A STUDY ON THE FACTORS AFFECTING THE ECONOMICAL LIFE OF HEAVY CONSTRUCTION EQUIPMENT

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1 A STUDY ON THE FACTORS AFFECTING THE ECONOMICAL LIFE OF HEAVY CONSTRUCTION EQUIPMENT Hongqn Fan and Zhgang Jn Department of Buldng and Real Estate, The Hong Kong Polytechnc Unversty, Kowloon, Hong Kong * Correspondng author (bshfan@net.polyu.edu.hk) ABSTRACT: Surveys found that large contractors replace approxmately 10% of ther equpment fleet unts annually n North Amerca. Cost mnmzaton model s a commonly accepted method for equpment replacement whch helps to dentfy these equpment unts whose total ownng and operatng cost reaches ther mnmum pont as canddates for replacement. Whle the model s conceptually clear wth the am of achevng mnmum equpment cost per unt of servce, ts use has some practcal dffcultes as the equpment mantenance and repar costs experence bumps and lumps n the ts lfe tme. In practce, dentfcaton of equpment unts for replacement are stll based on such metrcs as lmt of repar costs, lmt of major falures, lessons learned from prevous cases as well as expert knowledge. In ths research, we look nto the cost hstory of a large number of equpment unts n a contractor s equpment management nformaton system (MIS) and use decson tree modelng approach to dentfy these factors mpactng on the economc lfe of frst hand equpment, and extract rules leadng to dfferent cost patterns and therefore dfferent economc lfe spans of heavy equpment. C4.5 decson tree model s used to buld a top-down decson tree by recursvely splttng exstng cases based on the concept of nformaton gan. In addton to facltatng decsons n equpment replacement, the fndngs can also be used to explan the effectveness of varous mantenance strateges, compare the equpment cost performance among varous classes, makes, and amount of servces n ther lfe cycle. Keywords: Constructon Equpment, Replacement Analyss, Decson Tree Modelng, Decson Support 1. INTRODUCTION Heavy constructon equpment fleet s a crtcal resource for large contractors. To keep compettve n the market, the contractor needs to dentfy these canddates of equpment tems for tmely replacement. A survey found that nearly 10% of the equpment needs to be replaced annually on average n USA [4]. Although there are many equpment replacement theores, such as cost mnmzaton models, ther practcal use s rare as the total annual cost every equpment tem shows sgnfcant bumps and lumps, t s also dffcult to model the trend of equpment cost to defne the most lkely economcal lfe for a partcular type of equpment under the dynamc nfluences of multple factors. Ths paper ntroduces a machne learnng approach to address the equpment replacement problem. Decson tree nducton algorthm C4.5 proposed by Ross Qunlan [3] s used to perform nductve learnng from the real equpment cost data. A decson tree model s derved for descrbng the rule sets leadng to dfferent cost cohorts. Combned wth tradtonal mathematcal and statstcal approaches, the decson tree model can effectvely evaluate these factors of mpact on the fluctuaton of equpment costs, and dentfy the equpment canddates for replacement based on ther cost-related features. 2. LITERATURE REVIEW 923

2 Cost mnmzaton method, frst proposed by Taylor [5], s one of the earlest approaches for equpment replacement and s well accepted n academa and constructon, agrculture and forestry ndustres. Ths method ams to mnmze the annual ownng and operatng cost of a pece of equpment per unt of servce: the equpment annual costs drop sharply n the frst few years due to hgh deprecaton, and rse gradually n the followng years when the equpment repar costs escalate due to equpment agng, tear and wear. The method reles on varous theoretcal cost models to predct the future costs and dentfy the pont of tme at whch the annual unt cost reaches ts mnmum. Many mathematcal and statstcal models are proposed for practcal use n equpment replacement. Coller and Jacques [1] proposed a Geometrc Gradent-to-Infnte- Horzon method, for projectng expected future lfe-cycle costs for the exstng machne plus future replacements to an nfnte horzon; Vorster and Sears [6] suggested to use falure cost profles for consequental costs of equpment falures and ncorporated nto the equpment cost model for equpment replacement. Gllerspe et al. [2] addressed the equpment replacement n a research project by the Vrgna Transportaton Research Councl n corporaton wth U.S. Department of Transportaton, the focus of ther research s on the predcton of annual varable costs of a pece of equpment usng statstcal approaches, however the researcher acknowledged the dffcultes n the ncluson of large number of attrbutes nto the predctor varables, as well as the tedous tral and error method n statstcal analyss. 