Employing Fuzzy-Based CVP Analysis for Activity-Based Costing for Maintenance Service Providers

Transcription

1 Employng Fuzzy-Based CVP Analyss for Actvty-Based Costng for Mantenance Servce Provders Patcharaporn Yanprat and Jttarat Maneewan Abstract The objectve of ths paper s to propose a framework for proft plannng or the prcng of a mantenance servce under mprecse nformaton by organzatons adoptng an Actvty-Based Costng system. Fuzzy-based Cost-Volume- Proft (FCVP) analyss wth a case-based applcaton s presented. The fndngs reveal the fuzzy rules that can fulfll operatonal decsons to enhance the compettveness of the organzaton. Index Terms actvty-based costng, CVP analyss, fuzzy logc, mantenance servce prcng A I. INTRODUCTION CTIVITY-based costng (C) s a costng approach that assgns resource costs to cost objects such as products, servces, or customers based on the actvtes performed. It has ganed recognton by beng more accurate cost estmaton and by provdng traceable cost nformaton when compared wth tradtonal costng (TC) system. TC s a volume-based overhead costng system. Ths approach reles on the assumpton that each cost object uses the same amount of overhead. It uses sngle or second-stage allocaton bases on the unt-level characterstcs of the cost object and, therefore each cost object wll be charged the same amount. In addton, t focuses on measurng and controllng drect costs []. An C system dffers from a TC system n two sgnfcant ways. Frst, the cost pools of a TC system are defned as plant or departments whereas C defnes them as actvtes. Second, a TC system uses one or two cost drvers whereas the C system uses multple cost drvers that are related to unt-level, batchlevel and product-level characterstcs [2] to allocate the overhead costs of the actvtes to the cost objects. Moreover, the TC system serves well and s suffcent when technology s stable, when the varety of products s lmted, and when ndrect costs are nsgnfcant relatve to drect costs [3]. Wth the TC system under the contemporary busness envronment, cost dstortons wll ncrease as frms ncrease n varety of product, volume, sze, complexty, and resources used, and as costs ncurred on supportng actvtes Ths work was supported n part by Graduate Program n Engneerng Management and partal fnancal support by Graduate School, Kasetsart Unversty (Bangkhen Campus). Patcharaporn Yanprat s wth the Department of Industral Engneerng, Faculty of Engneerng, Kasetsart Unversty (Bangkhen Campus), Bangkok 0900, Thaland (phone: ; fax: ; e-mal: fengppy@ku.ac.th). Jttarat Maneewan s wth the Un Royal Internatonal Co.,Ltd., Bangkok 0220, Thaland (e-mal: jttarat.m@gmal.com). ncrease. Therefore, ths system tends to over-cost for largesze or hgh-volume products, and to under-cost for smallsze or low-volume products when product dversty exsts wthn the same operaton [4]. Under the aforementoned crcumstances, C has major advantages over TC because of ts ablty to trace overhead cost, whch allows for a more accurate unt costng. C helps to reduce cost dstortons and provdes more accurate costng of the cost objects. Inaccurate cost nformaton can lead to undesrable strategc results, such as unrealstc prcng, wrong product-lne decsons, neffectve resource allocaton and fnally to lower compettve advantage as a consequence [5]. Even though developng an C system s expensve and tme consumng, many frms realze ts beneft by tradng off ts cost. It s mplemented n varous types of busness but manly by manufacturng frms. Wth the successful exstng mplementaton of C, ts extensons are to marketng, servce, and not-for-proft organzatons such as logstcs management [6], educaton [7, 8], bankng [9], and IT nvestment [0], etc. In the feld of mantenance, the related lterature, especally on costng and prcng, receved much less attenton. To adopt C n mantenance, [] and [2] to propose a framework and ts applcaton n the costng of the n-house planned mantenance of an agrcultural servce organzaton, the fndngs show ts ablty to capture the planned mantenance cost elements and to provde nformaton to mprove the cost effcency of the organzaton s overall mantenance system. However, the proposed framework s stll lmted to n-house costng; therefore, the feasblty of an applcaton of C n a mantenance servce organzaton s an nterestng ssue. Not only servce costng, but also servce prcng s a prmary concern especally n small and medum sze organzatons that lack the experence of usng statstcal and mathematcal analyses n formulatng decson strateges. The objectve of ths paper s to propose a mantenance prcng framework for small or medum sze organzatons whch mplement the C system wthout any experence of usng statstcal and mathematcal analyses. On the other hand, they can use the proposed framework to make decsons on proft plannng or prcng under condtons of mprecse nformaton for mantenance servce operatons. In Secton II, a framework for proft plannng under condtons of mprecse nformaton for mantenance servce s ntroduced. In Secton III, the proposed framework s employed to llustrate ts applcaton n a case study company. In Secton IV, the mplementaton ssue of the framework s drawn n the concluson.

