Internatinal Jurnal f Perfrability Engineering, Vl. 6, N. 4, July 21, pp. 355-362. RAMS Cnsultants Printed in India Cnditin-based Vehicle Fleet Retireent Decisin: A Case Study 1. Intrductin R. JIANG and GUANGCAI SHI Faculty f Auttive and Mechanical Engineering, Changsha University f Science and Technlgy, Changsha, Hunan 41114, China (Received n Aug.18, 29, revised April 1, 21) Abstract: The vehicle replaceent decisin is a ulti-bjective ptiizatin prble subject t the acquisitin budget and gvernent regulatin cnstraints. This necessitates a cnditin-based replaceent plicy. In this paper, we carry ut a case study f the vehicle fleet replaceent prble. Based n the field data in a vehicle fleet anageent syste, we derive a set f cnditin paraeters fr representing the health level f a vehicle. A crrelatin analysis is carried ut t identify key cnditin paraeters. The identified paraeters are then cbined int a health index. The index is useful fr cnditin-based vehicle replaceent decisin. Keywrds: Vehicle fleet replaceent, cnditin-based replaceent, replaceent scre, health index. A transprt cpany ften wns hundreds r thusands f vehicles with a service life fr abut 1 15 years. A large nuber f vehicles have t be replaced each year, and hence an ptial vehicle replaceent (VR fr shrt) decisin can bring t the cpany with substantial cst savings [1, 2]. The VR prble is a ulti-bjective (e.g., reliability and cst) ptiizatin prble subject t acquisitin budget cnstraint (due t incurring a large aunt f investent) and gvernent regulatin cnstraint [3, 4]. The acquisitin budget cnstraint results in a situatin where the vehicles with the sae age ay be retired at different ties [5]; and the regulatin cnstraint (aiing t reduce air pllutant eissins) results in a situatin where ld vehicles ay be retired befre their ecnic lifeties have been exhausted [4]. Many ethds have been develped t address the vehicle fleet replaceent prble. These include fleet age prfile analysis, strategic fleet acquisitin and retireent del, aintenance cst trend analysis, life cycle cst analysis, average cst analysis, and the annual aintenance cst liit ethd [5]. In ters f the decisin utput, the ethds rughly fall int tw categries: (a) Ppulatin-riented ethds: The decisin utput f a ethd (e.g., an ecnic life [6, 7]) is applicable fr all the vehicles in the sae age grup. (b) Individual-riented ethds: The decisin utput is n an individual basis s that the vehicles in the sae age grup can be retired at different ties [2]. This necessitates the perfrance evaluatin f each vehicle based n technical infratin (btained fr a vehicle inspectin) and ecnical infratin (btained fr field data). *Crrespnding authr s eail: jiang@csust.edu.cn 355
356 Renyan Jiang and Guangcai Shi A large aunt f field data in a vehicle fleet anageent syste is available. This akes it pssible t evaluate the health level f each vehicle fr cnditin-based retireent decisin. In this paper, we present an individual-riented apprach and carry ut a case study, which deals with a sub-fleet in a pstal vehicle fleet. The inputs include vehicle age, cuulative kiletres (CK fr shrt), cuulative fuel cnsuptin, and cuulative aintenance cst. The VR dates are als partially knwn. We derive several cnditin variables fr the recrded paraeters. A crrelatin analysis is carried ut t identify key cnditin variables, which are further incrprated int a health index fr cnditin-based VR decisin. The paper is rganized as fllws. Sectin 2 gives the case backgrund. A preliinary data analysis is carried ut in Sectin 3. The vehicle health index is derived in Sectin 4. The paper is cncluded in Sectin 5. 2. Backgrund A ixed pstal vehicle fleet cnsists f 124 vehicles. We cnsider a sub-fleet f 15 vehicles, which are the sae type and del and started t perate n August 11, 1998. By the tie that data were cllected 13 vehicles had retired and 2 were still in service. The specific dates f VR are shwn in Table 1. Table 1: Replaceent Dates (bserved n July 1, 29) Date Dec. 28 Jan. 29 Jun. 29 In service 3 1 5 1 Vehicle n. 4 2 9 12 6 7 15 8 11 14 13 The gvernent regulatins fr the vehicles under cnsideratin are that the axiu age is 15 years and the vehicle with age f 1 years r ver ust pass se additinal annual tests. A vehicle anageent syste started t be run n January 1, 23, when the vehicle age was 4 years and 143 days (r initial age t = 4.3918 years). Fr each vehicle the syste recrds: CK reading k( t ) where t is the vehicle age, Cuulative il-cnsuptin l in litre r fuel cst C = 4.5l in RMB Yuan, and Cuulative aintenance cst C (crrective aintenance, spare part and tyre csts, etc.), which des nt include the verhaul cst because the budget fr verhaul (with an interval f 3-5 years) is separately cnsidered and fr a special surce. The data are updated per 6 nths. T reduce aintenance cst and iprve fuel ecny, the cpany ipleents an incentive plicy. The ain cntents are: (a) a fixed il-cnsuptin liit (in litre per kiletre) is set and the driver will wn r pay fr the difference between the actual and set il-cnsuptins, and (b) a axiu aintenance cst liit is set and the driver will pay fr the excessive part (this is why the syste des nt include the verhaul cst).
