Reexamining a Specific Vendor-buyer System with Rework and an Improving Delivery Plan Using an Alternative Approach

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1 Reexmining Specific Vendor-buyer System with Rework nd n Improving Delivery Pln Using n Alterntive Approch YUAN-SHYI PETER CHIU, FENG-TSUNG CHENG b, KUANG-KU CHEN c, HUEI-HSIN CHANG d,* Deprtment of Industril Engineering nd Mngement, d Deprtment of Finnce, Choyng University of Technology, Tichung 43, TAIWAN b Deprtment of Industril Engineering nd Systems Mngement, Feng Chi University, Tichung 407, TAIWAN c Deprtment of Accounting Ntionl Chnghu University of Eduction, Chnghu 500, TAIWAN * E-mil: chs@cyut.edu.tw (HUEI-HSIN CHANG) Abstrct: - This pper uses n lterntive pproch to reexmine prior study on joint determintion of mnufcturing lot-size nd shipment policy in vendor-buyer system with rework process nd n improving delivery pln. The proposed method is strightforwrd pproch in terms of lgebric derivtions. It is different from the conventionl method tht needs to pply the first-order nd second-order differentitions to the system cost function for proof of convexity before derivtion of the optiml production-shipment policy. The reserch result obtined in this pper is confirmed to be identicl to wht ws derived by the use of the conventionl method. The proposed lgebric pproch my ssist prctitioners who my not hve sufficient knowledge of differentil clculus in understnding the solution procedures of such rel world integrted production-shipment problem in supply chin environments. Key-Words: - Mnufcturing lot-size, Multiple deliveries, Algebric pproch, Production-shipment policy, Optimiztion, Production plnning Introduction In most inventory replenishment systems, when to order? nd how mny to order? re the two fundmentl questions to be nswered most often. The objective of these issues re obvious, tht is to minimize totl relted cost [-]. In mnufcturing firms when products re mde in the plnt, the questions become when to strt production run? nd wht will be the production lot-size? [3-4]. Chiu et l. [5] studied joint determintion of replenishment lot-size nd shipment policy for vendor-buyer integrted system with rework nd n improving delivery pln. Their work is s extension of conventionl economic production quntity (EPQ) model [6] with dditionl considertions on product qulity ssurnce nd specil cost-sving delivery policy. The clssic EPQ model ssumes tht ll items produced re of perfect qulity. However, in rel world systems due to process deteriortion nd/or mny other fctors, genertion of defective items is inevitble. Mny reserch rticles hve been crried out to ddress the imperfect qulity issue in production systems [7-4]. Shih [8] extended two inventory models to the cse where the proportion of defective units in the ccepted lot is rndom vrible with known probbility distributions. Optiml solutions to the modified system were developed nd comprisons with the trditionl models were lso presented vi numericl exmples. de Kok [9] considered lost-sles production/ inventory control model with two djustble production rtes to meet demnd. He obtined the prcticl pproximtions for optiml switch-over levels to such model under the service level constrints. Mk [0] developed mthemticl model for n inventory system in which the number of units of cceptble qulity in replenishment lot is uncertin nd the demnd is prtilly cptive. It ws ssumed tht the frction of the demnd during the stock-out period which cn be bckordered is rndom vrible whose probbility distribution is known. The optiml replenishment policy is synthesized for such system. A numericl exmple E-ISSN: Issue 5, Volume, My 0

