9 h nernaional Conference on Producion Research A PROCUREMENT PLANNNG MPROVEMENT BY UNG LNEAR PROGRAMMNG AND FORECATNG MODEL Ahakorn Kengpol, Peerapol Kaoien Deparmen of ndusrial Engineering, Faculy of Engineering, King Mongku s nsiue of Technology Norh Bangkok, Bangkok 8, Thailand Absrac As known ha an appropriae procuremen policy is one of indusrial compeiive advanages, an over or under invenory in procuremen sysem can significanly affec managemen in capial and sock of raw maerial. The objecives of his research, herefore, are o achieve arges of procuremen planning ha is o calculae he opimal invenory level, and o opimise he purchasing policies by applying linear programming and forecasing models, which is corresponded wih each of purchasing condiions. A he firs phase, he rend in maerial s price is analysed, hen Microsof Excel CB Predicor programme Add-ns is applied o forecas he resuls, afer ha he model is opimized by using program Microsof Excel Add-ns. Finally, he model had been esed o improve raw maerials purchasing since January 4 o June 5 (for 8 monhs), and hen compared he efficiency wih he acual purchasing. The research resuls show ha he mahemaical model can improve he raw maerials procuremen planning. Moreover, performance index in invenory policies are increased 83.33 %, performance index order quaniy in raio from Japan suppliers are increased 44.45 %, performance index supplier parnership are increased in 44.45 % and oal cos are decreased.68 %. The oher resuls, limiaions and recommendaions are also presened. Keywords: Procuremen Planning, linear programming, forecasing models NTRODUCTON An appropriae procuremen policy is one of indusrial compeiive advanages, an over procuremen can affec no only o he invenory and sorage area bu also budge spending on unnecessary procuremen works. On he oher hand, under procuremen can make lack of raw maerial which could cause inerruping coninuous process unil he produc can no be finished in ime. ome of pracical problems in raw maerial procuremen are for example, acual amoun of raw maerial is no in level as policy seing due o he procuremen saff lacks of knowledge in opimizing invenory level. As raw maerial procuremens are no in opimizaion level, he procuremen budge usually is spending higher han needed. There are some researches ha have been sudied and recommended ways o use mahemaical models o solve he procuremen problems. There are, for example, Guierrez e al. [] suggess o use Bounded/Limied nvenory model o calculae he amoun of invenory level. Marel e al. [] purpose a procuremen planning model which convers all decision making decision o mahemaical models. kouri and Parachrisos [3] aemp o improve a Coninuous Review nvenory Model from Vairakarakis [4], in order o sugges a way o se procuremen qualiies wihin limied budge by using elasiciy model. However, none of hem proposes a way o deal wih opimal invenory as well as purchasing policies. The objecives of his research are o achieves arge of procuremen planning ha is o mainain he suiable invenory level, and o achieve he purchasing policies by using mahemaical model, which is corresponded wih each of purchasing condiions. The model developed for his research has been esed in foreign raw maerials procuremen in paper indusry. The paper indusry has o use old corrugaed conainers (OCC) as main raw maerial o produce paper fiber before i can be evenually enhanced o become packaging papers. The coss of he OCC are he major facor of he paper producions and also play he main role in he producion capial. ncluding OCC invenory iself is complicaed o be conrolled e.g. lead ime and raw maerial ransporaion cos, and uni price of raw maerials are difference depending on heir sources ec.. cope of research. The daa of Foreign Raw Maerials Procuremen in paper indusry were used in his research (ingapore, Japan, Middle Eas, Ausralia and Unied Kingdom).. The improvemen of procuremen planning emphasize o mee all of policies such as he invenory level conrol policies which need o have enough of raw maerials for paper producion process minimum for 3 days and maximum for 37 days, he Japan raw maerial procuremen policy is no over han 7 percen and is no less han 6 percen of all foreign raw maerial procuremen, he capial is reduced o minimum by he conrol procuremen capial policies and parnership mainenance of supplier policies which regularly order o supplier. 3. The changing of ineres and curren were no included in he minimum capial consideraion. REEARCH METHODOLOGY N COLLABORATON WTH A FRM There are wo basic models in his research: forecasing model and linear programming model, which are collaboraed wih a paper manufacuring. The forecasing model conains single moving average, single exponenial smoohing, double moving average, double exponenial smoohing and winers mehod. The menioned model can be seen basically in a number of ex books in he field of quaniaive analysis. According o Figure : Research model, he price for daabase have o be analysed in forecasing model which have:
