EFFECTS OF TRANSPORTATION COST AND LEAD-TIME ON SELECTING MULTIPLE SUPPLIERS

Transcription

1 EFFECTS OF TRANSPORTATION COST AND LEAD-TIME ON SELECTING MULTIPLE SUPPLIERS by Rotchaart Krpuyapog Departmet of Logstcs Egeerg, School of Egeerg, Uversty of the Tha Chamber of Commerce, Bagkok, Thalad Emal: ABSTRACT Suppler selecto ams at determg two commo decsos, amely, whch supplers should be selected ad how much of ay partcular order should be splt amog them. To do so volves may crtera, factors ad codtos. Oe sgfcat factor s trasportato cost ad ts relatoshp to other parameters, ad partcular, vetory cost ad lead-tme. A model that cludes trasportato cost s preseted. The objectve fucto s to mmze total cost, comprsg purchasg, vetory ad trasportato. Computatoal results show that trasportato cost has a sgfcat mpact o the decsos. To determe the optmal order quatty, t has to be traded off wth vetory cost, because they coflct. I addto, lead-tme ca allow vetory cost reducto f the selected supplers have dfferet lead-tmes. Applcato of the proposed model ca offer trasportato ad total cost savg suppler selecto. KEYWORDS Suppler Selecto, Trasportato Cost, Ivetory Cost INTRODUCTION I orderg stock, a purchasg departmet selects sutable supplers ad decdes the proporto of the order to allocate to each. The buyer may assg the order ether to a sgle suppler or to multple supplers. A sgle suppler must be able to meet all codtos such as capacty, qualty ad delvery tme wthout qualfcato. If a sgle suppler caot hadle the etre order because t caot adequately meet all requremets for the order the the buyer splts the order amog multple supplers. Moreover, the buyer may be able to reduce vetory by splttg the order amog supplers wth dfferet delvery lead-tmes. Varous crtera ca be appled to evaluate potetal supplers. Dckso (1966) extracted twety-three crtera from the results of a questoare he set to purchasg agets ad maagers. He foud that qualty was the most mportat crtero, followed by delvery. Usg Dckso s crtera, Weber, Curret ad Beto (1991) revewed 74 academc papers publshed major jourals wrtte Eglsh. They foud that et prce was the most commo crtero dscussed 80% of papers. Delvery ad qualty were raked secod ad thrd by 58% ad 5% of papers, respectvely. Both surveys foud delvery was a mportat crtero; practtoers ad academc authors equally raked t. Lu ad Ha (2005) also foud delvery a sgfcat crtero for practtoers. They developed a varat of Saaty s Aalytc Herarchy Process (AHP), whch they called Votg AHP, whch maagers ad supervsors vote to rak crtera. I a case study of a furture compay, a thrd of voters voted delvery as the top prorty out of a feld of 8 crtera ad 1 subcrtera. From a operato s research perspectve, suppler selecto s a multple objectve problem. Whle total cost s prevalet objectve fuctos preseted the lterature, the costtuets of total cost vary. For example, Ghodsypour ad O Bre s (2001) o-lear teger programmg model for selectg supplers, total cost comprses aggregate prce, orderg ad vetory cost. Lao ad Rttscher (2007) developed a suppler selecto model assocated wth three objectves: total rejected tems due to qualty, total late delveres, ad total cost. Here, total cost cludes purchasg, orderg, vetory holdg, shppg ad -trast holdg cost. Most papers o suppler selecto focus solely o purchasg ad vetory cost, ad gore trasportato cost: a sgfcat cotrbutor to total cost as explaed by Aguezzoul ad Ladet (2007), Thomas ad Tyworth (2006), ad Tyworth ad Ruz-Torres (2000). Ghodsypour ad O Bre (2001) state that trasportato cost s mportat ad refer the cocluso of ther paper that total cost ther model cludes trasportato, specto, orderg ad storage costs.

2 However, ther model does ot express ay of these costs explctly. Tyworth ad Ruz-Torres (2000) studed the effect of trasportato cost o sole ad dual sourcg. They foud that trasportato costs could greatly affect choosg betwee sgle ad dual sources. A outcome of the tradeoff betwee trasportato cost ad vetory costs ad the structure of freght costs that cause hgher costs splttg orders. Kreg ad Wag (2005) proposed a model whch the total cost cluded trasportato as a fucto of delvery tme for dfferet modes of trasport. However, costrats ad optmzato techques are ot dscussed. I studyg multple-suppler selecto, Aguezzoul ad Ladet (2007) cluded trasportato cost wth total cost. Trasportato cost was based o two factors: dstace betwee supplers ad the buyer ad whether the trucks were fully lade. Trasportato cost may be sgfcat ad ca cotrbute to hgh total cost of the buyer. I addto, t affects other factors, partcular vetory cost. I ths paper, we propose a model for multple-suppler selecto that cludes trasportato cost. The objectve of the model s to splt orders amog selected supplers to mmze total cost, comprsg purchasg, orderg, holdg ad trasportato costs. ASSUMPTIONS AND NOTATIONS FOR THE MODEL As cosderato of all potetal factors ad codtos that could arse purchasg makes t extremely complcated ad dffcult to formulate a model, the followg some assumptos were made. Demad s kow ad costat over tme ad oly oe product type s cosdered Each suppler mght quote dfferet prces for the same product Each suppler has a lmted capacty The order s placed smultaeously to all selected supplers Ut prce of a order s varat of order quatty Delvery lead-tme from each suppler s kow ad costat I-trast holdg cost s ot cosdered ad o shortages are allowed Producto tme of both buyer ad supplers s ot cosdered Capacty for trasportato of each suppler s ulmted Budgetg for the buyer s ulmted Notatos of ths paper are defed as follow. Idex: = The dex dcator for supplers, = 1,, Parameters: P = Ut product prce from suppler ($) Prc = Total purchasg cost ($) F = Fxed trasportato cost charged by suppler ($) V = Varable trasportato cost from suppler ($) Trs = Total trasportato cost ($) A = Orderg cost for placg each order to suppler ($) Iv = Total vetory cost ($) h = holdg rate I avg = The average vetory level (ut) D = Aual demad that s kow ad costat (uts) d = Daly demad rate that s costat per ut tme (uts) l = Lead-tme (or delvery lead-tme) from suppler (days) c = Capacty of suppler (uts) C total = Total cost ($) Decso varables = Order quatty X = A proporto of total order quatty splt to suppler ; (0 X 1) = 1 f suppler s selected, (X 0) 0 otherwse

3 MODEL DEVELOPMENT The model s based o the buyer beg resposble for trasportato cost due to purchasg goods o a FOB (free oboard) bass. Therefore, the buyer cludes trasportato cost explctly the total cost. It accouts for lmted capacty of supplers. The model ams at mmzg total cost assocated wth purchasg, vetory ad trasportato cost, each of whch s detaled as follows. 1. Purchasg cost (Prc) s derved from summg the prce from each suppler multpled by proporto of total demad quatty splt to each suppler. Prc DPX 1 2. Trasportato cost (Trs) has two compoets: total fxed ad varable costs. Total fxed cost depeds o the umber of delveres ad fxed cost for each delvery. Whle total varable cost s calculated from proporto of total demad quatty allocated to each suppler multples by varable cost rate that s charged as total weght of order. Total fxed cost Total varable cost DF (2) 1 D 1 1 X V DX V () F Therefore, Trs D V X (4) 1. Ivetory cost (Iv) equals total orderg cost plus total holdg cost. D Iv A hp I avg 1 1 (5) The frst term s orderg cost, whch depeds o the total umber of orders. The secod term s holdg cost, whch ca be calculated from the average vetory holdg level (I avg ) descrbed Secto.1, multpled by holdg cost per tem (hp ), whch s ormally charged as a proporto of the product s prce. (1) THE AVERAGE LEVEL OF INVENTORY (I AVG ) The average vetory level deotes the holdg vetory for the repleshmet perod. It affects the amout of captal spet drectly o vetory ad o related facltes such as warehouse space, operators ad equpmet. The vetory system for ths paper, show Error! Referece source ot foud., exteds the represetato for two supplers by Lau ad Zhao (199). I Fgure 1, for multple suppler or order splttg, whe the vetory level s depleted to the reorder pot (R), the etre order s splt ad placed smultaeously wth all selected supplers, who may offer dfferet delvery tmes. FIGURE 1 INVENTORY SYSTEM

4 I geeral, s the vetory level after the order from the th suppler arrves. Therefore, the average vetory s the sum of all trapezod areas (I 1...I +1 ) uder the vetory curve dvded by the repleshmet cycle tme, T. Thus, comparg to vetory of sgle suppler (level ), t ca be see that splttg order ca allow vetory reducto, show as shaded area Fgure 1. That s: I 1I 2 I I avg 1 ; T (6) T d Hece, average vetory level for multple supplers s: X I avg dx l arg m l (7) The objectve fucto From all cost compoets, descrbed prevously at the begg of Secto, the total cost equato ca be summarzed below. C total D D X DPX F V X A hp dx l argml (8) Therefore, the estmated optmal order quatty ( * ) ca be determed from usg the partal dervatve of C total wth respect to ad the settg the output equal to 0: C total Hece, * 2D DF DA hp X 2 A F hp X 1 1 By substtutg for * C total, Eq (8), therefore, the objectve fucto of ths paper that ams to mmze total cost ca be wrtte as equato below. M Z X 1 X R d l 1 1 DX P V 2DA F hp X -dhp X l arg ml (9) (10) (11) Subject to these costrats, c, (12) ; 1 X 1 arg ml1 0 T ;, X, c, 0 ;, c are teger ad s bary decso varable The frst costrat s set to esure that allocated order quatty to each suppler does ot exceed the suppler s capacty. The secod s defed to satsfy the buyer s demad. The ext two costrats are set for o shortage ad o late delvery, respectvely. The last s a geeral compulsory codto of optmzato that o decso varable s a egatve value. (1) (14) (15) (16) A NUMERICAL EXAMPLE USING THE MODEL A umercal example s used to test the model ad demostrate the mpact of trasportato cost o suppler selecto. Three supplers suffce to ad uderstadg of the selecto of multple supplers. Presumg supplers 1, 2 ad quote product prces of $5, $6 ad $7, respectvely, ad each has a lmted capacty of 700 uts. The aual demad of the buyer s 2,880 uts ad each ut weghs 5 pouds. Demad rate s 80 uts a day. The orderg cost s $15 for each

5 suppler, whle the holdg rate s set at 20%. The buyer receves the order from suppler 1, 2 ad at 6, 5 ad 4 days, respectvely. Fxed trasportato cost s charged at the same rate of $100 for all supplers, whle varable costs deped o the total weght of product as show Table 1. The varable trasportato costs are adapted from Tyworth ad Ruz (2000). TABLE 1 VARIABLE TRANSPORTATION COSTS FOR SUPPLIER 1, 2 AND Suppler 1 Suppler 2 Suppler Weght (lbs) Cost ($/cwt*) Weght (lbs) Cost ($/cwt*) Weght (lbs) Cost ($/cwt*) , , , ,50 -, ,768 -, ,72-4, * The cwt s a hudredweght ut (1 cwt = 100 pouds) COMPUTATIONAL RESULTS AND DISCUSSIONS The results are dscussed regardg: 1) the examato of the effects of trasportato cost; 2) the selecto of supplers ad the proporto splt of the order amog them; ad ) the effects of lead-tme o suppler selecto. EFFECTS OF TRANSPORTATION COST For each suppler the effects of trasportato cost are compared for two models: the geeral suppler selecto model, gorg trasportato cost, hereafter called Ge-SPS, ad the proposed model, cludg trasportato cost, hereafter called Proposed- SPS. Ifte capacty s assumed to avod feasble solutos. Results for both models are show Table 2. For the cluso of trasportato cost are show Table. TABLE 2 RESULTS FOR GEN-SPS AND PROPOSED-SPS FOR EACH SUPPLIER Suppler 1 Suppler 2 Suppler Ge-SPS Proposed-SPS Ge-SPS Proposed-SPS Ge-SPS Proposed- SPS (uts) Prc ($) 14, , , , , , Iv ($) Trs ($) - 2, , ,128.2 C total ($) 14, , , , , , Dfferece -, , ,29.92

6 TABLE RESULTS FOR GEN-SPS ADDING TRANSPORTATION COST AND PROPOSED-SPS Suppler 1 Suppler 2 Suppler Ge-SPS Proposed-SPS Ge-SPS Proposed-SPS Ge-SPS Proposed-SPS Trs ($) 5, , , , , ,128.2 C total ($) 20, , , , , , Dfferece 2, , , I Table 2, the optmal order quatty for each suppler usg Ge-SPS s smaller tha that of Proposed-SPS. A smaller order quatty lowers vetory ad total cost. For each suppler, the dfferece row Table 2 shows the total cost for Ge-SPS s less that the Proposed-SPS, ragg from 17% to 27%. Whe trasportato cost s cluded total cost for Ge-SPS, the results chage as show Table. The trasportato cost s calculated for the optmal order quatty for each suppler. The Proposed-SPS s the same as before. However, addg trasportato cost to Ge-SPS swgs the dfferece betwee the models so that the total costs for Proposed-SPS are ow lower tha those for Ge-SPS, ragg from 5% to 14%. Small order quattes cause for Ge- SPS requres delveres to be more frequet, thereby cotrbutg to hgher trasportato cost. Comparg total cost for Ge-SPS betwee Table 2 ad Table, for supplers 1, 2 ad, t creases by 28%, 1% ad 0%, respectvely. Thus, trasportato cost affects suppler selecto. I addto, f trasportato cost s ot cosdered tally the model, the buyer has to sped more moey o trasportato ad cosequetly has a hgher total cost. Therefore, trasportato cost should be cluded the model. Results for applyg the model the selecto of multple supplers that cludes trasportato cost are preseted the ext secto. RESULTS FOR OPTIMIZING THE SELECTION OF MULTIPLE SUPPLIERS For the stuato where supplers have lmted capacty, Proposed-SPS was appled wth the am to determe whch supplers should be selected ad the optmal order quatty that should be splt amog them. The objectve fucto for ths example s formulated as equato below. M Z 1 2,880X Subject to, X c, 1to X ; 1 1 P V 22,880 A F 0.2P X P X l argml X arg m l (17) R 80 1 (20) 1 T ; l 1to (21), X, c, 0 ;, c are teger ad s bary decso varable (22) Ths mathematcal model s uses mxed-teger o-lear programmg that s ormally dffcult to be solved. Care must be take, as local optma may be foud stead of the global optmum. For the example ths paper, the 1 (19) 1 (18)

7 sample space of feasble solutos s ot too large to exceed the capacty ad soluto tme, so full search seems to be a reasoable opto to guaratee the global optmal soluto. From appled full search to assst wth computer programmg, the results are foud that the optmal order quatty of 1,111 uts, wth a splt to suppler 1 of 700 uts ad 411 uts to suppler 2. Ths causes purchasg, vetory, trasportato ad total costs of $15,471.00, $1,201.00, $5, ad $21,729.45, respectvely. Moreover, the soluto of the vetory ad trasportato costs were optmzed separately are show Table 4. TABLE 4 RESULTS OF INVENTORY (INV) AND TRANSPORTATION (TRS) COSTS OPTIMIZATION 1 2 Prc Iv Trs C total Iv optmzed , , , Trs optmzed 1, ,471 1, , , Table 4 shows that Icreasg vetory cost correlates wth decreasg trasportato cost, ad coversely. I addto, t shows the optmal order quatty for Iv optmzato of 688 uts gves a vetory cost of $556.60, whch s 54% less tha that for Trs optmzato but t causes hgher total cost. I optmzg Trs, purchasg, trasportato ad total costs are less tha for Iv optmzato, at $4,689 (0%), $2,071 (41%), ad $6,115 (28%), respectvely. Therefore, optmzg trasportato cost s better tha optmzg vetory cost, as savgs trasportato cost ca be made. However, as both costs coflct, they should be cosdered smultaeously, so they ca be traded off determg the optmum. EFFECTS OF VARIED LEAD-TIMES Lead-tme ca affect both vetory ad trasportato costs. The results of varyg lead-tmes are show Table 5. As lead-tme s vared, oly suppler 1 ad 2 are selected. Ths s possbly due to the lead-tme ot beg volved the calculato of the optmal order quatty, although t has a effect o vetory ad total costs. As stated earler, dfferet lead-tmes of suppler ca allow the buyer to reduce the vetory cost. However, such a reducto ca occur whe the selected supplers have dfferet lead-tmes: the larger the dfferece lead-tme the greater the reducto. TABLE 5 RESULTS FOR VARIED LEAD-TIMES Lead-tme (l ) 1 2 Prc Iv Trs C total , , , , , , , , , , , , , , ,79.24 CONCLUSIONS I summary, f trasportato cost s gored, the the decso for suppler selecto focuses oly o vetory cost, as t ca affect suppler selecto. I partcular, whe trasportato cost s cosdered decsos, the buyer has to balace vetory ad trasportato costs. As they affect each other, they should be cosdered smultaeously ad ot separately ad depedetly. I addto, the total cost was foud to be less f both costs are cluded. Moreover, vetory cost s lower accordace wth larger dfferet lead-tme of selected supplers. However, due to suppler selecto s multobjectve problem, takg other objectve rather tha total cost s a challegg topc for future research.

8 ACKNOWLEDGMENTS The author would lke to express apprecato to the sposorshp from the Uversty of the Tha Chamber of Commerce. I addto, she s extremely grateful to Dr Peter G Hggs, Seor lecturer of Swbure Uversty of Techology Australa, for hs revew ad edtg ths paper. REFERENCES Aguezzoul, A & Ladet, P 2007, 'A olear multobjectve approach for the suppler selecto, tegratg trasportato polces', Joural of Modellg Maagemet, vol. 2, o. 2 Dckso, GW 1966, 'A aalyss of vedor selecto systems ad decsos', Joural of Purchasg, vol. 2, o. 1, 02, pp. 5-17, Ghodsypour, SH & O'Bre, C 2001, 'The total cost of logstcs suppler selecto, uder codtos of multple sourcg, multple crtera ad capacty costrat', Iteratoal Joural of Producto Ecoomcs, vol. 7, o. 1, pp , Lau, H-S & Zhao, L-G 199, 'Optmal orderg polces wth two supplers whe lead tmes ad demads are all stochastc', Europea Joural of Operatoal Research, vol. 68, o. 1, pp , Lao, Z & Rttscher, J 2007, 'Itegrato of suppler selecto, procuremet lot szg ad carrer selecto uder dyamc demad codtos', Iteratoal Joural of Producto Ecoomcs, vol. 107, o. 2, pp , Lu, F-HF & Ha, HL 2005, 'The votg aalytc herarchy process method for selectg suppler', Iteratoal Joural of Producto Ecoomcs, vol. 97, o., pp , Thomas, DJ & Tyworth, JE 2006, 'Poolg lead-tme rsk by order splttg: A crtcal revew', Trasportato Research Part E-Logstcs ad Trasportato Revew, vol. 42, o. 4, Jul, pp , Tyworth, JE & Ruz-Torres, A 2000, 'Trasportato's role the sole- versus dual-sourcg decso', Iteratoal Joural of Physcal Dstrbuto & Logstcs Maagemet, vol. 0, o. 2 Weber, CA, Curret, JR & Beto, WC 1991, 'Vedor selecto crtera ad methods', Europea Joural of Operatoal Research, vol. 50, o. 1, pp. 2-18,