Facility Location Modeling in Multi-Echelon Distribution System: A Case Study of Indonesian Liquefied Petroleum Gas Supply Chain

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1 Aceh nternatonal Journal of Scence and Technology, 2 (1): RESEARCH PAPER Faclty Locaton Modelng n Mult-Echelon Dstrbuton Syste: A Case Study of ndonesan Lquefed Petroleu Gas Supply Chan lyas Masudn ndustral Engneerng Departent Unversty of Muhaadyah Malang, ndonesa, Eal: asudn@u.ac.d Abstract -Ths paper presents odel of ndonesan LPG supply chan by openng new facltes (new echelon) takng nto account the current facltes. The objectve s to nvestgate the relaton between dstrbuton costs such as transportaton, nventory cost and faclty locaton n ndonesan ult-echelon LPG supply chan. Fxed-charged capactated faclty locaton proble s used to deterne the optal soluton of the proposed odel. n the senstvty analyss, t s reported that the trade-offs between faclty locatons and dstrbuton costs are exst. Results report that as the nuber of faclty ncreases, total transportaton and nventory cost also ncrease. Keywords: LPG supply, locaton, nventory, transportaton ntroducton The Lquefed Petroleu Gas (LPG) supply chan n ndonesa can be dvded nto four echelons as shown n Fgure 1. n the ndonesan LPG network, PERTAMNA anages the LPG supply chan fro LPG procureent fro the frst echelon (refneres) to the fourth echelon (end-custoers) of dstrbuton syste. t s also ncluded the LPG transporters n each echelon, the storage facltes and the LPG stocks (Pertana, 2007). Snce the converson progra was ruled, the LPG deand between 2008 and 2010 n ndonesa has alost doubled fro 2.6 llon etrc tonnes to 5.5 llon etrc tonnes (Potten and Partners, 2011). The current ndonesan LPG dstrbuton syste ndcates that there s LPG shortage and scarcty at the consuers end despte there s an excessve LPG producton. Pertana ( 2007) reported that t produces 0.4 llon etrc tonnes (annually) of LPG hgher than the actual deand, however, n fact the shortage and scarcty stll occurs. For exaple, the ndonesan Governent reported that n Septeber 2008, January 2009 and January 2012, the level of LPG s stocks were n a crtcal level whch ncrease the prce of LPG by 10 30% of noral prce. Therefore, the current proble of satsfyng deand s not on the level of producton but on the effcent dstrbuton syste of LPG fro the exstng refneres to the end consuers. The purpose of ths research are to develop and suggest effcent LPG dstrbuton systes takng nto account nventory and transportaton decsons whch wll prove the custoer servce and nse the overall dstrbuton cost. Fgure 1. LPG dstrbuton syste (Pertana, 2007) n ter of cobnng transportaton and nventory decsons nto locaton-allocaton n ult echelon dstrbuton syste, prevous research proved that these coponents need to be consdered n odelng dstrbuton facltes. The reason s due to hgh-dependency aong faclty locaton, nventory and transportaton decsons (Srsoponslp, 1989; Nozck and Turnqust, 2001a; Shen and Q, 2007). The plcatons of ths nvolveent to the decsons n selectng faclty locatons are ore sgnfcant when the structure of supply chan syste and the herarchy of physcal dstrbuton are ult-echelon and ult herarchy syste (Narulla, 1984). Prevous researchers consdered faclty locaton probles wth transportaton decsons or faclty locaton proble wth nventory decsons costs, however ntegraton aong the n a sultaneous ultechelon and ult-herarchy locaton-allocaton odels have not gven uch attenton (Sahn and Sural, 2007). Melo (2009) noted that ost of locaton-allocaton proble dscussed (alone or ntegrated) productons and nventory. Moreover, n ter of the structures of the echelon, t s noted that ore than 80% of locaton- 37

