Australian Journal of Basic and Applied Sciences. Decision Support System Using Fuzzy AHP and Activity Based Life Cycle Costing

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1 AENSI Journals Australan Journal of Basc and Appled Scences ISSN: Journal home page: Decson Support System Usng Fuzzy AHP and Actvty Based Lfe Cycle Costng Freselam Mulubrhan, Anul Akmar Bnt Mokhtar and Masd Muhamed Unverst Teknolog PETRONAS, Mechancal Engneerng Department, Bandar Ser Iskandar, Tronoh, Perak, Malaysa A R T I C L E I N F O Artcle hstory: Receved 15 September 2014 Accepted 5 October 2014 Avalable onlne 25 October 2014 Keywords: Decson makng, Actvty based lfe cycle cost, fuzzy analytcal herarchy process, A B S T R A C T Decson makng n many ndustres s complex due to a degree of nherent uncertantes. These uncertantes can be quanttatve or qualtatve. Takng nto account only quanttatve factors lke cost doesn t brng a convncng decson makng analyss. In ths paper two methods; Actvty based lfe cycle costng (ABC-LCC) and Fuzzy analytcal herarchy process (FAHP) are used to determne the quanttatve and qualtatve uncertantes n the decson makng. The fnal decson s made by ntegratng the output of the above methods usng weghted sum method (WSM). A decson to buy a new pump or to contnue wth the old one s analyzed. It s found that usng ABC-LCC method the decson s to contnung wth the old one, however when FAHP s used the decson s to buy a new one. The ntegraton of these two method usng WSM t s found to select pump A, that means the fnal decson s to contnue workng wth the old pump rather than buyng a new one AENSI Publsher All rghts reserved. To Cte Ths Artcle: Freselam Mulubrhan, Anul Akmar Bnt Mokhtar and Masd Muhamed, Decson Support System Usng Fuzzy AHP and Actvty Based Lfe Cycle Costng. Aust. J. Basc & Appl. Sc., 8(15): 48-54, 2014 INTRODUCTION Decson makng n many ndustres s complex due to a degree of nherent uncertanty. These uncertantes can be quanttatve or qualtatve. Takng nto account only quanttatve factors lke cost doesn t brng a convncng decson makng analyss (Jesse A.et al., 2010). Due to ths ncreasng complexty and the need to ncorporate all type of uncertanty a decson support model should be developed to ad the process. One of the most powerful quanttatve decson makng tool s lfe cycle costng (LCC). Lfe cycle cost analyss s used as a decson support tool to ad decson makers to propose, compare, and select the cost effectve alternatves for mantenance, renewal, and captal nvestment (Rahman and Vaner, 2004). In order to determne accurate and effcent LCC, the costng method used has hgh mpact. The costng method used needs to have the ablty to grp the uncertantes rased, snce predctng the future s full uncertantes. Actvty Based Costng (ABC) model deals wth all the actvtes that wll ncur a cost and t has the best capablty to deal wth the uncertantes (Emblemsvåg and Bras, 2001). ABC methods are modern methods for estmatng cost regardng clear methodology and easer to compute. Due to ts convenent way to quantfy the qualtatve attrbutes of the optons presented, hence removng subjectvty n the result analytcal herarchy process (AHP) s hghly chosen as a qualtatve decson makng tool (Twar, 2006). In the tradtonal AHP method, the subjectve descrptons of revewers decson are often correspondng to exact value. As a result, the vague descrptons are often gnored by the researchers. In order to make the analyss results more reasonable, usng fuzzy set theory to deal wth the problems of fuzzness s very mportant (Yu, E. L, 1995). Fuzzy theory s based on fuzzy sets, whch s the expanson of crsp sets. Fuzzy theory overthrows the two/dual value (yes or no) so that ts mult-value could be pressed close to realty. FAHP and the LCC have dfferent measurement unt the frst one s n percentage and the second one s n dollar. Another method s needed to ntegrate ther values nto a sngle level of decson makng. Weghted sum model (WSM) s the smplest and most effectve method for ths applcaton (Trantaphyllou. et al., 1997). Weghted summaton makes the ncomparable attrbutes comparable, prortzes them by assgnng weghts and fnally reduces the amount of nformaton by aggregatng the weghted standardzed scores. Ths process provdes not only a rankng of the alternatves, but also comprehensblty and the strengths and weaknesses of the polcy alternatves (Qunn. et.al, 2007). Thus n ths study a decson support model whch ncorporate quanttatve and qualtatve uncertantes wll be developed by ntegratng ABC-LCC and FAHP. Correspondng Author: Freselam Mulubrhan, Mechancal engneerng department, Unverst Teknolog PETRONAS, Bandar Ser Iskandar, Tronoh, perak, Malaysa, E-mal: frty4u@gmal.com

