Improvement of Inventory Control for Defective Goods Supply Chain with Imperfect Quality of Commodity Components in Uncertain State

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1 Reearch Journal of Applied Science, Engineering and Technology 6(): , 203 SSN: ; e-ssn: Maxwell Scientific Organization, 203 Submitted: October 22, 202 Accepted: February 0, 203 Publihed: July 25, 203 mprovement of nventory Control for Defective Good Supply Chain with mperfect Quality of Commodity Component in Uncertain State Salah Alden Ghaimi, Rizauddin Ramli and Nizaroyani Saibani Department of Mechanical and Material Engineering, Faculty of Engineering and Built Environment, Univeriti Kebangaan Malayia, Bangi, Selangor, Malayia Abtract: n thitudy, we propoed a mathematical model for four-level defective goodupply chain with imperfect quality of commodity component in an uncertain tate to maximize profit of upply chain. t i aumed that the inpection of incoming part in upplier i randomly done and incomplete. Thi lead ome of the manufactured product will not be properly manufactured becaue of defective part and are conidered a defective good and in mot cae, the defective product can be repaired by replacing with the good part. The defective part will be collected and then returned to the upplier for repairing. Out propoed model conider defective part problem by optimizing the cot of production, maintenance, hipping, reworking on the defective good and part, hortage in retailer due to the production of defective good and cot of capital incurred by the companie. The model can anticipate the active upplier/manufacturer/ditributor and the quantity of part and good that mut be exchanged between them. Our propoed model i novel and we ued MNOS olver and LNGO oftware to olve the problem. The reult acertained the correctne and fine function of the propoed model. Keyword: Defective good, inventory control, LNGO, MNOS, upply chain, uncertain model NTRODUCTON One of important advantage in today competitive global market i reduction of defective product by manufacturer. The fraction of defective part during production have ignificant direct relationhip with the upplier. n recent year, Supply Chain Management (SCM) (Guo and Tang, 2008; Sana, 20; Lee and Kim, 2000; Tzeng et al., 2006) are the field which cover from trategic iue to operational model. n the pat two decade, the problem in upply chain management ha drawn a great attention from manufacturer and organization due to it optimal effect on their operation. Subequently, the manufacturer need to find alternative way to enure the continuou proviion of their product and utilize appropriate trategie to meet the market demand on time. n addition, there are factoruch a imperfect quality and defective raw material that can affect the efficiency of productivity (Sarker et al., 2008; Roy et al., 2009; Mondal et al., 2009). So the manufacturer need a dedicated facility to perform the tak of reworking thee defective good. Previoutudiehow that the election of an appropriate upplier i an important role in reducing cot (Golmohammadi and Mellat-Parat, 202; Banet and Leung, 2005; Aiaoui et al., 2007). However, when there are uncertain tate occur uch a market fluctuation, natural diater, currency drop and udden demand and return, a robut modelling involved tochatic approach i an eential need epecially when the location between the upplier, warehoue and manufacturer are at far ditance. Recent tudy by Amin and Zhang (203) on mathematical model for uncertain demand and return of a cloed-loop Supply Chain Network (SCN) wa employed to multiple plant, collection center, demand market and product. The reult of their tudy how the propoed tatitical model can handle uncertain parameter. Alo, the effect of uncertainty product portfolio demand and price on the optimal cloed-loop upply chain planning have been taken in account by Amaro and Barboa-Póvoa (2009). They ued GAMS/CPLEX for olving their model. The reult of their tudy provided great detail on the upply chain partner production, tranportation and inventory. n a recent tudy, Ramezani et