2 Aceh nternatonal Journal of Scence and Technology, 2 (1): allocaton research dealt wth sngle echelon structure (Sahn and Süral, 2007). Also, other research was also generally assued that the assgnents of custoers clearly follow the flow of herarchcal assgnent flow. n ter of the applcaton of ult-echelon faclty locaton-allocaton, t s noted that locaton-allocaton was appled n varous areas such as health care syste (Rahan and Sth, 2000, Okabe et al., 1997, Shen et al., 2003) and anufacturng-dstrbuton center (Ya Peng, 2011; Ya Peng and Y Zhong, 2007b; Ya Peng and Y Zhong, 2007a). However, there s a lted research n applcatons of ult echelon s locaton-allocaton proble on LPG cobnng transportaton and nventory decsons has been done prevously. Pror LPG research has focused on effcent faclty locaton based on transportaton costs (Fölsz et al., 1995; Van Roy, 1989). Ths paper odels faclty locaton-allocaton n ult-echelon consderng transportaton and nventory decsons takng nto account the exstng facltes and fnd the optu faclty locatons and custoer s allocatons. n ths research, the case study on LPG dstrbuton syste n ndonesa covers four echelons structures and consders ntra echelon supply. The nventory odel s developed based (Q, R) syste wth certan deand and servce level, whle transportaton odel s developed based on echelons nvolved fnd optu soluton based on the servce level appled n the proposed dstrbuton syste. The senstvty analyss s used to nvestgate the plcatons of the varables changes as faclty locatons, projected deand and servce level on costs assocated to developed locaton-allocaton odel. Exanng the probles of current dstrbuton syste and the lterature n optzaton locatonallocaton decsons n logstcs syste leads to desgn an optal dstrbuton syste consderng transportaton and nventory decsons. Ths study has the objectves to odel LPG s dstrbuton syste optally to prove the custoer servce by locatng optally the locaton of new facltes (regonal warehouses and feeder fllng. Then t s followed by nvestgatng the pacts of nventory and transportaton decson to locaton decson n ndonesa LPG s dstrbuton network. Materals and Methods Mxed nteger Lnear Prograng (MLP) s used to forulate the capactated locaton-allocaton odel and Branch and Bound procedures s appled to solve the proble. The data s collected fro the current ndonesan LPG dstrbuton syste whch conssts of 2 potental RWs, 52 potental FFSs and 52 FSs and 500 agents. LNGO package s used to solve the atheatcal forulaton n ths odel. The dea s to develop the Feeder Fllng Statons (FFS) located n the current Fllng Statons (FS). Proposed FFS are suppled by the Regonal Warehouses (RW) and wll feed FS and Agents. The Capactated Mult-Flows and Mult-Echelon Dstrbuton Network (CMF-MEDN) s appled n the proposed dstrbuton syste. Gven a dstrbuton network wth three dstrbuton ters n whch ter 1 represents the LPG supply fro RW (o) to FFS (), ter 2 represents the flow fro FFS () to FS (j) and the last ter represents the supply fro FS (j) to Agent (k). n addton, FFS () ay supply LPG drectly to Agent (k). Fgure 2. The proposed LPG herarchcal dstrbuton syste 38

3 39 Aceh nternatonal Journal of Scence and Technology, 2 (1): The paper odels four echelons of LPG dstrbuton syste fro RW to agent. As shown n Fgure 3, the nventory, transportaton and fxed costs are odeled together to optze RW and FFS locatons sultaneously. The locaton-allocaton odel n ths research as follows: ndex O = sets of RW O o, O = sets of FFSs, J = sets of FSs J j, k J B = sets of agents B b, p B Decson Varables W = 1 f the potental pont of for RW s located = 0, otherwse V l = 1 f the potental pont of l for FFS s located = 0, otherwse Xkl = allocaton of FS k that s suppled by FFS l Yl = allocaton of FFS l that s suppled by RW Zpl = allocaton of agent p that s suppled by FFS l Paraeters S = capacty of RW Sl = capacty of FFS l C = transportaton cost per unt dlk = dstance between FFS l and FS k dl = dstance between FFS l and RW F = fxed cost for opened RW Fl = fxed cost for opened FFS l Dlk= deand fro FS k to FFS l Dlk = deand fro FFS l to RW MnZ j o C. d k. X k C. d. Yl F. V 1 k H J o 1 k1 1 1 B Q 2 O 1 p1 1 O 1 1 J R X kl D Z Y Y D p D p B 1 k1 p1 S X k L * W Z p. Y S o. V F. w H 1 Q R 2 L. X k (1) Subject to: (2) j o (3) p (4) (5) kp (6) W 0,1 (7) V 0,1 (8) n equaton (1), the frst and second ter represent transportaton costs fro RW to FFS and fro FFSs to Agents. The thrd and fourth ter s fxed operatng cost n ter of RW and FFS decsons. The ffth and sxth expressons represent nventory costs n the opened FFSs and RWs. Equaton (2) represents FFS l deand constrant for allocaton of FS k. Equaton (3) represents RW l deand constrant for allocaton of FFS l. Expresson (4) represents FFS l deand constrant for allocaton of agent p. Constrant (5) represent regonal warehouse capacty. Expresson (6) s represents a lnk between FFS, FS and agent and equaton (7) and (8) are the nteger constrants. Results and Dscusson The optu result shows that RW 1 should be opened to cover 20 potental FFSs, 52 FSs and 52 agents cluster deand. The optu objectve s reached at teraton 83,769. The optu results also found the locatons of potental FFSs sultaneously as the extenson of FS facltes. Fgure 4 shows the potental FSs