2 ws used to illustrte the theory. The results indicted tht the optiml replenishment policy is sensitive to the nture of the demnd during the stock-out period. Mkis [] studied the optiml lot sizing nd inspection policy for n EMQ model with imperfect inspections. He ssumed tht the process cn be monitored through inspections, nd both the lot size nd the inspection schedule re subject to control. The in-control periods re ssumed to be generlly distributed nd the inspections re imperfect (tht is the true stte of the process is not necessrily reveled through n inspection). By using the Lgrnge's method nd by solving nonliner eqution, two-dimensionl serch procedure ws proposed nd employed to find the optiml lot sizing nd inspection policy. Chiu et l. [4] employed mthemticl modeling long with serching lgorithm to solve the mnufcturing run time problem with defective rte nd rndom mchine brekdown. They derived the optiml run time tht minimized the long-run verge cost for their proposed model. Nonconforming products sometimes cn be reworked nd repired to reduce totl production costs [5-]. Exmples for such situtions cn be found in plstic injection molding, or in printed circuit bord (PCB) ssembly, sometimes employs rework s n cceptble process to increse level of qulity. Yum nd McDowell [5] considered the lloction of inspection effort problem for seril system s 0- mixed integer liner progrmming (MILP) problem. Their model permitted ny combintion of scrp, rework, or repir t ech sttion nd llowed the problem to be solved using stndrd MILP softwre pckges. Yu nd Bricker [6] presented n informtive ppliction of Mrkov Chin Anlysis to multistge mnufcturing problem. They lso pointed out n error in the literture which hd remined undetected for mny yers. Teunter nd Flpper [8] considered single-stge single-product production system. Produced units ws ssumed to be non-defective, reworkble defective, or non-reworkble defective. The system switches between production nd rework. After producing fixed number (N) of units, ll reworkble defective units re reworked. They lso ssumed tht the rework time nd the rework cost increse linerly with the time tht unit is held in stock. For given N, they derived n explicit expression for the verge profit, using this expression the optiml vlue for N cn be determined numericlly. Li [0] presented n overlpping decomposition method to pproximte the throughput of production systems with rework loops. He decomposed the system into overlpped seril production lines, with the overlpping mchines modified to ccommodte the interctions with mchines nd buffers in other lines. The convergence of the itertive procedure nd the uniqueness of the solution were proved nlyticlly. The ccurcy of the estimte ws demonstrted numericlly nd illustrted by cse study t n utomotive ssembly plnt. Chiu et l. [] exmined finite production rte model with scrp, rework nd stochstic mchine brekdown. Stochstic brekdown rte nd rndom defective rte long with the reworking of nonconforming items were ssumed in their study. The objective ws to derive the optiml production run time tht minimize the long run verge production cost. In vendor-buyer supplier chins environments, multiple or periodic deliveries of finished products re commonly dpted in lieu of continuous issuing policy s ssumed by the clssic EPQ. Schwrz [] considered problem of one-wrehouse N-retiler inventory system. The objective ws to determine the optiml stocking policy tht minimizes system cost. He derived some necessry properties for the optiml policy s well s the optiml solutions. Heuristic solutions were lso provided for the generl problem nd tested ginst nlyticl lower bounds. Mny studies hve since been crried out to ddress vrious spects of supply chins optimiztion [3-4]. Selected rticles re surveyed s follows. Bnerjee nd Bnerjee [4] developed n nlyticl model for coordinted, orderless inventory system for the single product, single vendor, multiple purchsers cse. Such system ws mde prcticl in electronic dt interchnge t the time, for the exchnge of informtion between trding prtners. On the bsis of the potentil benefits of this technology, they proposed common cycle replenishment pproch, where the supplier lone mkes ll replenishment decisions, without ordering on the prt of the customers. Their model nd concepts were demonstrted by simple numericl exmple nd concluded tht EDI-bsed inventory control cn be ttrctive from economic, s well s other stndpoints. Srker nd Prij [5] considered mnufcturing system which procures rw mterils from suppliers nd processes them to convert to finished products. They proposed model tht ws used to determine n optiml ordering policy for procurement of rw mterils, nd the mnufcturing btch size to minimize the totl cost for meeting equl shipments of the finished products, t fixed intervls, to the buyers. Hll [6] exmined how ttributes of the distribution system ffect inventory ccounting nd EOQ/EPQ decisions. The pper developed rnge of "chrcteristic inventory E-ISSN: Issue 5, Volume, My 0