Cnditin-based Vehicle Fleet Retireent Decisin: A Case Study 357 3. Preliinary Data Analysis 3.1 Analysis f CK Figure 1 shws k versus t (started fr August 11, 1998). The dtted lines crrespnd t the vehicles that were retired relatively early, the fine lines crrespnd t the vehicles that are in perating r were retired relatively late, and the bld line is the average curve. Fr the figure, we have the fllwing bservatins: The relatin between the average kiletre reading and age is sewhat cnvex. This can be due t the behaviur t sufficiently utilize the vehicles befre the retireent r due t an increase in the transprt deand. It is nted that the lately retired vehicles have relatively large CK. This ay result fr the availability f a vehicle. In ther wrds, the CK reading indirectly reflects the availability f a vehicle and hence its health level. 3.2 Analysis f Cuulative Oil-Cnsuptin Figure 2 shws C versus k (started fr June 3, 23), which is a very gd prprtinal relatin. An epiric fitting is given by: C ( ).11298 k = k (1) Due t a very sall dispersin, C is nt a gd easure fr evaluating the health level f a vehicle. 1 8 8 6 k, 1 3 k 6 4 2 4 6 8 1 12 Age, years Figure 1: CK versus age C 4 2 2 4 6 8 k Figure 2: C versus k 3.3 Analysis f Cuulative Maintenance Cst Figure 3 shws C versus k (started fr June 3, 23). As can be seen, C is relatively dispersive, and hence can be a gd easure fr evaluating the health level f a vehicle. The average curve is als shwn in the figure and can be apprxiated by.95455 C ( ).2328 k = k (2) The fact that pwer paraeter is saller than 1 iplies that the aintenance cst increases with the usage slightly slwly dwn fr large k. This ay be because se aintenance actins were cancelled when the VR gets clse. 4. Evaluatin Mdel fr Health Level 4.1 Derived Cnditin Variables
358 Renyan Jiang and Guangcai Shi 4.1.1 Usage Rate / t Figure 4 shws / t versus t t. Fr the figure, we have the fllwing bservatins: Usage rate significantly varies with vehicles, iplying that it is a gd easure t represent the health level f a vehicle. The usage rate in the first half year f each year is bviusly lwer than the ne in the secnd half year. This ay result fr tw factrs: schedule f aintenance actins and fluctuatin f transprt lads. The usage rate at t t = 3.5 is relatively lw. This ay be because re vehicles underwent verhauls at the tie clse t that. In the last year befre the retireent, the usage rate keeps at a relatively high level. This ay be because the decisin-aker wants t sufficiently utilize the residual lives f the vehicles. 14 12 1 C 8 6 4 2 1 2 3 4 5 6 7 k Figure 3: C versus k / t 14 12 1 8 6 4 2 1 2 3 4 5 6 7 t-t Figure 4: Usage rates f vehicles 4.1.2 Fuel Cst Rate C ( k) / k Figure 5 shws the fuel cst rates (where k is the kiletre reading n June 3, 23). As can be seen fr the figure, a histry f C ( k) / k versus k can be divided int three phases: the initial lw il-cnsuptin phase, high il-cnsuptin phase, and steady lw il-cnsuptin phase. The first change fr the lw il-cnsuptin t the high il-cnsuptin ay be due t a wear-ut echanis, and the secnd change fr the high il-cnsuptin t the lw il-cnsuptin ay be due t vehicle verhauls. Since the steady lw il-cnsuptin rates are clse t each ther, the il-cnsuptin rate is nt a gd easure t represent the health level f a vehicle. 4.1.3 Maintenance Cst Rate C ( k) / k Figure 6 shws the aintenance cst rates and their average curve, which can be apprxiated by C k k k k =.315 + (3) 21121.2 612.52 The average curve has a iniu given by k k = 297.26. Since C des nt include the verhaul cst, the iniu pint ay crrespnd t verhauls. Since the aintenance cst rate significantly varies with vehicles, it is a gd easure t represent the health level f a vehicle.