4 Aceh nternatonal Journal of Scence and Technology, 2 (1): whch are recoended to open as FFS and the LPG assgnents fro RW 1 to FFS canddates. t s reported that the proposed dstrbuton syste of 2 potental RWs, 52 potental FFSs and 52 agents recoends to open 20 FFS canddates. A46 FS28 FS1 FS6 FS14 A1 A13 A52 FFS28 FFS1 A28 FS46 FS2 FS14 A2 A4 FFS2 A49 A48 A36 A29 FS50 FS48 FS37 FS29 FFS30 FS3 FS4 FS13 A3 A13 A14 A50 A47 A37 A30 FS50 FS47 FS36 FS30 FFS3 FS5 FS13 A5 A38 A34 FS31 FFS5 FFS32 A32 FS32 RW1 FS8 FS9 A8 A10 A33 A30 FS34 FFS9 A9 FFS33 FS33 FS6 FS10 FS12 FS15 FS17 FS19 A6 A11 A15 A17 A20 FFS11 A35 A34 A30 FS30 FS7 FS11 FS15 FS16 FS18 FS20 A10 A7 A12 A16 A18 FFS35 FS35 FS21 FS38 FS40 A17 A21 A22 A40 A38 FS43 FS38 FFS21 A39 FS39 FFS39 FFS23 FS22 FS23 A22 A23 A43 A41 FS43 FS41 FS24 FS25 A24 A25 FFS43 FFS25 A42 FS42 FS18 FS26 A26 A44 FS46 FS44 FFS26 FFS44 A45 FS45 FS18 FS27 A18 A19 A27 FFS27 A51 FS51 A25 A26 FFS51 A52 FS52 Fgure 3. Recoended FFSs and LPG assgnent The locatons of potental RW, FFSs, FSs and agent for the odel of 2RW-52FS-52A n the optal result can be shown n Fgure 3. The fgure shows the LPG dstrbuton network fro RW 1 to agent clusters. t s shown that the potental FFSs supply LPG to FSs and A. The LPG assgnents ndcate that soe FSs could be suppled by ore than one potental FFS. For nstance, the LPG deand of FS 14 s suppled by both FFS 1 and 2. Ths also occurs n the agent level that soe agent clusters are suppled by one or ore facltes. The output of the optal soluton reported that the costs assocated to the proposed dstrbuton are lower than the assocated costs n the exstng dstrbuton syste. Table 1 presents the gap of the assocated costs between the optal outputs of the proposed the exstng dstrbuton syste. t s noted that there s US$ llon savng per year of total cost by applyng the proposed dstrbuton syste. t s followed by nventory cost that reduces by 11 per cent per year. Table 1. Assocated dstrbuton costs n optal vs exstng dstrbuton syste Cost te Exstng dstrbuton Optal soluton Gap (US$ llon/year) (US$ llon/year) (US$ llon/year) Fxed cost nventory cost Transportaton cost 4,941 4, Total cost 5,149 5, The plcatons of Faclty Adjustent Based on the results, the nuber of potental faclty affects exponentally to total costs n dfferent nuber of FFS canddates. t s ndcated that the outputs of ths research are consstent wth prevous research reported that there s a relatonshp between faclty locaton decsons and nventory and transportaton costs 40

5 Aceh nternatonal Journal of Scence and Technology, 2 (1): (Nozck and Turnqust, 1998, 2001a).The locaton adjustent tres to copare the changes of FFSs locatons that pact on the LPG allocaton fro regonal warehouse and ther LPG allocatons to FSs and agent clusters. The plcatons of faclty adjustent to assocated costs of locaton-allocaton odel are shown n Fgures 4a-4d. Fgure 4a shows the trade-off between the adjusted nuber of FFSs and the nuber of LPG shortage (tonnes per year) occurs n echelon 3. t s shown that the nuber of opened faclty pacts on the nuber of LPG shortage n the dstrbuton syste. The shortage s calculated by coparng total exstng deand n echelon 3 and LPG allocaton fro opened FFSs to FSs. The fgure ndcates that the ore facltes are recoended to open; the less nuber of shortages n FSs. For exaple, total LPG shortages n echelon 3 and 4 reach 0 tonnes of LPG per year wth 20 FFSs and jups to 14,404 tonnes of LPG shortage per year n 18 FFSs. Fgure 4a. Nuber of FFS vs. shortage Fgure 4b. Nuber of FFS vs. nventory cost Fgure 4c. nuber of FFS vs. transportaton cost Fgure 4d. FFS nuber