plannng for he orage and drbuon of emergency medcal upple under he uncerany of demand and co. The man am of model wa o locae opmal orage and nvenory needed em o ore before he cr, and rreducng he r of warehoue a r of damage from earhquae cr. Afer he ar of a mulaed cr, he algorhm and hen pah o hopal o reduce ravel me were denfed [13]. Salmeron and Ape (2010) propoed an opmzaon model for plannng fundng for he acquon and poonng of relef ae. In h model, he decon of he fr age con of poonng relef upple uch a warehoue, medcal facle, re area and heler. Whle he econd age decon are o dcu logc under uncerany of demand and co. Wha no een n he model he relaonhp beween relef cener locaon (bac cover), and he pobly of falure of emergency oc of good [14]. Rawl and Turnqu (2010) propoed a mxed neger random plannng o deermne he locaon and amoun of dfferen ordered emergency good. Ther model uded ranpor newor acce under he demand and co uncerany [15]. Jabbarzadeh e al., provded a dynamc model o deermne he locaon of facle and drbuon of blood o hopal n crcal condon and ued Robu plannng model plannng due o lac of uncerany of demand n he modelng [16]. Camacho (2014) provded a wo level model for he drbuon of nernaonal aance for he humanaran logc, he relef ad from nernaonal organzaon and foregn counre amed a reducng he co of he oher counre affeced by he cr and wa followed by he drbuon of ad a effecve and qucly a poble. In h paper, he ued Sacelberg game o model wo level plannng [17]. Jeonga e al. (2014) n h paper preened a model of negraed logc ervce wh robu, r and effcacy parameer. Th model parally dvded no wo ub-raegc and operaonal model, and ude how o provde bac good and her drbuon [18]. 3- Problem defnon Due o he geographc and raegc poon of Iran and 90% of he errory beng locaed on he faul, he earhquae daer n our counry ha led o more loe. Tehran, a he raegc cy of Iran ha alway been prone o uch accden; Tehran n erm of earhquae condered among hgh r area (8 o 10 degree Mercall). Fgure 1 how ha Norh Tehran faul he large faul placed n he ouh Alborz mounan range n he norh of Tehran. Th faul ar from Lahara and Sohana o Farahzad and Hara and he We, a well. The faul n pah encompae Nyavaran, Tajrh, Zafaraneh, Ellahye and Farmanyeh. The hgh r of Tehran n he regon menoned requre cr managemen. 821

4 Mahdan e al.,2015 Fgure (1). 22 drc of Tehran faul n he norh and ouh of he cy A noed earler n h paper o develop a model o locae he area of cr managemen o locae he ecurng locaon wh he am of effecve relef wh mnmal co afer he cr. In fac, he afey requre everal equpped pon o mee drug demand. Th model ee o fnd a uable locaon for he conrucon of relef logc warehoue from he demand pon. Each bae conan a lea four ype of equpmen n dfferen number coverng he demand pon. Each ype of equpmen ha a ceran mean peed of each demand pon hould be afed n a ceran me, becaue n he real world mo of he me we do no have enough me o erve durng he cr and are o reach he dered pon n a ceran me perod. Afer deermnng wha equpmen cover wha demand pon from whch bae, deermnc model how he correcne of her performance; bu gven he unceran naure of he cr ome of he roue ued by he warehoue logc o mee he demand are faled. The Mone Carlo mulaon mulae he faled roue n Fgure 2f flowchar. Robu plannng model wa ued for unceran condon modelng afer elmnaon of he roue and he lelhood of any of hee falure. The reul of he model have been analyzed baed on a numercal example of robu plannng model plannng. Random number generaon o deermne he parameer of he problem n cerany Deermne j-h oc removed roue Problem olvng n general Ye I here a warehou e? Scenaro defnon No Exper opnon o deermne he probable faled roue xj decon varable equal o zero Generae a random number o deermne he number of all he roue down Problem olvng wh new preme Generae a random number o deermne he number of each warehoue roue down Fgure 2. Remove roue flowchar ung Mone Carlo mulaon 822