2 II. THE FRAMEWORK OF PROFIT PLANNING UNDER CONDITIONS OF IMPRECISE INFORMATION FOR A MAINTENANCE SERVICE PROVIDER Cost-volume-proft (CVP) analyss s a method for analyzng the relatonshp between costs; fxed and varable costs, output level and proft level servng for operatng decsons and marketng decsons such as settng prces, make or buy decsons on a gven product or servces, and replacng a pece of equpment, etc. Wth the restrctve assumptons on the certanty condtons of the tradtonal CVP analyss, an applcaton n real-world decsons that encounter uncertanty and rsk s the lmtaton of ths method. Although probablstc and stochastc approaches could be used to relax such restrctons, experence and knowledge of statstcs are requred, whch s nflexble n cases of unavalable data and n dynamc busness condtons that vary over tme. In addton, for mprecse nformaton such as sales demand, varable costs and fxed costs that are not constant over the plannng horzon, an applcaton of the fuzzy logc concept to the tradtonal CVP analyss s proposed to overcome such obstacles n [3]. The CVP analyss for C s presented n [4] and provdes a numercal example for a sngle product. Therefore, the framework on multple products wth fuzzy-based CVP analyss for an C system s proposed as follows. Frst, the framework of mantenance servce costng under the C system s proposed. Second, the CVP model for C system s developed. Thrd, ts extenson on the fuzzy logc concept wll be ntegrated nto the CVP model to generate the decson rules under the condton of mprecse avalable data. A. Mantenance Servce Costng for C System The framework for a mantenance servce costng system s proposed under the followng assumptons. Cost accumulaton s job costng under the cost measurement of standard costng, and overhead assgnment s under actvtybased costng. Therefore, all mantenance servce costs ncurred are assgned to jobs usng standard costs and standard quanttes for drect materals, drect labor, and overheads. The standard cost elements of drect materals and drect labor are the same as those proposed by [] whch s the common practce for mantenance servce provders. Drect materals are all materals and component parts that can be traced to each mantenance job at the standard rate and standard quantty based on the nvoce for materals. Drect labor s all of the sklled or sem-sklled labor that works on each job. Both drect costs wll be assgned drectly to the partcular servce job. For overhead, n other words support actvtes n the C system, the standard rate and standard cost drvers for the partcular actvty wll be costed at a predetermned rate. The basc supportng document s the job cost sheet that contans the necessary nformaton, dependng on the requred nformaton of the organzaton. The proposed framework for the support actvtes of the C system for mantenance servce, whether n-house or outsourcng servces, wll use a two-stage cost assgnment procedure. It starts from dentfyng resource costs, cost pools, and cost objects and then allocates resource costs to cost pools at the frst stage and s followed by the cost pools to cost objects n the second stage. In the TC system, the cost pools are the company or departments whereas actvtes and/or actvty centers are the cost pools n C. The TC system uses a cost drver such as drect labor hour or the number of jobs as the sngle companywde rate or departmental rates to assgn support/overhead costs n the second stage, whereas C uses resource/actvty consumpton cost drvers n both stages, whch provde more accurate product/servce costs than TC. Both stages are shown n Fg. and explaned n detal as follows. --Identfy the resource costs and actvtes used for provdng the mantenance servces. Resource costs can be classfed wth respect to the way n whch actvtes consume resources. In mantenance servce, they are a unt/job-level actvty, batch/customer-level actvty, and faclty/busness-sustanng actvty. --Fnd the resource consumpton cost drvers for the partcular actvty; whch are the