npu Daa Daabase Pric Forecasing Forecased Procuremen Pl Forecasing Models Procuremen Planning & nvenory Conrol Overall Receive & ock Classified by Opimum Procuremen Opimized nvenory Model Linear Programming Technique Figure : Research model. ingle Moving Average. ingle Exponenial moohing 3. Double Moving Average 4. Double Exponenial moohing 5. easonal Addiive 6. easonal Muliplicaive 7. Hol-Winers' Addiive 8. Hol-Winers' Muliplicaive The Mean Absolue Percenage Error (MAPE) is brough in o forecas fuure price ha will be used in oher models based upon minimum MAPE. The MAPE can be calculaed as followed MAPE = n = e Y Y = Real daa a ime e = residual a ime = n =,, 3,, n Y Yˆ Yˆ = forecased daa a ime For he case sudy of Paper indusry which can classify he raw maerial of hem and idenify procuremen quoa, especially for procuremen cos and procuremen ime. The hypohesis of equaion invenion for calculaion are sar from he beginning of monh (=) and he demand of presen monh (d ). The parameers for calculaion were idenified as Table Table : Variables & Parameers for Calculaion - Consumpion - d D d ingapore - Japan - J Middle Eas - Ausralia - A A A Unied Kingdom - U (),, = ingapore procuremen quaniies of presen monh, nex monh and nex wo monh, J = Japan procuremen quaniies of nex monh and nex wo monh = Middle Eas procuremen quaniies of nex wo monh A = Ausralia procuremen quaniies of nex wo monh U = Unied Kingdom procuremen quaniies of nex wo monh,, = The spare invenory level a he end of presen monh, nex monh and nex wo monh. d, d, d = The raw maerial demand of presen monh, nex monh and nex wo monh. - = The spare invenory level of pervious monh. A, A = The raw maerial quaniies ha will be in he sore for he presen monh and nex monh which are beforehand procured from Japan, Middle Eas, Ausralia and Unied Kingdom. The raw maerial pricing will be referred from he average price of raw maerial from Japan which are specified as sandard price. They are shown in Table. Table : s Parameers for Calculaion andard C C C ingapore s Japan s Middle Eas s Ausralia s Unied Kingdom s C = C +3 C = C +3 C =C +3 - C = C C J = C - - C =C +5 - - C A =C - - C U = C - ock -
9 h nernaional Conference on Producion Research C, C, C = The uni sandard price of raw maerial for presen monh, nex monh and nex wo monh. C, C, C = ingapore s uni sandard price for presen monh, nex monh and nex wo monh. C, C J = Japan s uni sandard price for nex monh and nex wo monh. C = Middle Eas s uni sandard price for nex wo monh. C A = Ausralia s uni sandard price for nex wo monh. C U = Unied Kingdom s uni sandard price for nex wo monh. From he parameer above, he minimum invenory model is explained below. Min T [ c ( ) + ( )] () i i h = ubjec o + + = d (3) Minock Maxock d + When = The period of ime =,,T (For he case sudy of his research, T maximum = ) i = The counry which deliver raw maerials i =,, n d = The raw maerials demand of period = The procuremen quaniies of period = The spare invenory level a he end of period = The sore area c h = Procuremen cos per uni. = The sorage cos per uni. Min ock = The minimum of invenory level which are calculaed from days d 3 Max ock = The maximum of invenory level which are calculaed from days d 3 The equaion models ha can solve problem of raw maerial procuremen and invenory conrol of paper indusrial can be summarized as below. c + c + c + c J + c J J + Min (7) c + c A + c U U + h + h + h ubjec o + + (8) A + = d (4) (5) (6) d () 37 d (3) 3 J + + + U + = d + + (4) d (5) 37 d 3 (6) 7,5 7,5 7,5 6 6 6 5,6 J 5,6, J, 4,, U, U.7 +.3.7.7.7 U.6 +.4.6.6.6 U (7) (8) (9) () () () (3) (4) (5) (6) (7) (8) (9) (3) (3) (3) (33) (34) + + A (35) + + + A + + J + + + U 3 REEARCH REULT (36) (37). Raw maerial quaniies from January 4 o June 5 is shown in Figure d (9) 37 d () 3 + A + = d + + ()
o c k ( d a y s ) 75 65 55 45 35 5 5 Jan - 4 F eb M aa pm a J un J ua ug e p O c N od e Monh Jan - F 5 eb M aa pm a J un Acual No Forecas - Conrol Raio No Forecas - No Conrol Raio Forecas - Conrol Raio Forecas - No Conrol Raio Policy of Maximum ock Policy of Minimum ock Percenage.4...8.6.4.. No Forecas - Conrol Raio.98 No Forecas - No Conrol Rai.4 Forecas - Conrol Raio.68 Forecas - No Conrol Raio.39 %RC Figure : Quaniy of raw maerial. Procuremen quaniy raio from Japan from January 4 o June 5 is shown in Figure 3..9.8.7.6.5.4.3... J a p a n Q u a n i y R a i o Jan - 4 F e b M aa pr M ay J u nj u l A u g e po c Monh N ov D ec J a n - 5 F eb M aa pr M a y Jun Acual No Forcas Conrol Raio No Forcas No Conrol Raio Forcas Conrol Raio Forcas No Conrol Raio Policy of Maximum ock Policy of Minimum ock Figure 3: Procuremen quaniy raio from Japan 3. Toal cos of procuremen from January 4 o June 5. They were classified by heir procuremens planning are shown in Figure 4 T o a l C o s ( U D ) 39,4, 39,3, 39,, 39,, 39,, 38,9, 38,8, 38,7, 38,6, 38,5, 38,4, $39,33,333 $38,99,43 $38,754,8 $39,38, $39,48,53 Acual No Forecas - Conrol Raio No Forecas - No Conrol Raio Forecas - Conrol Raio Forecas - No Conrol Raio Figure 4: Toal cos in procuremen 4. ummary of performance index by improving procuremen planning is shown in Figure 5 Percenage.. 