5 4- Mahemacal Model The followng a mahemacal lnear model wh objecve funcon o mnmze he co. The co con of hree, fr he co of eablhed bae and he econd relae o ranporaon vehcle and he hrd par he co of dealng wh he defc. A number of warehoue are eleced among he demand pon and he demand for a parcular drug from a warehoue afed only by one vehcle from one equpmen and warehoue. More mporanly ha meeng he need hould ae place n a ceran me pan. A ceran number of each ype of equpmen may be locaed n any bae. Three of he equpmen ou of four can mee demand hrough he land and a ype of equpmen done by ar. Moreover, locang warehoue deermned baed on he overall capacy of drug and demand n he regon. The decon varable parameer and deermnc mahemacal model wll be gven n he followng The decon varable x If he drug ype wh equpmen ype aen from he bae o he pon of demand j one and oherwe j zero. y I one when bae creaed and oherwe zero. z The ype drug amoun ha vehcle ype ae o from bae o he demand j. j Bae coverage radu for good The number of ype vehcle a bae Q The amoun of horage drug ype n demand j 4.2. Parameer F The co of orage eablhmen ' Q The amoun of he drug ored n he bae C Tranporaon co per un by he vehcle v Vehcle mean peed Tme of ervce delvery o demand pon j for drug B Increae radu of coverage for drug for each vehcle ype d The bae pon o demand j j w Penale for drug horage o he pon of demand j U Vehcle ype capacy for drug m The maxmum budge avalable for dealng wh he defc d Pon j demand for drug ype ' L The maxmum amoun of he drug ype ored n he bae e The oal amoun of drug ype 4.3. Deermnc model Mn z= f y + x.d.c + w.q j j j j.: Q e ' z Q', (14) (1) (2) 823

6 Mahdan e al.,2015 j w. Q m z = d' Q j, B., (3) (4) (5) Q' L. y, (6) M. x z, j,, (7) M. y z, j,, (8) x. d, j,, (9) j d. x j v, j,, (10) z u, j,, (11) x, y {0,1}, j,, (12) Equaon (1) repreen o mnmze conrucon and ranporaon co objecve funcon and he co of dealng wh he defc o mee he need n he area of demand. Equaon (2) repreen rercon relaed o he enre nvenory n all relef warehoue for each ype of drug. Equaon (3) repreen he orage capacy for each pecfc drug. Equaon (4) repreen rercon on fundng enrely aen no accoun for he defc. Equaon (5) repreen he equlbrum equaon of demand. Equaon (6) repreen lm o ncreae he radu of coverage for each un ncreae n ype of vehcle. Equaon (8) conran relaed o dependence x and z. Equaon (9) how he requred conrucon of orage for he allocaon of he vehcle o he depo. Equaon (10) how radu of warehoue coverage and he equaon (11) how he me lm for he average of each vehcle peed. Equaon (12) expree he capacy of vehcle and he la equaon abou bnary decon varable Scenaro model.: Mn z= f y + x.d.c + w.q j j j j Q' e, z Q',, j w. Q m z = d' Q j,, B.,, (14) (15) (16) (17) (18) (19) Q' L. y,, (20) M. x z, j,,, (21) M. y z, j,,, (22) x. d, j,,, (23) j 824

7 d. x j v, j,,, (24) z u, j,,, (25) x, y {0,1}, j,,, (26) Equaon 14 o 26 ac mlar o equaon 1 o 13 excep ha repeaed a per he cenaro and hown wh ndex. The model execued for each cenaro and he reul for each cenaro aved a c * and ued n he Robu plannng model Robu model Mn z= f y + x.d.c + w.q 0 j 0 j j.: f y + x.d.c + * w.q (1 + p) c j j j j Q' e, z Q',, j w. Q m z = d' Q j,, B.,, (27) (28) (29) (30) (31) (32) (33) Q' L. y,, (34) M. x z, j,,, (35) M. y z, j,,, (36) x. d, j,,, (37) j d. x j v, j,,, (38) z u, j,,, (39) x, y {0,1}, j,,, (40) Equaon 28 repreen a robu plannng conran ha gve he decon maer he auhory o have a pemc or opmc vew on he problem baed on he parameer p. Oher rercon are mlar o ha of cenaro lmaon. 5. The numercal example Range have been condered o varou parameer n he model due o he lac of real example n h regard hown n Table 1. The value of he parameer are deermned by random value whn h range for each olvng of he model. The mporan pon he random value ofen mae our problem lac he anwer, o we generae a number of random value, o poble o olve he problem. Table 2 and Table 3 provde ome of he parameer relaed o he vehcle and he demand, a well. 825