factors selected to approxmate resources consumed by an actvty. --Assgn the cost of the actvtes based on resource consumpton. --Determne the actvty cost drver that corresponds to the partcular cost herarches. There are three crtera for selectng allocaton bases to select cost drvers. They are causal relatonshp whch selects a cost drver that causes the cost, beneft nvolved by whch costs are assgned n proporton to the benefts obtaned, and reasonableness or farness whch s used when some costs cannot be related to the mantenance servce wth respect to causalty or benefts receved [5]. Fg.. Cost assgnment framework for mantenance servce provder under the C system -- Allocate actvty costs usng the selected cost drver as an allocaton base. Calculate actvty rate for the partcular actvty by dvdng the total actvty cost by level of cost drvers consumed. --Calculate the mantenance servce costs for the partcular job based on the estmated actvtes performed, ncludng actvtes related to the man functons and support functons of the busness. In cases where there are many resource costs and actvtes, the herarchy of cost allocaton may be complex, so the use of an expense-actvty-dependence (EAD) matrx and an actvty-product-dependence (APD) matrx could be an alternatve technque to smplfy the mplementaton and to communcate the C wthn the organzaton [6].

3 B. CVP Model for C System Where cost elements are classfed by the aforementoned method, based on the product/servce costng, they have to reclassfed, correspondng to the restrcted requrement n the tradtonal CVP model, nto fxed costs and varable costs ncludng the actvtes of the man functons and support functons related to provdng the mantenance servce. Based on C, mantenance servce cost s assgned and accumulated to each partcular mantenance servce type, and therefore the actvty-based CVP model for each mantenance servce type s developed wth the followng data requrement. --Cost of busness-sustanng actvty whch s B characterzed as fxed costs:. It does not vary wth the actvty cost drver. --For each customer, t s smlar to cost at batch-level actvtes because one customer may demand the servce for more than one job. It s defned as whch does vary wth the actvty cost drver. It s able to convert to the cost at job-level actvty usng the number of jobs for each customer. --Every servce job conssts of unt varable costs for the actvty-based cost drver plus drect materals cost and drect labor cost. The tradtonal CVP model as n () s developed for the actvty-based CVP model as n equatons (2)-(5). N PQ vq () N P Q (2) (3) v v v Q C v N P Q (4) N P Q (5) v Q m v m Q v m v Q Q = costs of non-flexble resources commtted to customer-level actvtes whch vary wth the actvty cost drver v = unt varable cost per job for the partcular of mantenance servce type v = unt varable cost per customer v = unt varable cost per job for the actvtybased cost drver v = unt varable cost per job consstng of drect materals cost and drect labor cost v = total unt varable cost per job for both of actvty-based and volume-based cost drvers Q = number of jobs C. Fuzzy-Based CVP Model for C System The actvty-based CVP model for a partcular mantenance servce type as shown n equaton (5) stll realzes the determnstc condtons of the tradtonal CVP analyss. Under real world problems facng uncertanty wth mprecse nformaton or mprecse knowledge of the decson maker, the utlzaton of the fuzzy set concept s employed to modfy the above model. --Construct trangular membershp functons of the nput varables whch could be based on experence, guesses, and the rule-of-thumb judgments of the experts or decson makers. As a result, the lngustc varables such as servce prce, number of jobs, fxed cost, varable cost, and proft are formulated wth non-crsp nformaton and are consstent wth the mprecse nature of those varables [3]. --Establsh a fuzzy rule for a partcular uncertanty varable. The number of the rules depends on the number of hedges for each fuzzy set. In