2 49 Freselam Mulubrhan et al, 2014 Methodology: In ths secton the develop decson support model s dscussed n detal. The general framework s shown below n Fg 1. Fg. 1: Schematc representaton for decson support model. A. Defne the problem and Identfy alternatves: Any decson makng process begns wth the dentfcaton of the problem under nvestgaton. There are dfferent alternatves wth, pros and cons, whch are helpful n solvng the dentfed problems. Analyzng the pros and cons has to be the frst step. B. Data collecton and analyss: The qualty of decson support model s hghly affected by the avalable data. In terms of tme, effort, and resources consumed, collecton of data s a major part of a ABC-LCC and FAHP study. Some of the typcal data sources for LCC are basc accountng records, cost reports, hstorcal databases, functonal specalst, techncal databases, cost proposals, contracts and other nformaton system for LCC. Some of the types of data collected from these sources are purchase prce, drect labor, lost producton, spare parts mantenance, materal cost, cost of preventve mantenance schedule, cost of repar, lfe of equpment, unscheduled breakdown cost, mean tme between falure for correctve mantenance (MTBF), producton delay hours, Mean tme to repar (MTTR), repar tme, and down tme. In AHP, the decson maker expresses judgments n terms of par wse comparsons through questonnares, ntervew and panel dscusson and the verbal judgments wll be translated nto numbers. C. Fuzzy Analytcal Herarch process (FAHP): Once the problem and the alternatves are dentfed the next step n FAHP s to decompose the entre problem nto herarchcal structures whch has three levels; the goal of the decson; the crtera; and the optons. The judgment of the decson maker wll be translated nto numbers. In FAHP ths numbers are expressed n trangular fuzzy number. The membershp functon of a trangular fuzzy number les n the nterval of [0, 1], & t s expressed as: M ( x) ( x / m l) ( l / m l),... x [ l, m], ( x / m u) ( u / m u),... x [ m, u]. (1) where l m u, u and l are the upper and lower value of the modal m of the fuzzy trangular number whch s denoted by (l,m,u) respectvely. If l=m=u, t becomes the ordnary number (.e. non-fuzzy, crsp). The support of m s the set {xєr/l,x,u} where R s a real number and µ A(x) s the membershp functon. There also nvolve an operaton n a fuzzy matrx. The sum, subtracton, and multplcaton of a two trangular fuzzy number are smlar to crsp numbers the only dfferent operaton s on the nverse. Extent analyss method s used to consder the extent of an object to be satsfed for the goal, that s, satsfed extent. In the method, the

3 50 Freselam Mulubrhan et al, 2014 extent s quantfed by usng a fuzzy number. For further detals on the method of prorty calculaton and extent analyss, refer to (Twar. N, 2006), (Chang, 1996). D. Actvty based lfe cycle costng: The frst step n ABC-LCC s formng actvty herarchy, when the herarchy s made an actvty network s formed. The ABC-LCC model s extensve. In ABC cost estmatng technques t s necessary to dentfy each actvtes n all the stages, snce the prncple of actvty based costng s that products or servces consume actvtes and these actvtes consume resources that generate costs. Ths makes the dentfed actvtes to be cost drvers (Emblemsvåg, 2001). Presentng all the actvtes and the drvers wll be a tresome. Therefore, only the hgh mpact drvers needs to be dentfed, these are, drects labor, number of components for replacng faled parts, and runnng hour. For dentfcaton of the relatonshp between actvty and resource drvers due to the expendture of actvty depends on a varety of drvers, t s convenent to use hstorcal data from whch the relatonshp can be establshed. In ths secton the probablstc approach, LCC model s developed. The general model for the LCC s therefore as shown Eqn 2. LCC C C M (2) aq op c where C aq