al. (203) introduced a new tochatic multi-objective model of forward/revere logitic network under uncertainty condition with the objective of maximization of profit, reponivene and minimization of defective part from upplier. The tochatic model involved three level in forward and two level in revere including upplier, plant, ditribution center, collection center and dipoal center, repectively. Other reearcher alo examined uncertainty model (Zeballo et al., 202; Lin et al., 20; Li and Liu, 202). Correponding Author: Salah Alden Ghaimi, Department of Mechanical and Material Engineering, Faculty of Engineering and Built Environment, Univeriti Kebangaan Malayia, Bangi, Selangor, Malayia 920

2 n uch uncertain tate of SCN, the inventory control model that overee concept of warehoue and imperfect product after manufacturing i alo needed (Chung et al., 2009). For example, literature by Jacob et al. (2005) and Lee and Kim (2000) propoed a hybrid method for olving the optimization problem of production-ditribution planning in SCN. Other reearch by Eroglu and Ozdemir (2007) ha developed a model of effective and returned good ahortage but it only can olve numeral example which howed that defective and uele good can decreae the overall profit. Another model i the Economic Production Quantity (EPQ) model for defective good (Jamal et al., 2004), however, the EPQ model doe not conider the reworking function of defective good. Furthermore, if the raw material are very expenive and have limited ource, the reworking tak can ave o much cot. Several method have been propoed for the improvement of efficiency and they howed that the correlation of imultaneou application of Total Quality Management (TQM), SCM and Jut in Time (JT) can enhance the effectivene of the companie ((Kannan and Tan, 2005). n thitudy, a new mathematical model for fourlevel defective goodupply chain by conidering imperfect quality of commodity component and optimization of cot i preented. The related cot which affect the total profit include the cot of production, maintenance, hipping, reworking on the defective good and part, hortage in retailer due to the production of defective good and cot of capital incurred in uncertain tate to maximize profit of upply chain network. MODELNG Supply chain network: The aim of the propoed model i to maximize the profit of the defective good in SCN in which will aociate with the cot of capital incurred by the companie. The conidered upply chain model i divided into four-level ahown in Fig.. The firt level (Level ) iupplier of part/raw material that convey the part to next level. Here, mot of the inpection of part are done baed on random election and not complete. The econd level (Level 2) i manufacturer which receive multiple type of incoming part from upplier. Here, the part are aembled in a manufacturing line to produce the good and end them to the next level. t i aumed that in the manufacturing proce, ome of the product may not be properly manufactured becaue of defective part and conidered a defective good. n mot cae, the defective product can be repaired by replacing with good part and the defective part are returned to the upplier for repair. The good produced are received by ditributor (Level 3) which will keep the good in their warehoue before ending them to variou retailer. n the Fig. : Structure of upply chain network tudied in thi reearch 92

3 warehoue, the duration of torage time will affect the rent. So, it i important to chedule the appropriate time to proce each time period o that thee cot can be minimized. The fourth level (Level 4) comprie of the retailer. n thitudy, the propoed model i adapted to maximize profit by optimize cot including production, maintenance, hipping, reworking on the defective good and hortage in retailer due to the production of defective good and cot of capital incurred by the companie. Mathematical model: The propoed SCN i formulated a a mathematical model. Here, we et-up the aumption, limitation, et, parameter, deciion variable, objective function and contraint in uncertain tate. Aumption and limitation of the model: The following aumption are made to develop the mathematical model: The amount of demand were given to the manufacturer for product and to the upplier for part at the beginning of the period. Duration of each period i equal to the total of production time and rework time in that period. Shortage of product in retailer i allowed. Shortage of part in manufacturer i not allowed. The model i deigned for multi-upplier, multimanufacturer, multi-warehoue, multi-retailer, multi-product and multi-component. The inpection of the product i perfect. However, inpection of the part i random. The reworking of imperfect quality product and part are allowed. Location of plant, warehoue, retailer and upplier are fixed Production capacitie of upplier and plant, torage of warehoue and retailer are known. The amount of parameter except capacity parameter are uncertainty. We alo conidered limitation for our model: The capacitie of manufacturer production, warehoue and retailer are limited. The torage capacitie for each perfect product are limited. Store capacitie and torage allocated capacitie are limited for defective good. For each period, the cutomer demand hould be provided. The production and reworking time are limited. Set: = Set of Manufacturing and Remanufacturing plant (... i... ) 922 J = Set of Warehoue (... j... J) L = Set of Product (... l... L) T = Set of Period (... t... T) K = Set of Retailer (... k... K) Parameter of the propoed model: M = Set of Supplier (... m... M) N = Set of Part (... n... N) S = Set of Scenario ( S) γγ iiiiii = Rework cot of per defective good l by manufacturer i during period under hww jjjjjj hdd iiiiii θθ iiiiii Tθ t = Holding cot of product l in ditributor j during period t under = Holding cot of product l in defective goodtore inide the manufacturer i during period t under = Time required to production of per good l by manufacturer i during period t under = Total of production time during period t under μμ iiiiii = Time of reworking required for good l by manufacturer i during t under µ iiiiii = Total of production time during period t under Tµ t = The total of reworking time during period t under = Production cot of per item by manufacturer i during period t under = Shipping cot each product l from manufacturer i to ditributor j during period t under cenario = Shipping cot each product l from ditributor j to retailer k during period t under Scenario = Shipping cot each defective good l inide manufacturer during period t (from production proce to defective goodtore and invere) under PPPP iiiiii tttttt iiiiiiii tttttt jjjjjjjj tttttt iiiiii = Shortage cot for each product l in retailer k during period t under = Selling price per unit of perfect product l in factory i during period t under = Probability of Occurrence in period t = Percentage of defective good l produced by manufacturer i during period t under ββ kkkkkk pppp iiiiii pp tt pp iiiiii = The cot of buying each part n from upplier m by factory i for producing good l in period t under = npection fee for each part n produced by upplier m and product l by factory i in period t under pppppp nnnnnnnnnn εε nnnnnnnnnn

4 dd kkkkkk = Product demand l by retailer k in period t under ττ nnnnnnnnnn = Shipping Cot of each part n from upplier m to factory for producing product l in υυ nmilt Ψ nnnnnnnnnn iiii tt period t under = Shipping cot of defective part returned n from factory i to upplier m before and after application in product l during period t under = Reworking cot of defective part returned n from factory i to upplier m before and after application in product l during period t under dddddd nmilt nnnnnn nmilt pppppp nnnnnnnnnn = Cot of capital incurred by the companie in period t under = Amount of part ordered n by factory to upplier m for product l during period t under = The part required n for manufacturing product l in factory i that produce by upplier m in period t under = Percentage of defective part n before application in product l in factory i produced by upplier m in period t under nnnnnnnn nnnnnnnnnn = The part required n for repairing defective product