8 Mahdan e al.,2015 Vehcle Table 2. Range pecfed for ome parameer F Tj dj Lower lm Upper lm Table 3. Parameer condered for vehcle Mean peed ) m/h) Tranporaon co Vehcle per un capacy β : Increae he range of good Equp Equp Equp Equp Table 4. Parameer condered for he demand pon Node The co of orage Demand facly A already noed, Mone Carlo mulaon approach ha been ued o produce cenaro whch are n accordance wh he flowchar n Fgure 2, for example, a crculaon n flowchar how ha afer generang random value baed on he ep led n h flowchar x roue are deroyed durng he even. Thee roue are nended for a pecfc cenaro are d 17, d 23 24, d 12 9, d 21 9, d 7 14, d Table 3 gve he value of he cenaro problem objecve funcon for he four cenaro ha hee value are ued a parameer on he fr conran of he Robu plannng model; fnally, he model objecve funcon value 28,243 currency un and pon 1, 4 and 8 are eleced a cr bae. Table 5. Opmum oluon for he 4 cenaro problem Scenaro 1 Scenaro 2 Scenaro 3 Scenaro 4 C* Concluon and Fuure Reearch Cr managemen and epecally naural daer need o conder everal facor, many of whch are aocaed wh a hgh range of uncerany. Every manager face decon-mang under uncerany n he face of he cr uaon. Thee decon ofen mu be made a oon a poble and o mnmze he lve and fnancal loe. Robu plannng model opmzaon mehod on he allocaon of reource can be a ueful program ued agan uncerany. In h paper, a ngle-purpoe model for cr uaon of naural daer uch a earhquae gven ha am o mnmze he co of conrucon and equpmen ranporaon and deal wh he defc on he newor. Each bae equpped wh four, each wh own average rae and ceran ranporaon co. Snce he demand pon hould be me for he perod pecfed n he real world, a me aen no accoun a demand repone me o approach he problem o he real world for each pon. Robu approach ued n order o mprove he performance of he model agan unexpeced even. The reul of he Robu plannng model compared o he cenaro model reul ndcae beer performance by Robu plannng model ha delver more opmal objecve funcon. 826

9 A he end hree uggeon are propoed for fuure reearch a he followng: ung radonal mehod ha own problem nce real-world problem are large-cale, o fndng heurc and mea-heurc nnovave mehod can grealy allevae he problem of radonal mehod. Gven he mulple objecve funcon wh dfferen prore, uch a maxmum coverage, relably and mnmzng he r, me of ervce and ec. whch brng he problem cloer o realy. ome pon demand may no fully be covered due o problem n he real world, hu he ue of ceran model or Fuzzy heore, ang no accoun he paral coverage, can mae he model more complee. REFERENCES [1] hp:// [2] Yavar, A. and Feredun, M and Shahanagh, K (2014) developng model for degnng relable mulmodal daer newor ndan journal of cence reearch, 4(3), [3] Torega, C. Swan, R. ReVelle, C. & Bergman, L. (1971). The locaon of emergency ervce facle. Operaon Reearch, 19(6), [4] Kno, R. (1987). The logc of bul relef upple. Daer, 11(2), [5] Kno, R. (1988). Vehcle Schedulng for Emergency Relef Managemen: A Knowledge Baed Approach. Daer, 12(4), [6] AR. Ahal (2006).Invenory pre-poonng for humanaran operaon. [7] Sepanov, A. & Smh, J. M. (2009). Mul-objecve evacuaon roung n ranporaon newor. European Journal of Operaonal Reearch, 198(2), [8] Fedrch, F. Gehbauer, F. & Rcer, U. (2000). Opmzed reource allocaon for emergency repone afer earhquae daer. Safey Scence, 35(1), [9] Saabara, H. Kajan, Y. & Oada, N. (2004). Road newor robune for avodng funconal olaon n daer. Journal of ranporaon Engneerng, 130(5), [10] Barbarooglu G, Arda Y. A wo-age ochac programmng framewor for ranporaon plannng n daer repone. The Journal of he Operaonal Reearch Socey 2004; 55(1):43e53. [11] H. Ja, F. Ordóñez, M. Deouy, (2007) Soluon approache for facly locaon of medcal upple for large-cale emergence, Compuer & Indural Engneerng, Vol. 52, No. 2, pp [12] M. S. Chang, Y. L. Teng, J. W. Chen, (2007) A cenaro plannng approach for he flood emergency logc preparaon problem under uncerany, Tranporaon Reearch Par E, Vol. 43, pp [13] H. O. Mee, Z. B. Zabny, (2010) Sochac opmzaon of medcal upply locaon and drbuon n daer managemen, Inernaonal Journal of Producon Economc, Vol. 126, No. 1, pp [14] Salmero n and Ape, (2010) Sochac Opmzaon for Naural Daer Ae Prepoonng Producon and Operaon Managemen Socey. [15] C. G. Rawl, M. A. Turnqu, (2010) Pre-poonng of emergency upple for daer repone, Tranporaon Reearch Par B: Mehodologcal, Vpl. 44, No. 4, pp [16] Jabbarzadeh, A, Fahmna, B and Seurng, S, (2014) Dynamc upply chan newor degn for he upply of blood n daer: A robu model wh real world applcaon Tranporaon Reearch Par E. [17] Camacho, V (2014) A b-level opmzaon model for ad drbuon afer he occurrence of a daer Journal of Cleaner Producon 3(2), [18] Jeonga, and Hongb, J and Xec, Y (2014) Degn of emergency logc newor, ang effcency, r and robune no conderaon Inernaonal Journal of Logc: Reearch and Applcaon 5(6)