3. PROBLEM STATEMENT A general contractor owns a large fleet of equpment to satsfy the needs for equpment resources n ts cvl and transportaton projects. The contractor notces there are large varatons of economc lfe spans for dfferent types of equpment; and these varatons also exst for the same class of equpment wth dfferent make, preventve mantenance (PM) hstory, accumulated unt of servces (hours or klometers), etc. The current annual equpment replacement exercse focuses on the metrcs of maxmum equpment use and the accumulated repar costs and personal judgment. The statstcal cost nformaton on equpment groups s useful but not specfc enough to gude the equpment replacement. Replacng a pece of equpment too early or too late s obvously a problem that wll ncrease the equpment nternal rate charged to projects and decrease the contractor s compettve edge n the equpment-ntensve heavy constructon market. Take the fleet of dump trucks as an example, the contractor needs to know what caused the dscrepancy between the manufacturer s recommended lfe and the actual lfe n the contractor s fleet, and how the combnaton of the nfluencng factors reduce or ncrease the equpment lfe span. If the mpact from these factors can be characterzed, the equpment replacement can be done wth more confdence and less guesswork. The future purchase of new equpment can also beneft from these fndngs, for example, comparson between dfferent makes/models under specfed condtons. 4. DECISION TREE INDUCTION: C4.5 ALGORITHM Decson tree nducton s one category of machne learnng algorthm for buldng a decson tree structure lnkng dfferent decson condtons wth dfferent results. A decson tree s a top-down structure wth the root node at the top, questons are asked wth dfferent answers leadng to the next level decson nodes or termnal leaf nodes. Wth a tree-lke mult-level structure, decson tree s equvalent to a set of decson questons asked consecutvely and a combnaton of dfferent questons/answers lead to dfferent results. Buldng decson tree from data s an nductve learnng process, a supervsed learnng algorthm s used to repettvely partton the data space nto subset of data wth more purer results. One major dfferent between dfferent decson tree algorthms s how to search for attrbute/value pars for splttng the data space. C

3 algorthm uses nformaton gan to judge whch attrbute and whch value to use for data splttng, whch s defned n the followng equatons: Entropy: the degree of purty n the dataset, does the dataset contan pure or ambguous nformaton on classfcaton results? Entropy( S) p logp c 1 2.[1] and consstent nformaton on equpment costs. The same splttng process s repeated on the subsets of data or chld nodes for further growng of trees down the paths, f the termnaton crtera are satsfed (too few number of cases or suffcently pure nformaton n the node) and take the chld nodes as leaf nodes n the tree structure, otherwse, take the chld node as a decson node and contnue the splttng process untl all the nodes are termnal leaf nodes. Where p s the proporton of orgnal dataset S belongng to Class, c s the number of classes Informaton gan: the amount of nformaton ncrease n the dataset after knowng attrbute A of dataset S Sv Gan( S, A) Entropy( S) Entropy( Sv) S v Values( A).[2] Where values (A) s the set of all possble values for attrbute A, S v s the subset of S for whch attrbute A has value v. Splt Informaton: the amount of nformaton n the dataset after parttonng by c-valued attrbute A c S S SpltInformaton log2 1 S S.[3] Where S ~S c are the c subsets of examples resultng from parttonng S by the c-valued attrbute A. Informaton gan rato: the rato between nformaton gan and splt nformaton Gan( S, A) GanRato( S, A).