l in factory i that produce by upplier m in period t under Variable of the model: pppppppppppp mmmmmm = Maximum profit of upply chain network bbbbbbbbbb nnnnnnnnnn = Amount of defective part n before application in product l in factory i produced by upplier m in period t under tttttttttttt nnnnnnnnnn = Total of defective part that be produce by upplier m for product l in factory in period t under tttttttt nnnnnnnnnn = Total of need part n for repair product in factory that be produce by upplier m in period t under nnnnnnnnnn nnnnnnnnnn = Total of required perfect part n for producing all of the perfect product l by factory produced by upplier m in period t under tttttt nnnnnnnnnn = Total of part n that ent from upplier m to factory for produce good l in period t under XX iiiiiiii = Amount of product l tranported from factory i to ditributor j during period t under YY jjjjjjjj = Amount of product l tranported from ditributor j to retailer k during period t under 923 QQ iiiiii = Economic production quantity of product l by factory i during period t under DDDDDD iiiiii CCCC iiiiii BB kkkkkk = Amount of defective good l produced by factory i during period t under = Amount of perfect product l produced by factory i during t before reworking under = Amount of the hortage of product l in retailer k during period t under Objective function: Profit maximum = Probability of good occurrence cenario [Total revenue - ((Total cot/ (iiii tt ) tt ))] pcilt. Qilt i= N M pcpnmilt. tpanmilt n= m= i= J t T t T K hwjlt. X Y j= t = i= t = k= hdilt. Defilt i= γ ilt. Defilt i= N M ε nmilt. tpanmilt n= m= i= L T S N M profitmax = ( p ). pilt. Qilt τnmilt. tpanmilt t ( ir l= t= = i= n= m= i= t ) J tcw. X i= j= J K tcr. Y j= k= tcdilt. Defilt i= N M υnmilt. tdefpanmilt n= m= i= N M ψ nmilt. tdefpa nmilt n= m= i= K βklt. B klt k = () Equation () how the objective function, the aim i to maximize profit by minimizing the total cot of upply chain. t include: Production cot of good Cot of part buying Cot of maintenance in the ditributor and defective goodtore Cot of defective good reworking npection cot of part Shipping cot of part from upplier to manufacturer Cot of logitic from manufacturer to ditributer Cot of logitic from ditributer to retailer Cot of logitic from manufacturer to defective goodtore and vice vera Shipping cot of part from manufacturer to upplier

5 Cot of defective part reworking Cot of hortage in retailer becaue of defective good production Cot of capital incurred by the companie CONSTRANTS N M N M npanmilt. Qilt = ntcpanmillt i,,, l t (2) n= m= n= m= Equation (2) required Part for manufacturing of product: dpanmilt = ntcpanmilt trpanmilt bdfpanmilt n, m,,,, i l t (3) Equation (3) determinate the ordered part: dpa tpa n, m,,,, i l t nmilt nmilt (4) Equation (4) Supply of all part are ordered by upplier: bdfpa = ppa. tpa n, m,,,, i l t nmilt nmilt nmilt (5) Equation (5) how the amount of defective part at the factorie before uing them: N M N M nrpanmilt. defilt = trpanmilt i,,, l t (6) n= m= n= m= Equation (6) invetigate the amount of required part for reworking: tdefpanmilt = bdfpanmilt trpanmilt n, m,,,, i l t (7) Equation (7) how all of the defective part: tpa V n, m,,,, i l t nmilt nmilt (8) Equation (8) how the limitation of part production by upplier: S = Q S ilt,, ilt ilt (9) Equation (9) how the retriction of the EPQ capacity in manufacturer: L S i= l= = X W jt, jt (0) Equation (0) and () conider the delivery capacity contraint for ditributor: J L S j= l= = J S j= = Y W kt, kt Y W klt,, klt (2) (3) Equation (2) and (3) decribe capacity contraint for retailer: Def = p. Q i,,, l t ilt ilt ilt Equation (4) how the amount of defective good: ( ) Co = p. Q i,,, l t ilt ilt ilt (4) (5) The amount of perfect good before reworking decribe by Eq. (5): Q = Co Def i,,, l t ilt ilt ilt (6) The total of produced product by manufacturer in each period are hown with Eq. (6): K klt k= i= d Q lt,, ilt (7) Equation (7) aure that the total demand to each manufacturer in per period do not exceed the production capacity of thoe manufacturer; alo, the all demand are covered by perfect product: K K klt klt ilt k= k= i= B = d Co l,, t K ilt i= k= Co d l,, t klt (8) (9) Contrain (8) and (9) how the amount of hortage in retailer due to production of defective product: K i= k= X = Y jlt,,, (20) Equation (20) invetigate the final inventory balance for per warehoue and it how that the inventory for each warehoue i zero at the end: S i= = X W jlt,, jlt () J j= Y = d klt,,, klt (2) 924