vs. total cost The senstvty analyss results show that there s a trade-off between nventory cost and the nuber of potental FFSs. n ths study, holdng nventory cost s assued as a constant value whch s US$ 138 per tonne per year. Fgure 4b presents the nventory cost based on the nuber of FFSs. t s reported that the nventory cost ncrease as the nuber of FFS ncreases. t eans that ore nventores are requred as the ore nuber of facltes are recoended to open. Conversely, the less nuber of facltes, the fewer nventores s requred to serve deands. The sgnfcant nfluence of transportaton factors n akng decsons about selectng faclty locaton has been nvestgated by Escalante and Maer-Speredelozz (2008) and Daskn et al. (2003). t s relevant wth the results n the senstvty analyss of ths study whch found that the trade-offs between the nuber of FFS and transportaton cost s exst. Transportaton cost s calculated along the echelons wth dfferent nuber of FFS opened n the dstrbuton syste. Total transportaton costs tend to ncrease as the nuber of potental FFS ncreases. These costs are calculated based on the volue of LPG transported to echelon 2 and echelon 3 and dstance between facltes. The fnal results revealed that the ore FFSs operate n the syste, the hgher expenses for transportaton costs. For nstance, by openng 9 FFSs n the proposed dstrbuton syste, total transportaton cost reach US$ 3,076 llon per year and ncreases sgnfcantly by per cent to US$ 4,871 llon as the nuber of FFSs ncrease by 6 FFSs. Total costs n ths research s deterned by totalng varable costs nvolved n the odel such as fxed costs, nventory and transportaton costs. The output of the odel ndcates that total costs n the odel ncrease sgnfcantly as the nuber of potental FFS ncreases (see Fgure 4d). For nstance, total cost of the proposed 41

6 Aceh nternatonal Journal of Scence and Technology, 2 (1): dstrbuton syste reach US$ 3,076 llon when 9 FFSs are opened and top up to US$ 5,042 llon as 20 FFS are recoended to open n the proposed dstrbuton syste. Servce level The uses of the servce level are coon n producton-dstrbuton and locaton-allocaton probles. Pror research usng dfferent levels of servce n the locaton-allocaton proble was carred out by Jeffery, Butler and Malone (2008) and Mranda and Garrdo (2009). n ths senstvty analyss, an nvestgaton of the changes of servce level at echelon 4 s ade to explore the plcaton to the proposed dstrbuton odel. The changes of deand fulfllent rate are odfed fro constrant nuber 4: B p1 1 Z dr. p D p dr = deand fulfllent rate for echelon 4 The results show that there are sgnfcant plcatons of the servce level changes on the global optal, the potental faclty locatons and LPG allocatons fro the potental regonal warehouse to agents. Consequently, the costs nvolved n the odel such as fxed cost, transportaton and nventory also changes. The followng sectons explore the plcatons of LPG allocaton rate (servce level) adjustent n echelon 4 on assocated dstrbuton costs. The adjustent of the proporton of LPG allocaton to echelon 4 has the plcatons on total shortages n the dstrbuton syste. Fgure 5a. servce level vs. shortages Fgure 5b. Servce level vs. total cost There s trade-off between the changes of echelon s servce level and total shortage n the dstrbuton syste. t s noted that the ncreasng servce level n the echelon 4 lead to ncrease total shortage n the dstrbuton syste (Fgure 5a). The plcaton of the allocaton adjustents also occurred on total cost. Ths plcaton s caused by the changes of the LPG allocaton fro the potental FFS to FS and agent. Fgure 5b descrbes the plcaton of servce level on total dstrbuton costs. t s noted that the hgher reducton of servce level at echelon 4 results a hgher total dstrbuton costs. For nstance, n 80 per cent servce level n echelon 4, total dstrbuton costs reach US$ 4,474 llon per year. Conclusons A new dstrbuton syste wth drect and ndrect LPG supples fro the potental FFS canddates to FSs and agents clusters has been proposed. A capactated four echelons locaton-allocaton odel has been presented by ntegratng fxed, nventory and transportaton costs. The proposed locaton-allocaton odel has been developed as xed-nteger prograng