s acquston cost, C op, s operatng cost, M c s mantenance cost. The fnal future cost wll be dscounted to the present by usng the nterest rate over the approprate study perods. aq N NPW C [ C M ]*1/(1 ) j1 op C kj where NPW s net present worth. N s the number of rregular future costs; k ndex for each compoundng perod; and effectve nterest rate whch s equal to 8% s dscount rate. E. Weghted sum model: The result whch s gong to be found from the qualtatve (FAHP) and from the quanttatve (ABC-LCC) has dfferent dmensonal value whch s prorty and cost. The fnal decson should ntegrate these two assessments n order to make all rounded decsons. Weghted sum model (WSM) s the smplest and most effectve method whch s used to compare the ncomparable attrbutes, prortes them by assgnng weghts and fnally reduces the amount of nformaton by aggregatng the weghted standardzed scores (Rantaphyllou, 1997). Ths process provdes not only a rankng of the alternatves, but also comprehensblty and the strengths and weaknesses of the polcy alternatves (Qunn. A. et.al.,2007). Normalzaton requres consderaton of dfferent characterstcs for each modular result. Hgh values are preferred for these results. The Equaton shown below calculates the normalzed vales of modular results. Symbol (a hgh ) s used for the normalzaton of hgh value preferred results R ah gh n ( R ) 1 (4) where R s a result correspondng to an alternatve from each modular assessment and n s the number of alternatves. The relatve mportance of each modular result s expressed as an nterval value from 0 to 1. The sum of the relatve mportance must be equal to one. Ths relatve mportance s used as a weght factor W j n the Equaton below, whch s used to calculate the overall value S of each alternatve. The sum of weghted normalzed values of all alternatves must be one. The hghest S value represents the most alternatve method. m S ajw j j1 (5) where S s relatve value of alternatve A and m s the number of module results. The relatve mportance of each modular result can be decded by the subjectve and ntutve assessment of decson makers and other stakeholders. RESULT AND DISCUSSION An old pump (Pump A) aged wth 8 year s operatng n a petrochemcal plant. At pump falure, the process shuts down and fnancal losses are ncurred as each hour of down tme results n a gross margn loss of US$10,000/hour of outage. The plant s plannng to buy a new pump (Pump B) for a replacement of the old one the plant has an estmated 10 years lfe and the plant wll be sold-out durng ths nterval. The plant wants to make a decson ether to buy a new one or to repar and mantan the old one. The data requred for the analyss s extracted from (Waghmode. et al., 2010), (Hennecke. 1999), (A gude to LCC Analyss for pumpng systems). 1. ABC-LCC (3)

4 51 Freselam Mulubrhan et al, 2014 All the actvtes whch are the drver of the cost and ther relaton are dentfed as shown n the Table 1 below. Table 1: Pump lfe cycle actvtes and cost drvers. Installaton and commssonng Actvty Major cost drvers Preparaton of foundaton Groundng Pump set algnment before pmpng Ppng Pump set algnment after ppng Electrc connectons Commssonng Personnel, and tme spent Operaton Day to day supervson Number of hours of pump operaton, personnel, and labour Day to day operaton Cost of energy and number of hours of pump operaton Correctve mantenance and repar Access to the faled component Tme to gan access to faled component, personnel, and tools used Dagnoss Fault solaton tme, personnel, manuals, techncal data, test equpments, and tools used Repar/replacement Actual hands on tme to repar/replacement, personnel, equpments and tools used Verfcaton and algnment Tme spent, personnel and tools used Dsposal Pump dsassembly Tme to dsassemble pump, personnel, and tool used Separaton Tme spent and personnel Part recovery Qualty of parts, and transportaton cost Dsposng Qualty of materal and cost of dumpng a. Acquston cost: The acquston cost contans C1 product plannng, C2 engneerng desgn, C3 product test and evaluaton, C4 software s used, C5 desgn documentaton and tranng, C6 raw materals, and C7 manufacturng.. etc. The general expresson for the acquston cost s; j 7 C aq C j j1 (6) The acquston cost contans all the cost of pump set whch s cost of pump; 5190, cost of