3 curves" to represent situtions encountered in integrted production/ distribution systems. The pper then showed how system ttributes define the inventory curve, nd the resulting EOQ/EPQ eqution. He concluded: () ccounting for inventory t both the origin nd destintion cn yield significntly different EOQ/EPQ results, but reltively modest regret; nd () filure to ccount for consolidtion effects mong multiple products sent to common destintion cn led to substntil errors. Srmh et l. [9] considered coordintion between two different business entities is n importnt wy to gin competitive dvntge s it lowers supply chin cost, so they reviewed literture deling with buyer vendor coordintion models tht hve used quntity discount s coordintion mechnism under deterministic environment nd clssified the vrious models. An effort ws lso mde to identify criticl issues nd scope of future reserch. Chiu et l. [3] incorported multidelivery policy nd qulity ssurnce into n imperfect economic production quntity (EPQ) model with scrp nd rework. They ssumed the reworking of repirble defective items in ech production run nd the finished items cn only be delivered to customers if the whole lot is qulity ssured fter rework. The expected integrted cost function per unit time ws derived. A closed-form optiml btch size solution to the problem ws obtined. Hoque [35] considered models of delivering single product to multiple buyers when the set-up nd inventory costs to the vendor re included. His models ssume close reltionship between mnufcturer nd buyers for costless wy of benefit shring. Three models were developed, two of which trnsfer with equl btches nd the third with unequl btches of the product. Optiml solution techniques re presented, sensitivity nlysis of the techniques is crried out, nd severl numericl problems re solved to support the nlyticl findings. A comprtive study of the results shows tht the supply by unequl btches performs better. This study lso highlights the limittion of methods used in obtining the lest miniml totl cost in the single-vendor single-buyer scenrio, nd the benefit of n integrted inventory is lso discussed. Chiu et l. [5] studies joint determintion of mnufcturing lot-size nd shipment policy in vendor-buyer system with rework process nd n improving delivery pln. They used the differentil clculus long with Hessin mtrix equtions to derive the optiml production btch size nd number of deliveries for such specific vendor-buyer system with rework. This pper employs n lgebric pproch [43-46] to reexmine their model. A strightforwrd lgebric derivtion is presented here with the intention of helping prctitioners (who my not hve sufficient knowledge of differentil clculus) on understnding the solution procedures of such rel world integrted production-shipment problem. As future reserch we would like to use gent bsed modeling to model the supply chin domin s this techniques provided significnt results in other complex domins such s finncil mrkets [47]. Problem Description & Modelling As stted in previous section, this study uses n lterntive pproch to reexmine model in Chiu et l. [5]. To ese the redbility, problem is described below using the exct nottion s in [5]. Consider rel life mnufcturing system where process my rndomly produce portion x of defective items t rte d. Under regulr operting schedule, the constnt production rte P is lrger thn the sum of demnd rte λ nd production rte of defective items d, where (P-d-λ)>0. All defective items re considered to be repirble nd they re reworked nd repired t rte P within the sme cycle when regulr production ends. All end items re delivered to the buyer by specific cost sving (n+) shipment pln. Under such delivery policy, the first instllment of finished products is delivered to customer for stisfying demnd during uptime t nd rework time t (see Fig. ). Then, fter the rework process when the remining of the production lot