[4] SpltInformaton( S, A) Ths gan rato s used to select crtera for splttng dataset S nto subsets. From the root node, the C4.5 algorthm scans over the dataset wth varous splttng optons : dfferent attrbutes and dfferent splttng values (for example, a conjuncton of the attrbute equpment age and value 5 composes a decson queston f the equpment age s less than 5 years ). The splttng crtera leadng to the largest nformaton gan rato ndcates the best combnaton of attrbute and splttng values, or the best parttonng of dataset wth subsets contanng pure 5. MODELING OF THE EQUIPMENT M&R COST USING C4.5 DECISION TREE ALGORITHM Among all the ownng and operatng cost tems, mantenance and repar (M&R) costs are the most uncertan element whch s the most dffcult to predct. The M&R costs cover such tems as preventve mantenance, work order repars (repars at the shop), and runnng repars (repars on the shft). The spendng s necessary to keep the equpment runnng wth mantenance actons and tmely repars. The predctve model on the annual equpment M&R cost s traned, valdated and used to facltate equpment replacement analyss. Data preparaton The M&R cost model s learned from a large collecton of equpment data on a group of 180 unts of dump trucks wth capactes of 6 tons and above, wth the followng features: The dump trucks belong to dfferent operatonal dvsons of the contractor 8 factors of potental mpact on equpment M&R cost are selected and shown n Table 1 The annual M&R costs of these unts are collected for the years for study Incluson of correlated varables tends to overestmate the contrbutons from one factor and make the model unstable, showng phenomena of multcollearty. A smple correlaton analyss found that the AnnualKM and AnnualFuelCost are hghly correlated, wth a correlaton factor of 0.89, therefore the Annual fuel volume s reserved as a more accurate measurement of equpment 925

4 servce as t takes the truck load level and envronment condtons nto consderaton. Tab. 1 Attrbutes for equpment group Dump trucks, 6 tons and above Factors of Impact Descrpton Nr Predctor Varables 1 Age, numercal varable age of the equpment unt, n years 2 Manufacturer, categorcal Manufacturer of the varable equpment unt 4 Dvson, categorcal Operatng dvson of varable the contractor 5 Class, categorcal Class of equpment varable 6 AnnualPMcost, Annual preventve numercal varable mantenance cost, n 2006 constant dollars 7 AnnualKM, numercal Annual travellng varable dstance, odometer readngs dfference from year start to end, n Klometers 8 AnnualFuelCost, Annual accumulated numercal varable fuel cost, n 2006 constant dollars Fg. 1 Annual Average Equpment M&R Cost versus Equpment Age For the study perod 2006~2010, the annual average equpment M&R cost dstrbuton over ther age s shown n Fgure 1. The annual cost change patterns are dffcult to descrbe except for cost fluctuatons from overhaul every 3~5 years. For ndvdual peces of trucks, ths s more dffcult to characterze as t shows great varatons over ts ages. To model the annual Total M&R cost usng C4.5, the cost data for each case s dscretzed nto fve cohorts ndcated by 1-very low,2-low, 3-average,4- hgh, 5-very hgh, wth equal frequency. Modelng and Valdaton Model s traned usng C4.5 algorthm, and Fgure 2 shows the partal model after tranng. The mnmum number of cases n the leaf node s set to 10, and the fgure shows only a few top level decson nodes due to the space lmt. Fg. 2 Partal Decson Tree Model for the annual M&R Cost 10-fold cross valdaton s used to valdate the accuracy and stablty of the model. The dataset s randomly dvded nto 10 subsets wth equal number of cases, wth one subset of data reserved for valdaton and the remanng 90% (nne subsets) used for tranng. Repeat the above 926

5 tranng and valdaton for each subset for a total of 10 dfferent tmes. The average predcton accuracy s 73.18%, see Table 2 for the confuson matrx table. The rows show the actual M&R cost cohorts, and the columns show the predcted cohorts. The decson tree structure s also transformed nto a set of rules, 30 rules are generated from the decson trees by trackng down each path of the decson tree from the root node. The followng shows a few of the dentfed nterestng rules: For dump trucks of 8-12 years age, and from manufacturer A, f the consumed fuel volume s more than 7,831 lters, the annual M&R cost s very hgh; For dump trucks from Manufacturer B, f the consumed fuel volume s between 2,397 and 7,831 lters, and the total PM hours s less than 209, the annual M&R cost s low For dump trucks from Manufacturer C, f the consumed fuel volume s more than 7,831 lters, and the total PM hours s more than180, the annual M&R cost s low or very low Table 2: Confuson Matrx Table Predcted Annual M&R Cost Cohorts very very Accuracy low low average hgh hgh very % low Actual Annual M&R Cost Cohorts % low % average % hgh very % hgh Nevertheless, not all the rule sets are nterestng, some are classfed as common knowledge or merely mply a fact but does not convey suffcent nformaton for decson actons. Another mportant output from the algorthm s the rankng of factors. As shown n Table 3, the most mportant factors nfluencng the annual M&R cost nclude Fuel volume consumed, elapsng age, manufacturer, and the total PM hours. The mportance of each nput varable s measured by the rato of nformaton gan and the orgnal amount of nformaton n the orgnal dataset wth respect to the M&R cost cohorts, as calculated by the followng defnton: Gan( S, A) Index of Importance= Entropy( S ).