cases where proft s the output varable, the level of total proft wll be derved from the combnaton of the dstnct fuzzy rules among the gven nput varables. --Generate fuzzy rules for output varables usng an actvty-based CVP model as n equaton (5) combned wth the developed fuzzy rules of the nput varables. An example of proft plannng, the varous alternatves for makng decsons under the combnatons of the fuzzy rules wth respect to the gven uncertanty varables, are obtaned as a result. Not only are the relatonshp scenaros among the uncertanty varables revealed, but also the decson makers are enabled to foresee the results of the selecton strateges, whch s smlar to the what-f analyss results. where: m C N P = type of mantenance servce; =, 2,., J = number of jobs per customer = number of customers = net proft = prce per job = total fxed costs for the tradtonal CVP model = cost of busness-sustanng actvty whch does not vary wth the actvty cost drver III. CASE APPLICATION A. Background of the Case Company The man lnes of busness of the company case are the supply of blowers and compressors used n materal handlng n manufacturng frms and also the provson of servces to customers mplementng planned preventve mantenance, repar, and overhaul for both knds of equpment. Referrng to customer evaluaton on the mantenance servce of the company, the overall performance on the qualty of servce s hgh when compared wth compettors, except on prce. Investgatng the root cause, t reveals that the company mplements cost accumulaton va job costng, standard cost measurement and overhead cost allocaton wth a TC system. All

4 overhead costs, whether related to the man functons or support functons are allocated to the two man lnes of busness n equal proportons. Thereafter, a sngle companywde rate of allocated overhead wll be allocated to the partcular mantenance servces at the same rate based on drect labor hours for the entre type of servce. As a result, t determnes the uncompettve prces of the servces n comparson wth compettors, whch as a consequence affect the proftablty of the company. B. Implementaton of the Framework In accordance wth the proposed C framework, cost herarchy, cost assgnment and overhead allocaton are undertaken for budgetng as shown n Fg.2. Based on the busness process and wth the lmted avalable hstorcal data ncludng fnancal and non fnancal data, 23 resource costs to account for 7 actvty centers and 4 actvtes, whch are classfed nto 24 company-sustanng actvtes, 4 customer-level actvtes and 3 job-level actvty for 26 types of servces are manpulated n combnaton wth the technques of the expense-actvty-dependence (EAD) matrx and the actvtyproduct-dependence (APD) matrx for smplfcaton. Lastly, wth the assgnment of drect materals and drect labor cost traced drectly to each type of servce and the total overhead cost whether from the man functon actvtes or the support functon actvtes of those three actvty levels wth respect to the gven level of cost drver, the total cost of the partcular mantenance servce type s obtaned. An example s shown n Table. TLE I TOTAL COST OF JOBS CLASSIFIED BY TYPE OF MAINTENANCE SERVICE Job code v m v v GM-A-IN, ,655 GM-A8-IN 3,82 23,693 3,542 7,400 GM-A9-IN, ,308 4,79 7,044 VM-B-OUT 9, ,045 28,396 33,729 C. Proft Plannng under the Imprecse Informaton Whle the dstorton of mantenance servce cost s reduced by adoptng the C system, the fuzzness n the servce prce s nvolved because the current prce s determned under the TC system leadng to uncompettve prcng as mentoned. In addton, the demand for a servce s also dffcult to forecast, and s, n practce, often based on the experence of the sales manager. Therefore, the CVP equaton for each type of mantenance servce can be formulated under proft maxmzaton as shown n the example n equatons (6)-(9). v Drect materal cost and drect labor cost Actvty Center I Drect traced Actvty Center II Actvty Cost Object Overhead allocaton level Level I General Admnstratve Accountng and Fnance Level II Account Fnance Level III : General Admn. 2: Record order and mantenance 3: Budgetng Level IV GM-A-IN Resource Costs Support Warehouse and delvery Import Human Resources 22: Sales plannng and report 23: tomer contact 24: tomer satsfacton evaluaton GM-A8-IN GM-A9-IN GM-A0-IN Sales and Marketng 29: Mantenance plannng Sellng and Engneerng Engneerng and Mantenance 39: Machne nstallaton 40: Testng report VM-B-OUT 4: Qualty assurance VM-B2-OUT Fg. 2. Cost herarchy for cost assgnment and overhead allocaton framework of the company case