6 The inventory of retailer i not more than demand; it how by Eq. (2): K t T t T Y X jlt,,, T(22) k= t = i= t = Limitation (22) explain that the amount of good hipped by each warehoue to the retailer in per period do not exceed the inventory of that warehoue: J j= X Q ilt,,, ilt (23) Equation (23) how the amount of tranported good from the manufacturer to the ditributor i le than or equal to the total production: L S θ. Q Tθ t ilt ilt t i= l= = (24) Table : Parameter and their value Parameter Value γ ilt Uniform (00, 300) hw jlt Uniform (5, 7) hd ilt Uniform (4, 6) θ ilt Uniform (9, 3) µ ilt Uniform (5, 7) pc ilt Uniform (2000, 4000) tcw Uniform (0, 5) tcr Uniform (7, 9) tcd ilt Uniform (4, 7) β klt Uniform (70, 90) p ilt Uniform (0000, 7000) npa nmilt Uniform (3, 0 ) ppa nmilt Uniform (0, 0.03) nrpa nmilt Uniform (, 3) p ilt Uniform (0, 0.) p t Uniform (0, 0.04) pcp nmilt Uniform (30, 45) ε nmilt Uniform (, 3) d klt Uniform (7000, 0000) τ nmilt Uniform (5, 9) U nmilt Uniform (3, 6) Uniform (3, 5) ψ nmilt Contraint (24) repreent the limitation of available time of production facilitie: L S i= l= = µ. Def T µ t ilt ilt t (25) Equation (25) how the limitation of available time for reworking: Tθ Tµ = T t t t t (26) Equation (26) explain the required time for production and reworking in each period i equal with the length of that particular production period: Qilt, X, Y, Bklt, Defilt, Coilt, profitmax, bdfpanmilt, tdefpanmilt, tpanmilt 0 nmi,,,,,,, (27) Where the amount of production, delivery to warehoue and retailer, hortage in retailer, defective good, perfect good, profit of the upply chain network, defective part before of proce in factory, total defective part and total part are non-negative value are hown in Eq. (27). Our propoed model i novel and we ued MNOS olver and LNGO oftware to olve the problem. For olving the mentioned model, we aumed the amount of parameter according to Table. RESULTS AND DSCUSSON We propoed a mathematical model of four-level defective goodupply chain by conidering imperfect quality of commodity component in uncertain tate to maximize profit of upply chain network. The 925 Table 2: Reult of even ample problem by different dimenion Sample problem Dimenion MNOS LNGO n, m, i, j, k, l, t, profit max Profit max,,,,,,, ,,,,, 2,,.2902E7.2902E7 3 2, 2,,,,,, , 2, 2,,, 2,, , 3,,, 2, 2,, E E7 6 2, 2, 2, 2, 2, 2, 2, E7-7 4, 2,,, 2, 2,, E8 - manufacturer ordered to upplier the required part quantity (dpa nmilt) to produce of ordered product by their cutomer (dd kkkkkk ). t i aumed that the inpection of part in upplier i randomly and not complete. So, all part are inpected before entering to the production proce in manufacturer (bbbbbbbbbb nnnnnnnnnn 7T). Alo, during the production proce ome of the product not properly manufactured becaue of damaged part in the production proce in manufacturer which conidered a defective good (DDDDDD iiiiii ). n mot cae, the defective product can be repaired by replace the correct part (tttttttt nnnnnnnnnn ). The defective part due to inpection and production proce of good in factorie will be collected and returned to the upplier for repairing (tttttttttttt nnnnnnnnnn = bbbbbbbbbb nnnnnnnnnn tttttttt nnnnnnnnnn ). The reult for even ample problem with different parameter are hown in Table 2. The firt column i number of ample problem, econd column dimenion; third and forth column are output of MNOS olver and LNGO oftware to find the profit of upply chain network. The ample problem 6 and 7 becaue of large ize dimenion could not be olved by LNGO. Table 3 report the value of the deciion variable of the ample problem 7 olved by MNOS. The reulthow the validation and correctne of the model.