is qulity ssured, fixed quntity n instllments of the rest of finished items re delivered to customer t fixed intervl of time during the production downtime t 3. Figure illustrtes vendor s on-hnd inventory level of perfect qulity items in the proposed n+ delivery model [5]. Figure depicts the on-hnd inventory level of defective items in the proposed n+ delivery model. Figure 3 depicts buyer s stock level in the proposed model [5]. The cost prmeters relted to the proposed model include unit production cost C, vendor s unit holding cost h, setup cost K per production run, buyer s unit holding cost h, unit rework cost C R, holding cost h for ech reworked item, fixed delivery cost K, delivery cost C T per item shipped. Additionl vribles re E-ISSN: Issue 5, Volume, My 0

4 Fig. The vendor s on-hnd inventory of perfect qulity items for the proposed model with rework nd (n+) delivery policy [5] Fig. The on-hnd inventory of defective items in the proposed model with rework nd (n+) delivery policy Fig. 3 The stock level t buyer side for the proposed model with rework nd (n+) delivery policy [5] E-ISSN: Issue 5, Volume, My 0

5 t = the production time needed for producing enough perfect items for stisfying customer s demnd during t nd t, t = the production uptime, t t 3 Q t n T H H H n = rework time, = production downtime, time to deliver the remining qulity ssured finished products, = production lot size per cycle, = fixed intervl of time between ech instllment of products delivered during t 3, = cycle length, = the level of on-hnd inventory for stisfying product demnd during vendor s uptime t nd rework time t, = mximum level of on-hnd inventory in units when regulr production ends, = the mximum level of on-hnd inventory in units when rework process finishes, = number of fixed quntity instllments of the remining finished items to be delivered to customer during t 3, I(t) = the level of on-hnd inventory of perfect qulity items t time t, I d (t) = on-hnd inventory of defective items t producer s side t time t, I c (t) = on-hnd inventory t buyer s side t time t, TC(Q,n+) = totl production-inventory-delivery costs per cycle for the proposed model, E[TCU(Q,n+)] = the long-run verge costs per unit time for the proposed model. I = demnd during production time t, i.e. I=λt. D = demnd during production uptime t, i.e. D=λt. From Figures nd, the following bsic equtions cn be obtined. Q T = () λ Q H + H t = = () P P d xq t = (3) P t = nt = T t + t (4) 3 n λ ( t + t) t = P d (5) dt = xq (6) Q xq H = λ ( t + t ) = λ + P P ( ) λ (7) H = Q x t + t (8) H = H + Pt (9) Thus, totl production-inventory-delivery cost per cycle TC(Q,n+) of the proposed model consists of the vrible mnufcturing cost, the setup cost, vrible rework cost, the qulity ssurnce costs include vrible repiring costs nd holding costs for reworked items, (n+) fixed nd vrible shipping cost, inventory holding costs for vendor for ll end items produced in t, t, nd t 3, nd buyer s holding cost. dt TC ( Q, n + ) = CQ + K + CR [ xq] + h ( t ) + n + K + C Q T H H dt t t t t + h H + H n ( t ) n + ( ) Ht3 H( t + t) D + I + h + n tn Tking into the rndomness of defective rte x, one cn use the expected vlues of x in cost nlysis nd obtins E[TCU(Q,n+)] s follows (the sme s Eq. (7) in [5]) hq λ E0 4λ E λ E λ λ P P P PP P P ( h h) Q λe ( x) λ E( x) λ λ λ n P P PP P P λ λ λ λ + h Q E E E + E P P P P PP (0) n+ K + K E TCU ( Q, n ) λ C + = + + CRE ( x) + CT Q ( ) λ λ h h Q E x λ hqλ where λ + E PP E 3 P PP P P x E0 = E ; E = E ; x x x E = E ; = E ( x) x () () 3 The Algebric Approch In this section, n lgebric pproch is presented to derive the optiml replenishment lot size nd the optiml number of deliveries. It is noted tht no differentil clculus is involved in the proposed E-ISSN: Issue 5, Volume, My 0

