Mixed Integer Linear Programming model for Crude Palm Oil Supply Chain Planning

Transcription

1 IOP Conference Series: Maerials Science and Engineering PAPER OPEN ACCESS Mixed Ineger Linear Programming model for Crude Palm Oil Supply Chain Planning o cie his aricle: Pasuka Sembiring e al 2018 IOP Conf. Ser.: Maer. Sci. Eng View he aricle online for updaes and enhancemens. his conen was downloaded from IP address on 05/03/2018 a 09:59

2 4h Inernaional Conference on Operaional Research (IneriOR) IOP Conf. Series: Maerials Science and Engineering (2018) doi: / x/300/1/ Mixed Ineger Linear Programming model for Crude Palm Oil Supply Chain Planning Pasuka Sembiring 1, Herman Mawengkang 1, Hendaru Sadyadharma 2, F. Bu ulolo 1, Fariana 3 1 Deparmen of Mahemaics, Universiy of Sumaera Uara 2 Universiy HKBP Nommensen, Medan, Indonesia 3 Malaikulsalah Universiy, Lhokseumawe, Aceh, Indonesia hmawengkang@yahoo.com Absrac. he producion process of crude palm oil (CPO) can be defined as he milling process of raw maerials, called fresh frui bunch (FFB) ino end producs palm oil. he process usually hrough a series of seps producing and consuming inermediae producs. he CPO milling indusry considered in his paper does no have oil palm planaion, herefore he FFB are supplied by several public oil palm planaions. Due o he limied availabiliy of FFB, hen i is necessary o choose from which planaions would be appropriae. his paper proposes a mixed ineger linear programming model he supply chain inegraed problem, which include wase processing. he mahemaical programming model is solved using neighborhood search approach. Keywords: Opimizaion, Crude Palm Oil, Mixed Ineger programming, Supply Chain, Neighborhood Search. 1. Inroducion Jha Crude palm Oil (CPO) indusry could belong o a business which needs a nework sysem, as his produc is no an end-produc. he nework sysem which performs he funcions of procuremen of maerials, processing hese maerials ino inermediae and finished producs, and he disribuion of hese inermediae/ finished producs o cusomers, is called supply chain sysem. All hese faciliies are used for fulfilling a cusomer reques. he challenges of supply chain are o produce he righ producs, in he righ quaniies, a he righ place, a he righ ime and a appropriae cos. Due o he complexiy of decision making process in supply chains, i is necessary o use modeling echniques ha can help idenify and implemen sraegies for designing high performance supply chain neworks [10, 13, 14]. he main reasons o use model for he decision making process are large scale naure of he supply chain neworks, hierarchical srucure of decisions, randomness of various inpus and operaions, and dynamic naure of ineracions among supply chain elemens [10]. Opimizaion model has become a high echnology in supply chain planning and managemen [4, 5, 7]. Nasiri [6] presened he modelling of an inegraed he supply chain sysem which involve raw maerial suppliers, several plans, disribuion cenres, warehouses and cusomers. Piewhongngam [11] analysed more complicaed case for he inegraed supply chain. hey considered he supply chain case which involved muliple feed mills, muliple planaion, and muliple producs. impe and Kallrah [2] addressed a mixed ineger linear programming model, which inegrae producion, disribuion and Conen from his work may be used under he erms of he Creaive Commons Aribuion 3.0 licence. Any furher disribuion of his work mus mainain aribuion o he auhor(s) and he ile of he work, ournal ciaion and DOI. Published under licence by Ld 1