5 GM A IN : N Q (6) P Q,789, 655 GM A8 IN : N 8 P8 Q8 3,82 7, 400Q8 (7) GM A9 IN : N 9 P9 Q9,605 7, 044Q9 (8) VM B2 OUT : N 26 P26Q26 4,645 34, 57Q26 (9) An example of servce type GM-A-IN wll be presented n ths paper because the rest wll be undertaken wth the same procedures. Dealng wth the uncertantes for makng a decson on proft plannng, fuzzy servce prce, fxed cost, varable cost and fuzzy servce volume wll be treated as nput varables whle proft s a fuzzy output varable. The membershp functons of fuzzy nput varables are constructed based on the polcy of antcpated managers of varous related departments of the company based on experence and rule-of-thumb as shown n Table 2. Low, moderate and hgh levels of servce prce are defned at 0-5%, 0-25%, and 20-35% respectvely, marked up from the estmated total cost obtaned from the C system. For servce volume per budgeted perod, the low and hgh levels are defned at ther possble values n provdng the servce whereas moderate level s at the servce volume of the prevous year. TLE II MEMBERSHIP FUNCTIONS OF INPUT VARILES Input varable Level Range Servce prce (USD) Low 2,548-2,930 Moderate 2,802-3,85 Hgh 3,057-3,439 Servce volume (Job) Low 2-4 Moderate 3-5 Hgh 4-6 The fuzzy set of membershp functons relates to mantenance servce prce level as defned n equaton (0) [3]. 3 P l l P (0) Where Pl s unverse fuzzy subset of prce levels; l s an ndcator of servce prce level, l =, 2, 3, representng low, moderate, and hgh, respectvely. An example for l = s llustrated n equatons (). 3 p x j P x; a, b, c () j x j a c where b, x s the elements of fuzzy subset P and 2 P x j s ts correspondng membershp value wth respect to low prce. Thus, membershp functons for low, medum, and hgh prce levels are llustrated n equatons (2)-(4), respectvely and n Fg 3. P x; 2548, 2739, 2930 (2) P x; 2802, 2993, 385 (3) 2 P x; 3057, 3248, 3439 (4) 3 Fg. 3. Membershp functons of prce levels Smlarly, the fuzzy set of membershp functons for servce volume s as shown n Fg. 4. Degree of membershp Degree of membershp ,548 2,739 2,930 3,2 3,32 Prce Servce volume Fg. 4. Membershp functons of servce volume levels The next step s to establsh the fuzzy rules assocated wth proft levels. The total number of rules s formulated from the combnaton of two fuzzy nput varables as shown n Table 3. TLE III FUZZY RULES OF INPUT VARILES Rule no. Prce level Servce volume level Hgh Low 2 Hgh Medum 3 Hgh Hgh 4 Medum Low 5 Medum Medum 6 Medum Hgh 7 Low Low 8 Low Medum 9 Low Hgh Based on the membershp functon of nput varables n Table 2 combned wth the fuzzy rules n Table 3, substtute ther values n equaton (6), thus the proft levels are calculated as n Table 4. At ths stage, a specal program lke MATHL can be used for the computaton or to portray the relatonshp among proft and the varatons of the nput varables where the expenses are hgh and requre some expertse. For small and medum companes only EXCEL can be used wth a lower cost of mplementaton. From Table 4, the membershp functons of proft levels can be determned by usng equatons (5)-(7) [7] as shown n Table 5 and Fg. 5. Wth respect to Tables 3-5, the fuzzy rules for proft plannng under the uncertantes are developed as shown n Table 6. Wmax Wmn d (5) K