wth the objectve to nze total dstrbuton costs and constraned by capacty, deand n each faclty and supply-deand lnk between facltes at each echelon. Our concluson s that the ntegraton of transportaton and nventory costs has a sgnfcant plcaton on total costs whch s the objectve of ths locaton-allocaton proble. The result shows that a regonal warehouse and 20 potental FFSs need to be opened for the proposed dstrbuton syste for the optal soluton. Coparng to the exstng dstrbuton syste, t provdes better custoer servce level wth the lower dstrbuton cost. References Daskn, M.S., Snyder, V.L., and Berger, T.R. (2003) Faclty locaton n supply chan desgn, Workng Paper No , Departent of ndustral Engneerng and Manageent Servces, Northwestern Unversty, Evanston, L. Escalante, R. and Maer-Speredelozz, V. (2008) Selectng faclty locatons and transportaton for ultnatonal corportaon supply chans. Proceedng of ndustral Engneerng Research Conference, Vancouver May CteSeer:

7 Aceh nternatonal Journal of Scence and Technology, 2 (1): Fölsz, F., Mészáros, C. and Rapcsák, T. (1995). Dstrbuton of gas cylnders. European Journal of Operatonal Research, 87(3): Jeffery, M., Butler, J.R. and Malone, C.L. (2008). Deternng a cost-effectve custoer servce level. Supply Chan Manageent: An nternatonal Journal, 13(3): Melkote, S. and Daskn, M.S. (2001). An ntegrated odel of faclty locaton and transportaton network desgn. Transportaton Research Part A: Polcy and Practce, 35(6): Melo, M. T., Nckel, S. and Saldanha-Da-Gaa, F. (2009). Faclty locaton and supply chan anageent - A revew. European Journal of Operatonal Research, 196(2): Mranda, P.A. and Garrdo, R.A. (2009). nventory servce-level optzaton wthn dstrbuton network desgn proble. nternatonal Journal of Producton Econocs, 122(1): Narulla, S.C. (1984). Herarchcal locaton-allocaton probles: a classfcaton schee. European Journal of Operatonal Research, 15(1): Nozck, L.K. and Turnqust, M.A. (1998). ntegratng nventory pacts nto a fxed-charge odel for locatng dstrbuton centers. Transportaton Research Part E: Logstcs and Transportaton Revew, 34(3): Nozck, L.K. and Turnqust, M.A. (2001a). nventory, transportaton, servce qualty and the locaton of dstrbuton centers. European Journal of Operatonal Research, 129(2): Nozck, L.K. and Turnqust, M.A. (2001b). A two-echelon nventory allocaton and dstrbuton center locaton analyss. Transportaton Research Part E: Logstcs and Transportaton Revew, 37(6): Pertana. (2007). Annual report 2007, Pertana, vewed 21 Noveber 2011, < Accesed on 12 Deceber Pottens, E. (2007). LPG ndonesa, bg plans, bg probles. LPG n World Markets. Rahan, S. and Sth, D. K. (2000). Use of locaton-allocaton odels n health servce developent plannng n developng natons. European Journal of Operatonal Research, 123(3): Sahn, G. and Sural, H. (2007). A revew of herarchcal faclty locaton odels. Coputers & Operatons Research, 34(8): Shen, Z.J. and Q, L. (2007). ncorporatng nventory and routng costs n strategc locaton odels. European Journal of Operatonal Research, 179(2): Srsoponslp, S. (1989). Warehouse locaton under ultple transportaton optons. PhD dssertaton, Unversty of Maryland, Maryland. Shen, Z. J. (2006). A proft-axzng supply chan network desgn odel wth deand choce. Operatons Research Letters, 34(2006): Shen, Z.J., Coullard, C and Daskn, M.S. (2003). A jont locaton-nventory odel. Transporton Scence, 37(1): Okabe, A. and Suzuk, A. (1997). Locatonal optzaton probles solved through Vorono dagras. European Journal of Operatonal Research, 98(3): Van Roy, T. (1989). Mult-level producton and dstrbuton plannng wth transportaton fleet optzaton. Manageent Scence, 35(12): Vdal, C. J. and Goetschalckx, M. (1997). Strategc producton-dstrbuton odels: A crtcal revew wth ephass on global supply chan odels. European Journal of Operatonal Research, 98(1): Ya-Peng, Z. (2011). Mult-node dstrbuton centre locaton odel under anufacturng and reanufacturng syste. Appled Mechancs and Materals, 39(2011): Ya-Peng, Z. and Y-Zhong, D. (2007). Optzaton odel for closed-loop logstcs network desgn n anufacturng and reanufacturng syste. Proceedng of Servce Syste and Servce Manageent nternatonal Conference n Chengdu, Chna June EEE: