STRATEGIES OF DELAY DELIVERY AND CONTROLLABLE LEAD TIME TO OPTIMIZE THE TOTAL COST IN SUPPLY CHAIN CONSIGNMENT INVENTORY

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1 Internatonal Journal of Producton Technolog and Management (IJPTM) Volume 10, Issue 1, Januar-June, 2019, pp. 9 18, Artcle ID: IJPTM_10_01_002 Avalable onlne at Journal Impact Factor (2019): (Calculated b GISI) ISSN Prnt: and ISSN Onlne: IAEME Publcaton STRATEGIES OF DELAY DELIVERY AND CONTROLLABLE LEAD TIME TO OPTIMIZE THE TOTAL COST IN SUPPLY CHAIN CONSIGNMENT INVENTORY Professor, Mechancal Engneerng Department Vaageswar College of Engneerng Karmnagar, Telangana State, INDIA ABSTRACT Ths paper descrbes about two strateges n consgnment nventor based suppl chan wth controllable lead tme and delang last delver comprsng a two level suppl chan nvolvng sngle vendor and mult buers. Ths model would gve mnmum jont total expected cost of the strateges nvolvng vendor and buer, smultaneousl to optmze quanttatve decson varables. Numercal examples are presented to demonstrate the beneft of the proposed strateges and the effect of changes on the cost and parameters are studed. Ke words: consgnment nventor; suppl chan; jont total expected cost; dela delver; controllable lead tme; crashng cost. Cte ths Artcle:, Strateges of Dela Delver and Controllable Lead Tme to Optmze the Total Cost n Suppl Chan Consgnment Inventor, Internatonal Journal of Producton Technolog and Management (IJPTM), 10(1), 2019, pp INTRODUCTION The global compettve and technolog has brought a bg challenge to the enterprses to meet the customer needs n the wa of servce and acceptable costs. In order to fulfl the customer needs, the entrepreneurs have to see the network optmzaton to customer mode network busness models wth the am of mnmzng cost and maxmzng servce wthout compromsng the qualt of customer need end product. Snce the nventores can cost approxmatel between 8 to 20 percentage of total product value, hence an effectve controllng of nventor s crtcal and most essental. The new demand ponted towards reducton n product total manufacturng cost, whch n turn ponted towards ther supplers and ths formed a chan reacton. Eventuall n ths aspect nventor s one of the most wdel dscussed area to mprove effcenc. Hence the vendor plas a ke role n the mantan the nventor. Snce 1980, the populart of Vendor Managed Inventor (VMI) has grown wth 9 edtor@aeme.com

2 the ntroducton of ths concept n Wal-Mart, Procter & Gamble, and later ntated b other companes ncludng Campbell Soup, Johnson & Johnson and b European frms. To reduce nventor cost n busness, Suppl Chan (SC) has become a sutable tool. Suppl chan s the process of plannng, mplementng, and controllng the actvtes as effcentl as possble. From the manufacturng perspectve, suppl chan echelon conssts of storng raw materals, work-n-process nventor, and fnshed goods from pont-of-orgn to pont-of-consumpton. Hence, nventor plas a ke role along the suppl chan echelons. Houlhan [1] credted for beng frst to conng the term of Suppl Chan (SC) wth concepts and vewng t as a new strateg for global compettve busness decsons. Man defntons of SC have been mentoned n the lterature and n practce, although the underlng phlosoph s the same. Smch-Lev et al. [2] defned Suppl Chan as unque approach utlzed to effcentl ntegrate the varous echelons such as supplers, manufacturers, warehouse and stores, so that merchandse s produced and dstrbuted at the rght quanttes, to the rght locaton and at the requred tme n order to mnmze echelon cost, whle satsfng servce level requrements. However, most of the quanttatve models n suppl chan ssues s domnated b the framework of mult-echelon seral sstems where, a relatonshp n between a sngle vendor and mult buers are to be consdered. Consgnment Inventor (CI) s one of the most effectve approach n the suppl chan echelon nventor control strateg. Because, the approach leads to reducton of vendor nventor whch uses the buer warehouse to stock the fnshed products. In consgnment nventor, the paments for suppler nventor s not released untl goods have been sold at the consumer place. The vendor managed nventor wth consgnment nventor arrangement s one of the polc that has been observed n the automotve ndustr. It s the work of Valentn and Zavanella [3] whch has provded a prmtve foundaton for most of the later work related to ths polc. The numercal model of Bragla and Zavanella [4] wll be consdered as the base model. Moreover, Bragla and Zavanella [4] provded a comparson wth the classcal model of Hll [5,6]. Srnvas and Rao [7,8,9,10] had classfed the Consgnment Inventor strateg nto four dfferent models such as; 1). Basc Consgnment Inventor model, 2). Consgnment Inventor model wth dela delver, 3). Consgnment Inventor model wth Informaton sharng, and wth dela delver, and 4). Consgnment nventor wth controllable lead tme strateg. The concluded that the CI polc mplementaton could be advantageous. Ths paper s structured n to four sectons: Introducton n secton I, secton II descrbes the Consgnment nventor strateg wth dela delver and controllable lead tme, secton III llustratve examples, IV tpcal results and conclusons. 2. CONSIGNMENT INVENOTY STRATEGIES In ths paper among four CI models whch has mentoned n Srnvas and Rao [7,8,9,10], the author have dscussed and made a comparatve analss usng numercal examples of two most mportant strateges of consgnment nventor namel dela delver and controllable lead tmes wth sngle vendor mult buer model n SC whch s vewed as a classfcaton of dvergent SC wth end to mult ends case. The sgnfcance of producton to demand rato s also dscussed along wth other varables edtor@aeme.com

3 Strateges of Dela Delver and Controllable Lead Tme to Optmze the Total Cost n Suppl Chan Consgnment Inventor Notatons used are summerzed below h v vendor stock holdng cost/unt/unt tme h b buer stock holdng cost/unt/unt tme Av batch set-up cost (vendor) Ab order emsson cost (buer) p vendor manufacture rate (contnuous) D product demand unts/ tme seen b the buer (contnuous) average total costs of the sstem / tme T C π L C L standard devaton of customer demand / tme buer back order cost lead-tme length for the buer lead tme crashng cost / ccle normal probablt denst functon cumulatve probablt denst functon n number of shpments /producton batch buer range z safet factor c ccle tme The followng assumptons are used one setup of contnuous revew nventor replenshment sstem for an nfnte horzon of sngle vendor multple buer buer and vendor holdng cost s ndependent of tems transported but proportonal to ts holdng of stock tme customer demand rate and the delver lead tme for each buer are contnuous wth known, statonar probablt dstrbutons, where as demand s normall dstrbuted shortages ma be allowed D 1 p n producton rate producton capact D n b n and 1 CI-k 1 k 1 < n Consgnment nventor wth dela delver (CI-k 1 ) In consgnment nventor strateg, the maxmum level of buer s nventor ma reach at an nstance durng ccle tme. One soluton offered b Bragla and Zavanella [4] s to delang the last delver to buer. The prncple assumpton s that the delaed delver s retaned b vendor untl buer s read to take the last shpment. Ths assumpton s reasonable approxmaton to realt when there s no nformaton sharng between vendor and buer. Hence t doesn t allow exceedng the maxmum lmt S n the buer s nventor. In ths stuaton, the shpments f an wth vendor must wat at vendor s place. Bragla and Zavanella [4] has consder the consgnment nventor onl for sngle vendor sngle buer. Whereas, n ths work t has been extended to sngle vendor multple buers. Consgnment nventor wth dela delver model formulaton The jont total expected cost = vendor set up cost + vendor holdng cost + buer orderng cost + buer holdng cost + shortage cost 11 edtor@aeme.com

4 Av n Ab 2 1 CI k 1 1 D D 1 TC hvc k c 2p 1 n 1 n n p 2 hb 1 1 Dc Dc j ( n k ) q n k 1 D 1 2 n p j n p ( z) L 1 p D k 1 1 hbz L (1) 1 c Iteratve analss used n CI-k step 1: set n = 1; step 2: set n +1 = n +1; step 3: set 1 k =1; step 4: compute JTEC (c, n, * * 1* * f JTEC,,, 1 k, z); c n k z JTEC c * 1* * n 1, n ( n 1), k( n 1), z( n 1) * * 1* * step 5: then c, n, k, z are the optmal parameters and the mnmum jont total expected cost * * 1* * JTEC c, n, k, z Consgnment nventor wth controallable lead tme Ths model s used a newl developed concept, the buer wll negotate wth vendor to reduce the lead tme as much as t can be possble to a pont where t s acceptable to the vendor wthout dsturbng stable producton and delver schedule. The nventor level s revewed contnuousl and f an shortages exsts ma be allowed wth full backordered. It has to be noted that the delver lead tme s null, however the batch s to be manufactured, so as to there exsts a sstem lead tme other than zero. Wth ths b addng an addtonal cost, the sstem lead tme can be controlled. Thus, the lead tme s reduced one at a tme startng from frst ndependent component because t havng mnmum unt crashng cost per unt tme, and then the second ndependent component, and so on. When the lead tme s reduced/controlled, ts correspond handlng cost for that unt tme s also reduced, but the crashng cost s added to total cost of buer. The total length of sstem lead tme whch ensures the order transt even though lead tme s crashed and shortages f an are permtted. Snce lead tme s a decson varable n ths model, the extra costs ncurred b the vendor wll be full transferred to the buer f shortened lead tme s requested ma be consdered as an nvestment n the busness. Consgnment nventor wth controallable lead tme model formulaton L wll be the lead tme wth components 1, 2, 3 whch s to be crashed to mnmum duraton, and the th component has a normal duraton b and mnmum duraton a and the controllable lead tme crashng cost per unt tme s C ; such that C 1 C 2 Cn., then L s expressed as, let L0 b 1 (2) L L C ( b a ) o j j j j1 n 1 j then, n 1 L b C ( b a ) j j j j j1 j edtor@aeme.com

5 Strateges of Dela Delver and Controllable Lead Tme to Optmze the Total Cost n Suppl Chan Consgnment Inventor the lead tme crashng cost per ccle C L s gven b 1 (3) C C ( L L) C ( b a ) C 0 L, L[ L, L ] L j1 j j j L 0 1 j1 Jont total expected cost for CI-LT model, JTEC = vendor set up cost + vendor holdng cost + buer orderng cost + buer holdng cost + shortage cost + lead tme controllable crashng cost v b 2 CI LT 1 C hv c 2 p 1 n T 1 A n A c D hb Dc Dc j Dc n 1 D 1 2 n p j n p ( z) L C hb z L c c L 1 1 (4) where, ( z) ( z) z[1 ( z)], ( z 1) = f[(z), (z)] The total cost functon s optmzed subjected constrants of total shpments, shpment quantt, lead tme, crashng cost. Iteratve analss used n CI-LT step 1: set n = 1, step 2: set n +1 =1, step 3: fnd JTEC* (c, n, L, z) step 4: n1 n11 and n2 n2 1 repeat the teraton tll the jont total expected cost s mnmum wth correspond to all the constrants. 3. ILLUSTRAIVE EXAMPLES The nput data used here s refer to Ben-Daa and Raouf [11], Bragla and Zavanella [4], Ouang et al.[12], Srnvas and Rao [7,8,9,10] hv= 4/ unt/ear, hb= 5/unt/ear, D 1,2.10 = 1000, 1300, 800, 1000, 1500, 600, 1200, 1500, 1000, 800 unts/ear, (p/d ) rato = 3.2, 1,2,..10 = 44.72, 50, 35.7, 30, 30, 20, 30, 30, 30, 20, A v = 400/setup, A b = 25/order, = 50/unt. The lead tme components are L (=0,1,2,3) = 14,10.5,7,5.25 and ts correspondng crashng cost are C (L=0,1,2,3) = 0,1.4, 5.6, The results show that wth more buers n the suppl chan echelon the total cost savngs are ncreased for sngle vendor mult buer (through Fgures 1-7). The controllable lead tme component s reduced up to mnmum lead tme,.e., thrd lead tme component. Whereas n case of sngle vendor sngle buer, the controllable lead tme component s reduced up to second lead tme component [Srnvas and Rao, 10] edtor@aeme.com

6 % of savng n cost when shftng from CI-k to CI-LT JTEC Fgure 1. JTEC varaton n CI-k and CI-LT The total expected cost would be less n CI-LT model when compare to CI-k model (Fgure 1) and t reduces whle ncreasng buer maxmum stock, t shows that for the gven strateg can make more customer choce avalablt. In CSP-LT model, the JTEC s senstve to lead tme components and crashng cost reducton components. It s n the nterest of vendor and buer for choosng the structure of lead tme reducton and ts correspondng crashng cost components as well as ts lead tme components. 25 CI-LT CI-k S max. ( buer maxmum nventor ) CS- LT Buers Fgure 2. Percentage of savng n cost whle movng from CI-k to CI-LT Whenever the CI-k strateg shfted to CI-LT dependng on the requarement the Fgure 2 shows the benefts that would be obtaned. In these two models the maxmum buer stock vares closel but the mnmum buer nventor wll have approxmatel 40 to 50 % dfference whch contnues wth ncrease n buer sze (Fg.3), whereas the vendor nventor wll have more n CI-k model compare to CI-LT model (Fg.4) and dfference also have mpact on customer demand fulflment edtor@aeme.com

7 dela delveres Avg. vendor nventor Avg. buer nventor smn. Smax. Strateges of Dela Delver and Controllable Lead Tme to Optmze the Total Cost n Suppl Chan Consgnment Inventor CI-k CI-LT Buers Fgure 3. Maxmum and Mnmum stock levels CS-k CS-LT Bbuers Fgure 4. Varaton of average vendor and buer nventores whle ncreasng buers CI-k Buers Fgure 5. Dela delveres n CI-k model In dela delver model, the delveres shall reduce whle ncreasng the buer n the echelons (Fg.5), and hence sgnfcantl reduces the average buer nventor wth fve eght buer and further wth ncrease n buers. Hower the shpments n CI-k model ncreases and 15 edtor@aeme.com

8 Shortage quantt shpments delvered to buers where as n CI-LT model the shpments stablzes from buer 6 onwards (Fg.6). It s due to the stablzaton of buer max. and mn. stock CI-k 5 CI-LT Buers Fgure 6. Number of shpment delvered transported from vendor to buers The Fg.7 depcts clearl that the shortage quantt s more n dela delver model compare to controllable lead tme and also a lttle varaton would take place whle ncreasng buer sze CI-k CI-LT Buers Fgure 7. Effect of shortage quantt whle ncreasng buers The curved lne called effcent fronter shown n Fg.8 s generated b teratvel that mnmzes the suppl chan cost on the maxmal p/d rato. The pont A corresponds wth a p/d rato of 3.2 at whch lowest JTEC cost occurs for all consgnment nventor models wth stablzaton. If an suppl chan strateg on the effcent fronter s undomnated n the sense that there s no strateg exsts whch s at least as good wth respect to JTEC. Moreover, t s found from the research artcles of [3,4,12,13,14,15] that the had consdered producton to demand rato as 3.2, but the could not menton the reason for choosng such value. In ths paper the author has explaned n detal regardng ths capact constrant p/d rato and ts nfluence on total cost. At p/d rato 3.2, the JTEC gettng stead state (Fg. 8) edtor@aeme.com

9 % of savng n JTEC Strateges of Dela Delver and Controllable Lead Tme to Optmze the Total Cost n Suppl Chan Consgnment Inventor A p / D rato Fgure 8. Effcent fronter effect of p/d rato on the percentage of savngs 4. CONCLUSIONS Ths artcle s focused on the development and analss of consgnment nventor of suppl chan to mnmze jont total costs of vendor and buers n stochastc envronment. The consgnment nventor management polc wth controllable lead tme has proven to be most sutable for facng new Suppl Chan challenges wth stochastc demand for sngle vendor mult buer. The developed models are not onl make tradeoff but wll also enable decson makers to deal wth erratc judgments thoroughl. Hence concluded that CI-LT model s preferable when uncertant n customer demand and lead tme s more and when uncertant n demand and lead tme s less CI-IS-k 1 model s preferable. The total cost of controllable lead tme model depends on lead tme components and crashng cost components. The fxaton of producton to demand rato s found to be crucal and s ver senstve to total costs apart from other varables. An extensve analss has been made n ths case and fnall fxed at p/d rato of 3.2. The proposed model gves cost savngs of approxmatel 9% compare to [3]. It s observed that % of cost savngs ncreases as number of buers ncreases. The CI-LT strateg could be best sutable for low or md-prce tems and when the demand s stochastc n nature. REFERENCES [1] Houlhan, J. B, Internatonal suppl chan management, Int. J of Phscal Dstrbuton and Materals Management, 1985, vol.15, pp: [2] Smch-Lev, D., Kamnsk, P., and Smch-Lev, E. Desgnng and Managng the Suppl Chan: Concepts, Strateges, and Case Studes, 2000, McGraw-Hll, New York. [3] Valentn, G. and Zavanella, L. E., The consgnment stock of nventores: ndustral case and performance analss, Int J Prod Econ, 2003, vol.81-82, pp [4] Bragla, M. and Zavanella, L.E, Modelng an ndustral for nventor management n Suppl Chans: the Consgnment Stock case, Int J Prod Res, 2003, vol.41, No.16, pp [5] Hll, Roger. M, The sngle-vendor sngle-buer ntegrated producton-nventor model wth a generalzed polc, Eur J Oper Res, 1997, vol.97, pp [6] Hll, Roger. M, The optmal producton and shpment polc for a sngle-vendor snglebuer ntegrated producton nventor problem, Int J Prod Res 1999, vol.37, pp edtor@aeme.com

10 [7] Srnvas Ch, Rao CSP, Consgnment stock polc wth controllable lead tme for effectve nventor management n [8] suppl chans, Int J Manuf Technol Manag, 2007, vol.10(2/3),pp [9] C. Srnvas and C.S.P. Rao, Optmsaton of suppl chans for sngle vendor mult buer consgnment stock polc under controllable lead tme usng genetc algorthm, Int. J. Manufacturng Research, Vol. 2, No. 2, 2007, pp [10] Ch. Srnvas, C.S.P. Rao and Y.V.Rao, Consgnment stock polc usng genetc algorthm for effectve nventor management n suppl chans, Int. J. Servces Operatons and Informatcs, Vol. 3, No. 2, 2008, pp [11] and Rao, C.S.P, Optmzaton of suppl chans for sngle vendor mult buer consgnment stock polc wth genetc algorthm Int J Adv Manuf Technol, 2010 vol.48, pp [12] Ben-Daa, M. and Raouf, A, Inventor models nvolvng lead tme as a decson varable, J Ope Res Socet, 1994, vol.45, pp [13] Ouang LY, Wu KS, Ho CH, Integrated vendor buer cooperatve models wth stochastc demand n controllable lead tme, Int J Prod Econ, 2004, vol.92, No.3, pp: edtor@aeme.com