motor; 23750, cost of base frame; 550, and cost of couplng; 250. All the costs are n dollar ($). Wth the gven data the acquston cost for the new pump, pump B s therefore equals $ b. Installaton and commssonng cost: Snce the old pump, Pump A s already nstalled t s only the nstallaton cost of pump B wll be calculated. The nstallaton and commssonng task s subdvded nto seven dfferent actvtes, Table 2 show the related data of these actvtes. TABLE 2: Actvtes and Cost Drver for Installaton (Waghmode. et al., 2010), Personnel Tme unt(h) Cost/unt Total cost Tollng cost Actvty B B B B B Preparaton of foundaton Groutng Pump set algnment before ppng Ppng Pump set algnment after ppng Electrc connectons Commssonng Total The cost of all the actvtes can be as follows (Waghmode. et al., 2010), I C m 1 [( t a. n p. C ) C l t ] (7) where I c s the cost of nstallaton, t a s the estmated tme for each actvtes, n p s the number of labour needed for each actvty, C l s the labor cost, and C t s the cost of toolng for nstallaton. Usng the above equaton and the gven data, the total cost of nstallaton s $1,627. c. Operaton cost: The hgh mpact cost drvers n ths phase are number of operaton hours, personnel, and cost of energy. The operaton cost can be estmated usng Eq (8) as shown blew. Cop t * ( Ce( KW ) Cl ) (8)

5 52 Freselam Mulubrhan et al, 2014 where C e s cost of consumed energy ($/KWH) and C l s the labor cost for the operaton per hour. Energy consumpton s calculated by gatherng data on the pattern of the system output. Cost of energy for pump can be estmated as shown below (Waghmode. et al., 2010), (Hennecke. 1999). Q. H C e C pw 366. p. m (9) where C pw s cost per nput power ($/kw), Q s the pump flow rate (m 3 /h) whch s 300 and 205 for pump A & B respectvely, H s the pump head (m) 90 for pump A and 300 for pump B, η p s the pump effcency whch s 76 and 75 for pump A & B, η m s the motor effcency 92 for pump A and 90 for pump B, the energy cost per KWh s $0.1KWh, and the labour cost of operaton s $1/h, the total cost of operaton for the lfe cycle s calculated usng Eq. (9) and t s equal to $1,052,224 for pump A and $1,878,437 for pump B. d. Mantenance and Downtme cost: The falure data of the pumps s collected for the past four years for the old pump; Pump A. and t s eght falures are recorded wthn ths tme whch s gven n hour; the tme of the falure s, 545, 1945, 3119, 3799, 4631, 5081, 6024 and Snce there are no hstorcal data for the new pump; Pump B, the falure data s taken from another plant that uses a smlar knd of pump. The falure data collected s for the four consecutve years of the pumps frst operaton t s gven n hours as follow; 3026, 4759, 5874, and Number of falure for reparable system depends on the repar assumpton taken. The state of the repar assumpton can be determned usng general renewal process (GRP) model (Haryono. W. W.). There are two types of GRP models, type I and type II. In GRP type I model the system age of only the prevous falure epoch.e., the tme between the prevous two falures s mproved. Let V denote the vrtual age of the reparable system after the th Correctve mantenance acton, and let V 0 = 0. GRP type I vrtual age model ndcates that, V V qy 1 (10) where q s mantenance effectveness 0 < q < 1. Y 1, Y 2, Y 3, Y 4 Y n, s the tme between falure. Under ths model, each correctve mantenance acton removes a porton, 1 q, of the age accumulated durng the most recent perod of reparable system functon. GRP type II model s extenson of GRP type I model. The dfference between them s on assumpton about mpact of reparng on the damaged ncurred (Syamsundar. A et al., 2012). GRP typeii reflects the realty where the mantenance acton reduces the cumulatve damage of all the prevous falures. It s governed by the followng equaton: V q V1 Y (11) Note that f q = 0, then correctve mantenance s perfect, f q=1, then t s mnmal and f 0 < q < 1, then the correspondng repar assumpton s somewhere n between perfect and mnmal (Relasoft publshng). Under ths model, the tme to reparable system falure s a Webull random varable havng scale parameters > 1 and shape parameters η. As stated n Wahyu (Haryono. W. W.), maxmum lkelhood estmaton (MLE) s more consdered to estmate GRP model parameter (q,, η). Greater the MLE value of the model, best