3 4h Inernaional Conference on Operaional Research (IneriOR) IOP Conf. Series: Maerials Science and Engineering (2018) doi: / x/300/1/ markeing and involved plans and sales poins. heir paper describes how o cover he relevan feaures required for he supply chain managemen along wih a muli-sie producion nework. Dumrongsiri [1] proposes he producion planning of palm oil and he capaciy planning of palm oil processing plans in hailand. He creaes a mixed ineger linear programming model for he inegraed producion planning. Chungsiriporn [9] use a nonlinear programming model for CPO producion planning wih minimizaion of waer consumpion a he milling process. However hey only consider he opimizaion process o ge he CPO. Anoher CPO producion planning which consider only a he milling process is discussed in Amelia [12]. hey consider fuzzy logic approach o provide a simpler mechanism in order i would be possible o find he relaionship beween he processing variables and he amoun of CPO and palm kernel losses. Suksa-ard and Reaweewan [3] develop an opimizaion model in s supply and demand sysem for a CPO producion planning. heir model is o decide which marke of CPO should be seleced, and also o find ou how much demand should be served in he seleced marke. Sadyadharma [8] presen a muli-obecive opimizaion model for a susainable producion planning of CPO considering uncerainy in he reliabiliy of financial risk. 2. Problem Descripion he producion process of crude palm oil (CPO) can be raced as he milling process of fresh frui bunch (FFB) ino end producs palm oil. he process usually hrough a series of seps producing and consuming inermediae producs. hese FFB, inermediae and end producs (CPO) are necessarily o be invenoried, allowing one o produce and consume hem a differen momens and raes in ime. I should be noed for palm oil he ime o keep FFB in invenory is very shor. We consider a CPO milling company who own milling facories, however he company does no have is own palm planaion. In order he company would be able o produce CPO from is millings, i needs o buy FFB from I public palm planaions. he siuaion is hus he same as in he wo-echelon supply chain sysem. he managemen needs o decide from which palm planaion o serve he milling facory and hen o pu he CPO ino invenory (warehouse) aferward o deliver he CPO o he k cusomers. 3. Mahemaical Model According In his case, he CPO companies is o decide opimally 1. From which palm planaion he FFB should be bough 2. Quaniy of FFB o be bough from he chosen palm oil planaion 3. Quaniy of CPO o be produced 4. Quaniy of CPO o be delivered o each cusomer 5. Quaniy of Wase produced in he milling process such ha o minimize he overall operaional coss. here are several assumpions are necessary o be considered.. 1. FFB are always available from palm oil planaions, 2. he demands of CPO from cusomers are deerminisic, 3. Ou of sock never occur. Noaions o be used. Decision variables x i Quaniy of FFB (on) o be bough from planaion I for milling in ime period y Quaniy of CPO (on) o be produced a milling in ime period z k Quaniy of CPO (on) o be delivered from milling o cusomer k in ime period v Quaniy of liquid wase (on) produced afer he milling process in milling in ime period w Quaniy of solid wase (on) produced afer he milling process in milling in ime period 2

4 4h Inernaional Conference on Operaional Research (IneriOR) IOP Conf. Series: Maerials Science and Engineering (2018) doi: / x/300/1/ i A binary variable which is 1 if FFB for milling is bough from planaion I and zero oherwise Parameers i ransporaion cos (Rp.) from planaion I o milling per kilomeer d i k Disance (km) from planaion I o milling Producion cos (Rp.) a milling ransporaion cos (Rp.) o deliver CPO from milling o cusomer k Cos (Rp.) for processing liquid wase a milling i ransporaion cos (Rp.) for solid wase a milling Overall price (Rp.) o buy FFB from planaion i for milling in ime period Cm Milling capaciy (on) a milling J in ime period CP Producion capaciy (on) a milling J in ime period CAi Quaniy of FFB (on) available a planaion i I in ime period Ses are defined as follows. I denoes he se of oil palm planaions J denoes he se of CPO milling K denoes he se of cusomers denoes he se of ime period he obecive of he decision o be made is o minimize he overall operaional coss. Mahemaically he obecive funcion can be expressed as follows: Minimize ( )( d ) x y z i i i k k ii J J J kk v w i i J J ii J here are several requiremens mus be me regarding o limi he decision variables. x Cm J, ii i y J J ii J Cp x CA J, i i i ii z y k K, k J v w x J, i ii ii J n i (1) (2) (3) (4) (5) (6) (7) 3

5 4h Inernaional Conference on Operaional Research (IneriOR) IOP Conf. Series: Maerials Science and Engineering (2018) doi: / x/300/1/ x,,,, i y z k v w 0, i {0,1}, i I, J, k K, (8) Expression (2) saes ha he quaniy of FFB o be bough from oil palm planaion i I for milling J should be o he capaciy of milling J in ime period Consrain (3) describes ha he quaniy of FFB o be processed in milling J should be o he producion capaciy of milling J in ime period.consrain (4) presens ha he quaniy of FFB o be bough from oil palm planaion i I for milling J should be o he availabiliy of FFB in he planaion i I, if he planaion is chosen, in ime period Equaion (5) o sae ha he quaniy of CPO o be delivered o cusomer k K from milling J should be o he quaniy produced in milling J in ime period Consrain (6) represens he quaniy of solid and liquid wase from milling J should be he quaniy of FFB have been processed in ime period.expression (7) is o ensure ha here would be only n planaion available o supply FFB for each milling J. Consrains (8) sae he ype of decision variables. 4. Algorihm Le x = [x] + f, 0 f 1 be he (coninuous) soluion of he relaxed problem, [x] is he ineger componen of non-ineger variable x and f is he fracional componen. Sage 1. min{,1 } i* Sep 1. Ge row i* he smalles ineger infeasibiliy, such ha f f i i (his choice is moivaed by he desire for minimal deerioraion in he obecive funcion, and clearly corresponds o he ineger basic wih smalles ineger infeasibiliy). Sep 2. Do a pricing operaion v i* i* e B 1 v i i* Sep 3. Calculae Wih corresponds o d min i Calculae he maximum movemen of nonbasic a lower bound and upper bound. Oherwise go o nex non-ineger nonbasic or superbasic (if available). Evenually he column * is o be increased form LB or decreased from UB. If none go o nex i*. Sep 4. Solve B * = * for * Sep 5. Sep 6. Sep 7. Do raio es for he basic variables in order o say feasible due o he releasing of nonbasic * from is bounds. Exchange basis If row i* = {} go o Sage 2, oherwise Repea from sep 1. 4