[5] The rankng of factors based on ther ndex of mportance s summarzed n Table 3. Tab. 3 Rankng of Factors of Impact based on Ther Index of Importance Nr Nodes Index of Importance 1 FuelVolume Age Manufacturer PMTotal Apart from ther nfluence n the tree buldng through data parttonng, these factors contan mportant nformaton on the equpment M&R cost. Fuel volume consumed s a domnant ndcator for the M&R cost, as t s related to the amount of servce delvered by the equpment. As equpment rate of use s gong down wth ts ncreasng age, elapsed tme (Age) s a predctor not as good as the fuel volume, although t s also an mportant factor that must be accounted for. Manufacturer s an mportant ndctor as equpment unts from some manufacturers s more relable than ther counterparts, or some unts perform poor wth extended lfe span. The total PM hours are mportant but they do not change sgnfcantly the M&R cost so long as the manufacturer s recommended PM programs are followed. As more vgorous PM programme s not ncluded n ths dataset, ther effects cannot be reflected n the results. Dvson and Class are not shown n the table as ther ndexes of mportance are 927

6 close to zero, showng they do not have any mpact on the equpment cost fluctuatons. 6. DISCUSSIONS ON THE M&R COST MODEL The derved M&R cost model s very useful for dscoverng nterestng rules for equpment replacement decson support as the rule sets quantfy the effects on cost change patterns caused by the varous factors of mpact. These nherent rules are dffcult to dentfy by doman experts. The dentfed rules can help to conduct the equpment replacement analyss on a partcular pece of equpment. For a partcular pece of equpment, dentfed rules can help the decson maker to predct the equpment M&R cost level n the comng years. Although t s not possble to predct the future M&R cost wth a very hgh accuracy, the model can ncorporate the nfluencng factors and mprove the predcton results wth sgnfcant mprovement. Other typcal use of dentfed nterestng rules sets nclude: comparson of equpment cost performance among manufacturers durng the expected lfe span; comparson of equpment PM strateges by evaluatng f mproved PM frequences really could help to reduce the equpment repar costs for a certan group of equpment. The most nterestng rules dentfed are these on the lowest cohort (1) and these on the hghest cohort (5) of the annual M&R cost. By contrastng these combned condtons leadng to the most desrable and the worst case scenaros, the decson makers can learn lessons and mprove ther practce n equpment mantenance management. 7. CONCLUSIONS The paper summarzes our research on the descrptve and predctve analyss of equpment M&R cost and ts nfluencng factors usng C4.5 decson Tree nducton algorthm. Decson rules can be generated from the exstng equpment data for decson support n equpment replacement. Factors of mpact on the varatons of equpment M&R cost are dentfed, prortzed, and used for decson analyss. The research supplements the tradtonal equpment replacement theory by combnng the fact-based cost-related rules nto the tradtonal equpment replacement models, reducng the uncertantes and hypothess nvolved n practcal applcatons. 8. ACKNOWLEDGMENT The research s supported by the General Research Fund (GRF) Nr of Research Grant Councl, Hong Kong SAR, Chna REFERENCES [1] Coller, C. A. and Jacques, D. E., Optmum Equpment Lfe by mnmum Lfe-cycle Costs, Journal of Constructon Engneerng and Management, ASCE, Vol. 110, No. 2, pp , 1984 [2] Gllerspe, J.S. and Hyde A. S., The replacement/repar decson for heavy equpment, Report VTRC 05-R8, Vrgna Transportaton Research Councl, November [3] Qunlan, J. R., C4.5: Programs for Machne Learnng. Morgan Kaufmann Publshers, Mateo, CA., 1993 [4] Reed Busness Informaton, Annual Report and Forecast. Supplement to Constructon Equpment, January 2007 ssue, New York, NY. [5] Taylor, J. S., A Statstcal Theory of Deprecaton Based on Unts Cost, Journal of the Amercan Statstcal Assocaton, pp , 1923 [6] Vorster, M.C. and Sears, G.A., Model for Retrng, Replacng, or Reassgnng Constructon Equpment, Journal of Constructon Engneerng and Management, ASCE, Vol. 113(1), pp ,