wll be the statstcal ft for the gven data. The scale and shape parameters of webul and the meantme between falure and number of falure of pump are calculated for three repar assumpton as shown n Table 3. Snce the soluton cannot be obtan analytcally numercal methods s appled by Webul ++8 software. TABLE 3: Relablty Parameters, Mean Tme between Falure and Number of Falures. Shape parameter Scale parameter α MTBF Number of falure β/month Pump A Perfect repar e In between e Imperfect repar Pump B Perfect repar e In between e Imperfect repar e Mantenance cost s therefore can be estmated usng M c T / MTBF ( C s. p Ct MTTR ( l * n)) (12) where T s the lfe span of the pump, MTBF s the mean tme between falure, C s.p s cost of spare part for reparng a falure, f the pump s repared wthout replacng any parts C s.p s gong to be zero. C t s cost of tools; MTTR s mean tme to repar, l s cost per labor and n s number of labor for each actvty. The cost of mantenance s estmated by the actvtes t performs. Gven the cost of spare part s $200, toolng cost and mean tme to repar for actvtes; access to the faled component, dagnoss, and verfcaton and algnment s $3& 3hr respectvely, and for actvty repar/replacement t s $6 and 6hr respectvely, number of personnel for all the actvtes s 4, and the cost per tme for each personnel s $8. Perfect repar results n a

6 53 Freselam Mulubrhan et al, 2014 hgher expected cost, smlarly the mperfect or the mnmal repar wll cause a mnmum expected cost but wll lead to an ncrease number of falure. However under the combnaton strategy parts whch face major falure wll get perfect repar whle other parts whch face mnor falure wll face an mperfect repar. Ths strategy seems to be a more practcal and fnancally attractve choce and the mantenance cost s estmated for ths assumpton whch s found to be $ for pump A and $73815for pump B. e. Net present worth: The total LCC of Pump A s and for Pump B The acquston cost s made at the present tme and doesn t need any dscountng. It s assumed that the Installaton wll be fnshed wthn the next 6 month, whch wll be dscounted perod of the cost. The operaton, mantenance and decommssonng cost are gven to the total lfe of the pump and t wll be consdered as the future cost at the end of 10 yrs from now. 1/ 2 10 NPW AC Cc *(1 ) ( Cop MC).( 1 ) (13) The total net present cost s found to be for Pump A and for Pump B. 2. FAHP: The two pumps wll be evaluated wth three crterons ths are Ease of Operaton (EO), Safety (S) and envronmental condton (ENV). Based on the documents and ntervewng three experts let the par wse comparson, the fuzzy evaluaton matrx be as gven (n trangular fuzzy) n Table 4. Table4: Expert Opnon on the Crteron EO S ENV EO (1,1,1) (2/7,1/3,2/5) (2/5,1/2,2/3) S (5/2,3,7/2) (1,1,1) (2/3,1,3/2) ENV (3/2,2,5/2) (2/3,1,3/2) (1,1,1) The frst analyss s made between each crteron. The value of fuzzy synthetc extent wth respect to the th object s, SI, therefore for each crteron the extent value s represented by S EO, S S, & S ENV S EO = (1.686, 1.833, 2.067)* (9.019, , ) T = (0.13, 0.17, 0.23) S S = (4.167, 5, 5.5) * (9.019, , ) T = (0.32, 0.462, 0.61) S ENV = (3.167, 4, 5) * (9.019, , ) T = (0.242, 0.37, 0.554) Usng the degree of possblty concept the compared weght value s found. V (S EO S S ) = V (S S S EO ) =2.55 V (S EO S ENV ) =-0.07 V (S S S ENV ) =1.33 V (S ENV S EO ) = 1.88 V (S ENV S S ) = Thus the weght vector s found to be W = (0, 1, 0.718) T, through normalzaton, the weght vectors wth respect to the decson crtera s found to be W= (0, 0.58, 0.417). Next each Pump, Pump A (P A ) & Pump B (P B ) wll be compared under each of the crtera separately. Ths s shown n the Tables 5 below. Table 5: Expert Opnon on the Alternatves EO PA PB S PA PB PA (1,1,1) (5/2,3,7/2) PA (1,1,1) (2/5,1/2,2/3) PB (2/7,1/3,2/5) (1,1,1) PB (3/2,2,5/2) (1,1,1) ENV PA PB PA (1,1,1) (2/7,1/3,2/5) PB (5/2,3,7/2) (1,1,1) Fnally, addng the weghts for each canddate and multplyng by the weght of the correspondng crtera, a fnal score s obtaned that s 0.18 for pump A and 0.82 for pump B. Based on the ease of operaton, safety and envronment t s pump B that should be preferred. However t s necessary to ncorporate the qualtatve assessment wth the quanttatve one, the next secton deals wth the weghted sum model to ncorporate these assessments. 3. Weghted sum model: As stated above WSM s used to compare to ncomparable attrbutes and serves to obtan a fnal decson whch changes the two modular results nto weghted factors that are standardsed to be calculated. The summary of the two modular results are shown n Table 6 below. The weght factors were calculated based on Eq (5)