8. 6. 4... Acual 55.56 33.33 6.67 No Forecas - Conrol Raio.... 94.44 66.67 No Forecas - No Conrol Raio. Forecas - Conrol Raio 77.78 Forecas - No Conrol Raio 6.67 AE RAE RAE Figure 5: ummary of performance index by improving procuremen planning 5. Percenage of reduced cos (%RC) is shown in Figure 6 Figure 6: Performance index of cos Reducion 6. Reduced cos afer change he invenory level policies for 4- days, -9 days, 3-37 days, 38-45 days and 46-53 days respecively. The comparison beween he resul and oal acual cos is shown in Figure 7 Percenage of Reduced Cos 3..5..5..5. -.5 -. -.5 -. ock 4 - days ock - 9 days ock 3-37 days Policy of nvenory Level Acual ock 38-45 days ock 46-53 days Figure 7: Reduced cos afer changing 4 REEARCH UMMARY invenory level The efficiency by improving procuremen planning o achieve he organizaion policies are shown in Table 3 Table 3: ummary of performance index by mproving Procuremen Planning The acual procuremen. Know he price of raw maerial before and conrol for procuremen raio. Know he price of raw maerial before bu do no conrol for procuremen raio 3. Predicion for he price and conrol for procuremen raio 4. Predicion for he price bu do no conrol for procuremen raio AE RAE RAE RC 6.67 33.33 55.55-66.67.98 94.44..4 77.78.68 6.67.39 Remarks: AE = ock Achievemen Efficiency
9 h nernaional Conference on Producion Research RAE = Japan Quaniy Raio Achievemen Efficiency RAE = uppliers Relaion Achievemen Efficiency RC = Reduced Cos The resuls above are summarised as below:. The predicion resuls of uni price of raw maerial which use 8 predicion echniques and compare beween each period of planning. The 8 predicion echniques are ingle Moving Average, ingle Exponenial moohing, Double Moving Average, Double Exponenial moohing, Winers Mehod (Addiive), Winers Mehod (Muliplicaive), Classical Decomposiion (Addiive) and Classical Decomposiion (Muliplicaive). From all of 8 predicion periods, The bes predicion resul is Winers Mehod (Muliplicaive), he second was Winers Mehod (Addiive) and Exponenial moohing was he hird. The reason is Winers Mehod is designed for seasonal daa which has similar endency.. According o he acual foreign procuremen siuaion of he purchaser saff which have o predic he uni price of raw maerial and follow he policies of he organizaion by conrol he procuremen raio for 6-7% of raw maerial procuremen. The research resuls show ha he mahemaical model can improve he raw maerials procuremen planning. Moreover, performance index in invenory policies are increased 83.33 %, performance index in order quaniy raio from Japan are increased 44.45 %, performance index in supplier parnership are increased 44.45 % and oal cos are decreased.68 %. The research resuls can be summarized ha he mahemaical model can deliver he procuremen planning based upon several arges as he policies which were se in he same ime and can reduced he oal capial more han.5%. 3. The applied of mahemaical model was used o improve he raw maerials procuremen planning. Then i can increase he performance index o achieve he invenory quaniy policy for all of esed cases, can increase he performance index of parnership beween suppliers for all of esed cases and also can decrease he procuremen cos for all of esed cases, however, i can increase he performance index in raio procuremen conrol only when increase he condiion of raio procuremen conrol because if decrease he condiion of raio procuremen conrol hen he mahemaical model end o decrease he procuremen cos. 4. To know he price before placing orders or o predic he uni price of raw maerial accuraely he firm is able o conrol he raw maerial procuremen raio and reduces cos effecively. 5. The order quaniy raio conrolled from Japan has an effec o he abiliy of invenory conrol bu do no effec o he abiliy of supplier parnership. 6 REFERENCE [] Guierrez J., e al.,, A New Characerizaion for The Dynamic Lo-ize Problem Wih Bounded nvenory, Compuers & Operaions Research, 3, 383-395. [] Marel A., Diaby M., Bocor F., 995, Muliple ems Procuremen Under ochasic Nonsaionary Demands, European Journal of Operaional Research, 87, 74-9 [3] kouri K., Papachrisos.,, A Coninuous Review nvenory Model, wih Deerioraing ems, Time-Varying Demand, Linear Replenishmen Cos, Parially Time-Varying Backlogging, Applied Mahemaical Modeling, 6, 63 67 [4] Vairakarakis G.L.,, Robus Muli-em Newsboy Models wih A Budge Consrain, Producion Economics, 66, 3-6 5 CONCLUON AND RECOMMENDATON This research consrucs he mahemaical models by specified he ime period of procuremen planning and invenory quaniy checking wih he frequency of monh per imes. However, he acual work siuaion which can be changed all he ime for he price of raw maerial, he ime of ransporaion and invenory quaniies, can effec he frequency of procuremen planning period and evenually can cause higher procuremen coss.