Cnditin-based Vehicle Fleet Retireent Decisin: A Case Study 359 Accrding t [5], an ecnic replaceent age (which crrespnds t the age fr which the aintenance csts significantly increase fr an equilibriu value) can be deterined based n a aintenance cst trend analysis. Fr the current case, we let 15 ( i) 1 C ( t) r ( t) = (4) 15 i= 1 C / k.13.12.11.1.9.8.7.6 1 2 3 4 5 6 7 k-k Figure 5: Fuel cst rates f vehicles C/u.5.4.3.2.1 1 2 3 4 5 6 7 k-k Figure 6: Maintenance cst rates f vehicles Figure 7 shws r ( t ) versus t. As can be seen fr the figure, the iniu pint ay crrespnd t verhauls, and r ( t ) has a significant increase after t 9.4 years. As a result, the ppulatin-riented ecnic replaceent age is abut 9.4 years. This result can be referenced fr the vehicle fleet replaceent decisin..25.2 r(t).15.1.5 Overhauls Ecnic replaceent age 5 6 7 8 9 1 11 t Figure 7: Ecnic replaceent age based n aintenance cst trend analysis 4.2 VR Scre and Crrelatin Analysis Assue that the replaceent decisin is ade at t t = 6 r t = 1.3918 years. Let s d dente the replaceent scre f a vehicle at the decisin instant. A sall value f s d iplies that the vehicle has a high pririty t be replaced first. Fr the current case, we assign a replaceent scre 1, 2, 3, and 4 t thse vehicles that were r will be replaced in the first thrugh furth batches respectively. Table 2 shws the replaceent scres and relevant cnditin variables at the decisin instant. A crrelatin analysis between the replaceent scre and cnditin paraeters will help t identify significant variables fr individual-riented replaceent decisin.
36 Renyan Jiang and Guangcai Shi The crrelatin cefficient r is a easure f strength f linear relatinship between tw variables [8]. The crrelatin cefficient r( sd, θ ), where θ dentes the paraeters set shwn in the first rw f Table 2, is given in the last rw f Table 2. T judge the significance f a linear crrelatin, we need t deterine a critical value f the crrelatin cefficient. Accrding t [9], given a crrelatin cefficient r the significance f the linear crrelatin f tw variables can be tested using the fllwing statistic t transfr r t a Student's t -value: t r r 2 = / 1 r r t t 2 = / 1+ (5) The critical value f t assciated with the 8% level, ne tail, and the degrees f freed 15-1 = 14 is.8681. Naely, the critical value f r is.6555. The crrelatin cefficients whse abslute values are larger than.6555 are: r( sd, / t) =.7421, r( sd, C / k) =.6914. This iplies that / t [ C / k ] is psitively [negatively] related t the health level f a vehicle. These are cnsistent with the cnclusins btained in the previus analysis. Table 2: Replaceent Scres, Cnditin Paraeters and Crrelatin Cefficients s d k C C / t C / k C / k 1 87.369 64.5849 11.8384 92.676.1134.212 1 863.52 65.1726 11.316 99.32.1127.2195 1 945.683 68.3892 11.1642 95.248.1134.333 1 647.175 43.488 8.973 76.572.1126.362 1 8.366 57.1253 1.573 85.946.1128.2934 2 899.47 68.265 11.923 19.154.1127.1975 2 927.284 67.685 12.9634 118.6.1133.1489 2 794.928 57.9362 11.371 113.814.1127.2618 2 928.468 71.1522 1.7329 112.54.1122.2155 2 917.485 7.1847 9.9269 18.1.113.1733 3 937.819 7.3625 1.133 11.438.1132.1849 3 84.372 55.5791 7.122 99.14.1132.435 3 91.784 64.773 12.3481 117.436.1133.1558 4 936.727 73.751 1.426 119.568.1133.1549 4 919.621 68.9436 11.131 119.466.1132.1576 r ( s d, θ ).4362.4124 -.697.7421.3275 -.6914 4.3 Health Index We define a health index as belw: C H = a b, a, b > t where a and b are paraeters t be deterined. A large value f H iplies a healthy vehicle. We deterine a and b by iniizing (6) 15 ( i) ( i) 2 ( (, ) d ) (7) i= 1 Y = H a b s Using the data in Table 2 and the abve apprach, we have: a =.3274, b = 63.42 The health index cnsists f tw cpnents: t and C. T exaine their cntributins t H, we lk at