7 54 Freselam Mulubrhan et al, 2014 Table 6: Table Summary of fnal and normalzed assessment result. Summary of assessment result Summary of normalzed assessment result FAHP ABC-LCC FAHP ABC-LCC Total Prortzaton PUMP A 0.18 $ PUMP B Concluson: A decson support model s model s developed by ntegratng the concept of ABC-LCC and FAHP usng WSM. Actvty based method s used to dentfy the actvtes and cost drvers n acquston, operaton and mantenance phase and FAHP s used to ncorporate the subjectve assessment. Two Pump sets, Pump A (the exstng one) and Pump B (the new one) s taken as a case for ths paper. The acquston cost of the new pump; Pump B s found to be less than 1.2% of the total LCC, whch shows that t s necessary to have a long-term outlook to the nvestment decson-makng process rather than tryng to save money n the short-term by smply purchasng assets wth lower ntal acquston costs. The operaton cost s the hghest cost for both the pumps whch s n between 88 to 93%. The mantenance cost s the hghest for the old pump; Pump B, due to ts agng falure. The number of falures whch ncur mantenance cost s determned for three mantenance assumptons; that s when the repar condton s as good as new, as bad as old and when t s n between. The number of falure s calculated by usng the GRP. The mnmal repar strategy for all components results nto lower expected cost whle perfect repar strategy for all components results nto hgher expected cost. From the output of the ABC-LCC t s found that Pump A has hgher total cost, however the result of the FAHP shows that Pump A has a lower prorty. Usng WSM as a fnal decson makng method pump A s selected. That means the fnal decson s to contnue workng wth the old pump rather than buyng a new one. REFERENCES Chang, D.Y., Applcatons of the extent analyss method on fuzzy AHP. European Journal of Operaton Research, 95(3): Emblemsvåg, J., B. Bras, Actvty-Based Cost and Envronmental Management A Dfferent Approach to ISO14000 Complance. ISBN Sprnger. Boston: Kluwer, Emblemsvåg, J., Actvty-Based lfe cycle costng. Manageral edtng journal, 16: Haryono, W.W., On Approaches for Reparable System Analyss. Laboratory of Statstcal Industry, Department of Statstcs FMIPA ITS Surabaya Hennecke, F.W., Lfe cycle costs of pumps n chemcal ndustry. ELSEVIER Chemcal Engneerng and Processng, 38: Jesse, A.A., A. John Steel, F.W. John, A hybrd approach to assess decommssonng optons for offshore nstallatons. Ngera Annual Internatonal Conference and Exhbton, Abuja, Ngera. SPE MS Pump lfe cycle cost: A gude to LCC Analyss for pumpng systems, Offce of Industral Technologes Energy Effcency and Renewable Energy U.S. Department of Energy, Euro pump, Hydraulc Insttute Qunn, A., Classfcaton for accuracy and nsght: A weghted sum approach. 6th Australasan Data Mnng Conference, 70: Rahman, S. and D.J. Vaner, Lfe cycle cost analyss as a decson support tool for managng muncpal nfrastructure. CIB 2004 Trennal Congress: Toronto, Ontaro, pp: Relasoft publshng, user s gude WEIBULL++,ALTA verson 8 RelaSoft Corporaton Rantaphyllou, T.E., B. Kovalerchuk, L. Mann and G.M. Knapp, Determnng the most mportant crtera n mantenance decson makng. Journal Of Qualty In Mantenance Engneerng, 3(1): 16-28, Syamsundar, A., K. Muraldharan and V.N.A. Nakan, General Repar Models for Mantaned Systems. Sr Lankan Journal of Appled statstcs, 12: Twar, N., Usng the Analytc Herarchy Process (AHP) to dentfy Performance Scenaros for Enterprse Applcaton. Trantaphyllou, E., B. Kovalerchuk, L. Mann and G.M. Knapp, Determnng the most mportant crtera n mantenance decson makng. Journal Of Qualty In Mantenance Engneerng, 3(1): Waghmode, L., A. Sahasrabudhe, P. Kulkarn, Lfe Cycle Cost Modellng of Pumps Usng an Actvty Based Costng Methodology. Journal of Mechancal Desgn by ASME, 132 / , Yu, E.L., The Study of Fuzzfyng Multplcatve Analytc Herarchy Process. Master Dssertaton, Tungha Unversty.