6 solution process. It is lso noted tht Eq. () hs two decision vribles Q nd n, nd they re in terms of coefficients ssocited with nq -, Q -, Q, nd Qn -. First let,, 3, 4 nd 5 denote the following: = λ C+ CRE x + CT (3) = λk (4) = λ( + ) (5) K K h λ E0 4λ E λ E λ λ 4 = P P P PP P P λ λ λ λ λ + h E 0 E 3 0 E + E + E P P P P PP PP ( ) λ λ h h E x λ hλ E 3 P PP P P λ E( x) λ λe x + ( h h) P P PP = λ λ + + E 3 P P 5 Thus, Eq. () becomes (6) (7) (, + ) = E TCU Q n nq Q Q Qn (8) Further rerrngement, Eq. (8) becomes (, ) E TCU Q n + = + Q 3 + 4Q (, ) E TCU Q n + = + Q + Qn + Qn Q n + 5 (9) ( 3 ) + ( Q 4 ) ( 3 )( Q 4 ) + ( 3 )( Q 4 ) ( Q n) + ( 5 ) ( Q n) ( 5 ) + ( Q n) ( 5 ) Therefore, one obtins (, + ) = + ( 3 ) ( 4 ) E TCU Q n Q Q Qn Q n + + (0) () Thus, E[TCU(Q,n+)] is minimized, if the second nd the third squre terms in Eq. () equl zeros. Tht is nd ( ) ( Q ) = () ( ) ( Q n) = (3) 5 0 or nd or n* Q* 3 = (4) 4 5 n* = Q* (5) 5 3 = (6) 4 4 Results nd Discussion Substituting Eqs. (3) to (7) in Eq. (5) nd with further derivtions, one hs λ λe x P P ( K + K )( h h) λ E ( x) λ λ E * PP P P n = λ λ λ E0 λ E hλ E 3 h + h P P + + P PP + P λ E0 4λ E λ E λ K P P P PP P ( h h) + λ E ( x) λ E PP P (7) Becuse n only tkes on integer vlue, let n + denote the smllest integer greter thn or equl to n (derived from Eq. (7)) nd n - denote the lrgest integer less thn or equl to n. Therefore, n* is determined to be either n + or n -, known constnt. Therefore, one cn now retret E[TCU(Q,n+)] s cost function with single decision vrible Q. Similrly, considering n s constnt, Eq. () cn be rerrnged s where or (, ) E TCU Q n+ = + Q z + Qz (8) z = n + ; z = + n (9) E TCU Q n Q Q z z (, + ) = + + (, + ) = + ( ) ( ) E TCU Q n Q Q z z + z z (30) (3) Thus, E[TCU(Q,n+)] is minimized if the second squre term in Eq. (3) equls zero. Or Q z = (3) z E-ISSN: Issue 5, Volume, My 0

7 Substituting Eqs. (3) to (7) in Eq. (3), nd with further derivtions, one hs * Q = or ( ) λ λ ( λ ) + λ( + ) n K K K h λ E0 4λ E λ E λ λ P P P PP P P λ λ λ λ λ + h E 0 E 3 0 E + E + E P P P P PP PP h h E x λ hλ E 3 P PP P P ( h h) Q λe ( x) λ E( x) λ λ λ n P P PP P P * Q = λ n+ K + K λ E0 4λ E λ E λ ( θ ) λ h P P P PP P P + ( h h) P PP P P λ λ E x λ h λ ( ) λ (33) h h λe x λ E x λ λ E n P P PP P P E0 λe0 λe λe E + h λ P P P P PP PP (34) One notes tht Eqs. (34) nd (7) re identicl to tht in Chiu et l. [5]. It follows tht the long-run verge cost E[TCU(Q,n+)] is E TCU ( Q, n+ ) = + z z (35) 5 Numericl Exmple This section verifies the results by using the sme numericl exmple in [5]. Recll the following system prmeters: λ = 3400 units per yer, P = 60,000 units per yer, x = rndom defective rte which follows uniform distribution over intervl [0, 0.3], P =,00 units per yer, C = $00 per item, K = $0,000 per production run, C R = $60, repired cost for ech item reworked, h = $0 per item per yer, h = $40 per item reworked per unit time, h = $80 per item kept t the customer s end, K = $4,350 per shipment, fixed cost, C T = $0. per item delivered. Applying Eq. (7) one obtins n*=.44, since n* only tke on integer vlue one cn use two djcent integers, plugging them in Eq. (34) nd then into Eq. (35). The resulting costs re E[TCU(65,3)] =$47059 nd E[TCU(56,4)]=$ Therefore, the optiml production-shipment policy is (Q,n+)= (65,3), nd the long-run verge cost is $470,59. Totl cost for the proposed model results reduction of $7,458 or 3.4% svings of totl other relted costs. Figure 4 illustrtes the effect of the expected defective rte E[x] on the long-run verge cost function E[TCU(Q,n+)]. It is noted tht the forementioned solution procedure cn be pplied to ny given system of the sme chrcteristics. Fig. 4 Effects of rndom defective rte on the long-run verge cost function E[TCU(Q,n+)] E-ISSN: Issue 5, Volume, My 0

8 One notes tht s x increses, cost E[TCU(Q,n+)] increses significntly due to the qulity ssurnce cost (i.e. the cost for reworking the nonconforming products). 6 Conclusions Chiu et l. [5] used the conventionl method, the differentil clculus long the Hessin mtrix equtions to derive the optiml production-shipment policy mnufcturing system with rework process nd specific cost sving delivery pln in vendor-buyer supply chins environments. This pper presents n lterntive pproch to reexmines the solution procedure of their problem without hve to refer differentil clculus. Such strightforwrd lgebric pproch ssist prctitioners who my not hve sufficient knowledge of differentil clculus in understnd with ese such n integrted productionshipment system. For future reserch, one interesting direction will be to exmine the effect of rndom demnd for the