6 4h Inernaional Conference on Operaional Research (IneriOR) IOP Conf. Series: Maerials Science and Engineering (2018) doi: / x/300/1/ Sage 2. Pass 1: Pass 2: adus ineger infeasible superbasics by fracional seps o reach complee ineger feasibiliy. adus ineger feasible superbasics. he obecive of his phase is o conduc a highly localized neighborhood search o verify local opimaliy. 5. Conclusion In his paper, we consider an inegraed supply chain producion disribuion planning faced by decision maker (DM) of a CPO milling indusry. his indusry needs o buy FFB from several oil palm planaion. Due o he limied availabiliy of FFB hen he DM has o decide from which planaions would be appropriae o mee he producion capaciy of he milling indusry. We develop a mixed ineger linear programming model for he inegraed of producion and disribuion planning problem of he crude palm oil indusry. We solve he model using a direc search approach. References [1] A. Dumrongsiri. Mahemaical model for producion, logisics and plan capaciy planning of oil palm bunches. 1 s Mae Fah Luang Universiy Inernaional Conference, [2] C. H. impe, J. Kallra, Opimal planning in large muli-sie producion neworks. Eur. J. Oper. Res. 126, , [3] Ch. Suksa-ard, M. Reweean. Opimizaion of Supply and demand balance in a palm oil supply chain, hammasa Inernaional Journal of Science and echnology, Vol. 18(2), 2013, [4] D. CARLSSON, M. RONNQVIS, Supply chain managemen in foresry Case sudies a Sodra Cell AB. European Journal of Operaional Research, 163 (2005), [5] F.. S. CHAN, K. VIKAS, Performance opimizaion of a leagiliy inspired supply chain model: a CFGSA algorihm based approach. Inernaional Journal of Producion Research, 47(3) (2009), [6] G. R. Nasiri, R. Zolfaghari, H. Davoudpour. An Inegraed supply chain producion-disribuion planning wih sochasic demands. Compuers & Indusrial Engineering, Vol. 77, 2014, [7] H. LI, M. AMINI, A Hybrid Opimizaion Approach o Configure Supply Chain for New Produc Diffusion: A Case Sudy of Muliple-Sourcing Sraegy. Inernaional Journal of Producion Research, 50 (2012), [8] H. Sadyadharma, Z. Nasuion, A. R. Maondang, Herman Mawengkang. Susainable producion planning of crude palm oil indusry under uncerainy. Inernaional Journal of Engineering Research and echnology, Vol. 2(8), 2013, [9] J. Chungsiriporn, S. Prasersan, C. Bunyakan. oward cleaner producion of palm oil mills: Par 2 Minimizaion of waer consumpion and process opimizaion. Asian Journal on Energy and Environmen, Vol. 7(1), 2006, [10] J. S. K. LAU, G. Q. HUANG, K. L. MAK, L. LIANG, Agen-Based Modeling of Supply Chains for Disribued Scheduling. IEEE ransacions on Sysems, Man, and Cyberneics SMC, 36(5) (2006), [11] K. Pewhongngam, S. Pahummakul, S. Homkhampad. An ieracive approach o opimize producion-disribuion planning for an inegraed feed Swinecompany. Inernaional Journal of Producion Economics, Vol. 142(2), [12] L. Amelia, D. A. Wahab, A. Hassan. Modelling palm oil producion using fuzzy exper sysem. Exper Sysem wih Applicaions: An Inernaional Journal, Vol. 36(5), 2009, [13] S. BISWAS, Y. NARAHARI, Obec Oriened Modeling and Decision Suppor for Supply Chains. European Journal of Operaional Research, 153(4) (2004), [14] Y. Gapal, M. Nourelfah, wo efficien heurisics o solve inegraed load disribuion and producion planning, Reliabiliy Engineering and Sysem Safey, Vol. 144, pp ,