7 Table 3: Sample problem 7 olved by MNOS QQ iiiiii QQ = 6992 QQ 2 = 6906 nnnnnnnnnn nnnnnnnnnn bbbbbbbbbb nnnnnnnnnn tttttttt nnnnnnnnnn tttttt nnnnnnnnnn DDDDDD iiiiii nnnnnnnnnn bbbbbbbbbb tttttttt tttttt DDDDDD =.226E5 nnnnnnnnnn 2 =.0593E5 nnnnnnnnnn 2 =.0082E5 nnnnnnnnnn 22 nnnnnnnnnn 2 =.697E5 nnnnnnnnnn 22 = nnnnnnnnnn 22 nnnnnnnnnn 222 =.004E5 nnnnnnnnnn 3 = nnnnnnnnnn 32 =.3329E5 nnnnnnnnnn 32 =.4367E5 nnnnnnnnnn 322 =.0724E5 nnnnnnnnnn 4 =.2280E5 nnnnnnnnnn 42 =.3800E5 nnnnnnnnnn 42 =.2597E5 nnnnnnnnnn 422 =.093E5 = 234 bbbbbbbbbb 2 = 298 bbbbbbbbbb 2 = 269 bbbbbbbbbb 22 = 3 bbbbbbbbbb 2 = 2928 bbbbbbbbbb 22 = 53 bbbbbbbbbb 22 bbbbbbbbbb 222 = 420 bbbbbbbbbb 3 = 446 bbbbbbbbbb 32 = 564 bbbbbbbbbb 32 5 bbbbbbbbbb 322 = 567 bbbbbbbbbb 4 = 2009 bbbbbbbbbb 42 = 33 bbbbbbbbbb 42 = 3368 bbbbbbbbbb 422 = 280 = 4 tttttttt 2 = 709 tttttttt 2 tttttttt 22 = 24 tttttttt 2 tttttttt 22 = 78 nnnnnnnnnn 22 tttttttt 222 = 559 tttttttt 3 = 4 tttttttt 32 = 752 tttttttt 32 tttttttt 322 = 742 tttttttt 4 tttttttt 42 = 644 tttttttt 42 = 704 tttttttt 422 = 636 =.2284E5 tttttt 2 =.0694E5 tttttt 2 =.035E5 tttttt 22 = 27 tttttt 2 =.990E5 tttttt 22 = 4809 tttttt 22 nnnnnnnn 222 =.0239E5 tttttt 3 = tttttt 32 =.346E5 tttttt 32 =.4472E5 tttttt 322 =.0855E5 tttttttt 4 =.248E5 tttttt E5 tttttt 42 =.3004E5 tttttt 422 =.437E5 = 47 DDDDDD 2 = 35 CCCC iiiiii CCCC = 6945 CCCC 2 = 659 BB kkkkkk XX iiiiiiii YY jjjjjjjj BB BB 2 = 35 BB 2 = 47 BB 22 XX = 6993 XX 2 = 6906 YY = 9790 YY 2 = 9689 YY 2 = 7203 YY 22 = 727 CONCLUSON n thitudy, a mathematical model for four-level defective goodupply chain network with imperfect quality of commodity component in uncertain tate to maximize profit of upply chain ha been preented. The propoed model i adapted to maximize profit by optimizing the cot including production, maintenance, hipping, reworking on the defective good/part, hortage in retailer due to the production of defective good and cot of capital incurred by the companie. The uniquene of the model i that ability to forecat the active upplier/manufacturer/ditributor and the quantity of part/good that mut be exchanged between them. Finally, the model determined the amount of produced good and component and the reulthow the correctne and fine function of the model. REFERENCES Aiaoui, N., M. Haouari and E. Haini, Supplier election and order lot izing modeling: A review. Comput. Oper. Re., 34: Amaro, A.C.S. and A.P.F.D. Barboa-Póvoa, The effect of uncertainty on the optimal cloed-loop upply chain planning under different partnerhip tructure. Comput. Chem. Eng., 33: Amin, S.H. and G. Zhang, 203. A multi-objective facility location model for cloed-loop upply chain network under uncertain demand and return. Applied Mathematical Modelling. 37(6): Banet, C. and J.M.Y. Leung, nventory lotizing with upplier election. Comput. Oper. Re., 32: -4. Chung, K.J., C.C. Her and S.D. Lin, A twowarehoue inventory model with imperfect quality production procee. Comput. nd. Eng., 56(): Eroglu, A. and G. Ozdemir, An economic order quantity model with defective item and hortage. nt. J. Prod. Econ., 06: Golmohammadi, D. and M. Mellat-Parat, 202. Developing a grey-baed deciion-making model for upplier election. nt. J. Prod. Econ., 37: Guo, R. and Q. Tang, An optimized upply chain planning model for manufacture company baed on JT. nt. J. Bu. Manage., 3: Jacob, J.C., J.H. Moll, P. Kraue, R.J. Kuter, J.J.M. Trieneken and A.C. Brombacher, Exploring defect caue in product developed by virtual team. nform. Software Technol., 47:

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