sme model. Acknowledgements Authors thnk Ntionl Science Council of Tiwn for supporting this reserch under Grnt Number: NSC H MY. Authors would like to express their sincere pprecition to nonymous reviewers for their vluble comments nd suggestions to the erlier version of mnuscript. References: [] H. Wgner, T. M. Whitin, Dynmic version of the economic lot size model. Mngement Science, Vol. 5, 958, pp [] G. Hdley, T. M. Whitin, Anlysis of Inventory Systems, Prentice-Hll, Englewood Cliffs, NJ., USA, 963. [3] F. S. Hillier, G. J. Liebermn, Introduction to Opertions Reserch. McGrw Hill: New York; pp , 00. [4] S. Nhmis, Production & Opertions Anlysis, McGrw-Hill Inc., New York, 009. [5] Y-S. P. Chiu, Y-C. Lin, S. W. Chiu, C-K. Ting, Joint determintion of lot-size nd shipment policy for vendor-buyer system with rework nd n improving delivery pln. Africn Journl of Business Mngement, Vol. 6(), 0, pp [6] E. W. Tft, The most economicl production lot. Iron Age, Vol. 0, 98, pp [7] R. E. Brlow, F. Proschn, Mthemticl Theory of Relibility. Wiley: New York; 965. [8] W. Shih, Optiml inventory policies when stock-outs result from defective products. Interntionl Journl of Production Reserch, Vol. 8 (6), 980, pp [9] A. G. de Kok, Approximtions for lost-sles production/inventory control model with service level constrints. Mngement Science, Vol. 3, 985, pp [0] K. L. Mk, Inventory control of defective products when the demnd is prtilly cptive. Interntionl Journl of Production Reserch, Vol. 3 (3), 985, pp [] V. Mkis, Optiml lot sizing nd inspection policy for n EMQ model with imperfect inspections. Nvl Reserch Logistics, Vol. 45 (), 998, pp [] F-T. Cheng, C-K. Ting, Determining economic lot size nd number of deliveries for EPQ model with qulity ssurnce using lgebric pproch. Interntionl Journl of the Physicl Sciences, Vol. 5 (5), 00, pp [3] C-H. Chen, C-L. Lu. Optimum profit model bsed on order quntity, product price, nd process qulity level. Expert Systems with Applictions, Vol. 38 (6), 0, pp [4] Y-S. P. Chiu, H-D. Lin, H-H. Chng, Mthemticl modeling for solving mnufcturing run time problem with defective rte nd rndom mchine brekdown. Computers & Industril Engineering, Vol. 60 (4), 0, pp [5] B. J. Yum, E. D. McDowell, Optiml inspection policies in seril production system including scrp, rework, nd repir: n MILP pproch. Interntionl Journl of Production Reserch, Vol. 5, 987, pp [6] K-Y. C. Yu, D. L. Bricker, Anlysis of mrkov chin model of multistge mnufcturing system with inspection, rejection, nd rework. IIE Trnsctions, Vol. 5 (), 993, pp [7] C-C. Chern, P. Yng, Determining Threshold Control Policy for n Imperfect Production System with Rework Jobs. Nvl Reserch Logistics, Vol. 46 (-3), 999, pp [8] R. H. Teunter, S. D. P. Flpper, Lot-sizing for single-stge single-product production system with rework of perishble production defectives. OR Spectrum, Vol. 5 (); 003, pp [9] A.M.M. Jml, B.R. Srker nd S. Mondl, Optiml mnufcturing btch size with rework E-ISSN: Issue 5, Volume, My 0

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10 Methods And Computtionl Techniques In Electricl Engineering (MMACTEE'08), Technicl University of Sofi, Bulgri, My -4, 008, pp.4-0, Vol. I, ISBN: , ISSN [43] Y-S.P. Chiu, H-D. Lin, H-H Chng, Determintion of production-shipment policy using two-phse lgebric pproch. Mejo Int. J. of Science nd Technology, Vol. 6 (), 0, pp [44] S. W. Chiu, Production lot size problem with filure in repir nd bcklogging derived without derivtives. Europen Journl of Opertionl Reserch, Vol. 88, 008, pp [45] H-D. Lin, Y-S. P. Chiu, C-K. Ting, A note on optiml replenishment policy for imperfect qulity EMQ model with rework nd bcklogging. Computers nd Mthemtics with Applictions, Vol. 56, 008, pp [46] Y-S. P. Chiu, K-K. Chen, H-H. Chng, Solving n economic production lot size problem with multi-delivery policy nd qulity ssurnce using n lgebric pproch. Journl of Scientific & Industril Reserch, Vol. 69 (), 00, pp [47] F. Neri, A Comprtive Study of Finncil Agent Bsed Simultor Across Lerning Scenrios. In Agents nd Dt Mining Interction, Editors: Co L., Bzzn A., Symeonidis A., Gorodetsky V., Weiss, G., Yu P., LNCS, Vol. 703, 0, Springer, pp E-ISSN: Issue 5, Volume, My 0