6 W0 W mn (6) W k W d ; k =, 2, 3,., K (7) k where d = dstance between two adjacent lngustc values W = maxmum proft value max W mn = mnmum proft value K = number of lngustc values TLE IV COMPUTATION RESULTS OF PROFIT VARILE Rule no. Prce level Servce volume Proft level level 3, ,99 2 3, , , ,77 7 2,739 3, , , , ,629 TLE V MEMBERSHIP FUNCTIONS OF OUTPUT VARILES Output varable Level Range ($) Proft Very low,462-2,405 Low 2,405-3,348 Moderate 3,348-4,29 Hgh 4,29-5,234 Very hgh 5,234-6,77 Thus, membershp functons of proft levels are shown n Fg. 5. Degree of membershp ,462,934 2,406 2,878 3,350 3,822 4,294 4,766 5,238 5,70 Proft Fg.5. Membershp functons of proft levels TLE VI FUZZY RULES OF PROFIT PLANNING Rule no. Prce level Servce volume Proft level level Hgh Low Low 2 Hgh Moderate Hgh 3 Hgh Hgh Very hgh 4 Moderate Low Very low 5 Moderate Moderate Moderate 6 Moderate Hgh Hgh 7 Low Low Very low 8 Low Moderate Low 9 Low Hgh Moderate In accordance wth the proft rules n Table 6, much nformaton can be drawn such as rule, f the company plans to ncrease proft from a low level at $,462-2,405 to a moderate level at $3,348-4,29, there are two optons whch could be undertaken by rules 5 and 9. The frst s to ncrease the servce volume from 2-4 jobs per year to 3-5 jobs per year whle the prce level could be reduced from $3,057-3,439 to $2,802-3,85, whereas fxed and varable costs are constant over the plannng horzon. The second s to ncrease the servce volume from 2-4 jobs per year to 4-6 jobs per year whle the prce level could be reduced from $3,057-3,439 to $2,548-2,930. Where current prcng strategy encounters an uncompettve prce as mentoned earler, enhancng compettveness va prce reducton could be acheved by usng rule 6 wth the compensate of proft level. The proposed model provdes valuable nformaton for operatons under condtons of uncertanty of servce prce, servce volume, and the proft of the company at prompt yeldng less tme consumed as well as enhancng user-frendlness. IV. CONCLUSION The proposed CVP analyss s a practcal approach for mplementaton n a multple product CVP analyss. The mantenance servce cost for the entre servce type s estmated under the C system n provdng valuable nformaton for the budgetng process. Although only one type of mantenance servce llustrates proft plannng, the rest of the servce types could be extended wth the same procedure, except that the lngustc values for the partcular varables are dfferent from one to another dependng on the degree of mprecse nformaton and the experence of antcpated decson makers. Takng the benefts from the C system, proft plannng or prcng under lmted or mprecse nformaton utlzng fuzzy logc could be smplfed to set ts rules. ACKNOWLEDGMENT The authors would lke to express ther sncere grattude to the selected case company for provdng data and to the Department of Industral Engneerng, Faculty of Engneerng, Kasetsart Unversty (Bangkhen Campus) for ts contrbuton n publshng ths paper. REFERENCES [] E.J. Blocher, K.H. Chen, G. Cokn, and T.W. Ln, Cost Management: A Strategc Emphass. 3 rd, Sngapore: McGraw-Hll, 2005, ch. 4 and 5. [2] J.J. No and B.H. Klener, How to mplement actvty-based costng, Logstcs Informaton Management. vol. 0, no. 2, pp , 997. [3] M.C. Andrade, R.C. Flho, A.M.Espozel, L.O.A. Maa, and R.Y. Qassm, Actvty-Based costng for producton learnng, Internatonal Journal of Producton Economcs, vol. 62, pp , 999 [4] R. Cooper, The rse of actvty-based costng Part one: What s an actvty-based cost system, Journal of Cost Management, Summer, pp , 988. [5] M. Gupta and K. Galloway, Actvty-based costng/management and ts mplcatons for operatons management, Technovaton, vol. 23, pp. 3-38, [6] T. Prttlä and P. Hautanem, Actvty-based costng and dstrbuton logstcs management, Internatonal Journal of Producton Economcs, vol. 4, pp , 995. [7] S. McChlery, J. McKendrck, and T. Rolfe, Actvty-based management systems n hgher educaton, Publc Money & Management, vol. 27, no. 5, pp , [8] J. Ells-Newman and P. Robnson, The cost of lbrary servces: actvty-based costng n an Australan academc lbrary, The Journal of Academc Lbraranshp, September, pp , 998.

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