Cnditin-based Vehicle Fleet Retireent Decisin: A Case Study 361 a b C wa =, wb =, (8) H t H k C where H = a + b t k. Table 3 shws the values f H, w a and w b. As can be seen fr the table, the ain cntributin ces fr. This is cnsistent with the result t f the crrelatin analysis. It is nted: r( sd, H ) =.7962 > ax{ r( sd, / t), r( sd, C / k) }. (9) Naely, the crrelatin cefficient between the replaceent scre and health index is larger that the ne between the replaceent scre and its cpnent. Table 3 als shws the rank nuber ( R i ) f vehicle i. A sall value f R i iplies a sall value f H. It can be used t evaluate the cnsistency between the cpany s replaceent decisin and prpsed health index. Incnsistencies between the actual decisin and health index ccur: (a) Vehicle 2 [Vehicle 5] shuld be replaced in the third [secnd] batch but replaced in the secnd [third] batch, and (b) Vehicle 9 [Vehicle 12] shuld be replaced in the furth [third] batch but replaced in the third [furth] batch. Cnsidering the fllwing facts: The replaceent decisin can be pprtunity-based (e.g., an advanced replaceent is pssible fr a relatively health vehicle if a cstly preventive aintenance has t be perfred shrtly), and The incnsistencies are inr, the prpsed health index appears apprpriate, and can be used t prvide a relatively accurate initial ranking fr VR decisin. Table 3: Health Index and Its Cpnents Cntributins Vehicle i H Rank, R i w a w b 3 1.691 4.693.37 4 1.8595 5.72.2998 6 1.1953 3.6185.3815 8.2229 1.5233.4767 14.9535 2.62.398 1 2.3216 8.745.2595 2 2.9214 13.837.1963 7 2.664 6.6918.382 11 2.3171 7.7294.276 13 2.445 9.7631.2369 5 2.4435 1.7551.2449 9 2.9662 15.9216.784 15 2.8572 11.7956.244 1 2.9327 14.7994.26 12 2.9123 12.7965.235 Average.7289.2711
362 Renyan Jiang and Guangcai Shi 5. Cnclusins In this case study, we have presented a cnditin-based apprach fr evaluating the health level f a vehicle. The apprach is useful fr vehicle fleet replaceent decisin. The ain cnclusins have been: 1) The CK easure indirectly reflects the vehicle availability and hence is psitively related t the vehicle health level. 2) Based n the aintenance cst trend analysis, the ecnic life has been estiated as 9.4 years in this case study. Hwever, it is pssible fr a vehicle nt t be used t its ecnic life due t the regulatin cnstraint. 3) The crrelatin analysis is useful fr identifying key cnditin paraeters. It has been fund that the replaceent decisin is strngly crrelated with the usage rate and aintenance cst rate f a vehicle. 4) The usage rate and aintenance cst rate have been incrprated int a single health index, which is highly crrelated t the replaceent scre. The prpsed health index is useful t prvide an initial ranking f vehicle health level fr using in VR decisin. Currently, we are applying the prpsed apprach t anther ini vehicle fleet t further validate the apprach. T prte greater use f this apprach in industry, the apprach will be incrprated t a vehicle fleet decisin supprt sftware package. Acknwledgeent: The authrs thank Ms. M. Zhang fr her wrk in cllecting partial data used in this study. This research is supprted by the Key Prject f Scientific Research Fund f Hunan Prvincial Educatin Departent (N. 6A4). References [1] Sis B.W., B. G. Laarre and A.K.S. Jardine. Optial buy, perate and sell plicies fr fleets f vehicles. Eurpean Jurnal f Operatinal Research, 1984; 15(2), 183-195. [2] Dietz D.C. and P.A. Katz. U S West ipleents a cgent analytical del fr ptial vehicle replaceent, Interfaces, 21; 31, 65 73. [3] Dill J. Estiating eissins reductins fr accelerated vehicle retireent prgra. Transprtatin Research Part D 9 24; 87 16. [4] Spitzley D.V., D.E. Grande, G.A. Keleian and H.C. Ki. Life cycle ptiizatin f wnership csts and eissins reductin in US vehicle retireent decisins. Transprtatin Research Part D: Transprt and Envirnent, 25; 1(2), 161-175. [5] Rueda A.G. and F.G. Miller. Cparative analysis f techniques fr deterining bus replaceent intervals. Maintenance Manageent Internatinal, 1983; 3(3), 271-286. [6] Scarf P.A. and M.H. Hashe. On the applicatin f an ecnic life del with a fixed planning hrizn. Internatinal Transactins in Operatinal Research, 1997; 4 (2), 139-15. [7] Jiang R. and M. Zhang. Vehicle fleet replaceent decisin: se pssible plices. WCEAM- IMS 28, Beijing, 76-766. [8] Blischke W.R. and D.N.P. Murthy. Reliability: deling, predictin, and ptiizatin. Jhn Wiley, New Yrk; 2. [9] Fisher R.A. Statistical Methds fr Research Wrkers. Oliver and Byd, Edinburgh; 197. Renyan Jiang (Fr his bigraphy, please see IJPE, Vl. 6, N. 3, March 21, page 287) Guangcai Shi is a PG student at Changsha University f Science and Technlgy. He wrks in the directin f reliability and ulti-criteria decisin analysis.