Bali Trans Sarbagita: Comparison between Utility maximization and Regret Minimization

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1 Bal Trans Sarbagta: Comparson between Utlty maxmzaton and Regret Mnmzaton Prawra Fajarndra BELGIAWAN a, Anugrah ILAHI b, Kay W AXHAUSEN c a, Postdoctoral researcher, Insttute for Transport Plannng and Systems (IVT), ETH Zurch, Zurch, CH-8093, Swtzerland a E-mal: fajarndra.belgawan@vt.baug.ethz.ch b, Doctoral Student, Insttute for Transport Plannng and Systems (IVT), ETH Zurch, Zurch, CH-8093, Swtzerland b E-mal: anugrah.lah@vt.baug.ethz.ch c, Professor, Insttute for Transport Plannng and Systems (IVT), ETH Zurch, Zurch, CH-8093, Swtzerland c E-mal: axhausen@vt.baug.ethz.ch Abstract: Wth the ntroducton of new BRT system, Denpasar Greater Area, Bal (Sarbagta), Indonesa now have a new alternatve n addton to the currently avalable alternatves such as feeder, car, and motorcycle. We compare random utlty maxmzaton model (RUM) wth random regret mnmzaton model (RRM) usng data from 526 respondents of Sarbagta. We obtan 14,055 observatons n a total of three categorcal dstance; short, medum, and long, whch each category has ten stated preference experments. Our model ft results suggest that RUM outperforms RRM n all dstance category. We found that for long dstance, travel tme s nearly elastc for BRT, feeder, and car, whle cost s elastc for car. Thus, the mplementaton of a polcy to reduce BRT travel tme mght gve a substantal ncrease n the probablty of choosng the mode, whle polcy to ncrease car cost mght gve a substantal reducton n the probablty to choose a car. Keywords: Sarbagta BRT, Random Regret Mnmzaton, Value of Travel Tme Savngs, Demand Elastctes. 1. INTRODUCTION In Denpasar Greater Area, Bal (Sarbagta Area), one of the agglomeraton areas n Bal, Indonesa, the Mnstry of Transportaton has mplemented a new BRT system called Trans Sarbagta (Prayudyanto et al. 2016). Ths new BRT system mplementaton was amed to provde more hgh-qualty servce to the people. The government was hopng that ths system could reduce the traffc congeston and at the same tme ncrease the accessblty of the people of Sarbagta. Wth the ntroducton of new BRT system, people of Sarbagta now have a new alternatve n addton to the currently avalable alternatves such as feeder, car, and motorcycle. When facng several alternatves, t s reasonable to say that people tend to choose an alternatve whch maxmzes ther utltes. Ths concept s wdely known as random utlty maxmzaton (RUM). In transportaton research, one of the famous modelng technque to choose a mode of transportaton s multnomal logt (MNL). Recently there s a growng nterest n mplementng an alternatve modelng technque whch s called random regret mnmzaton (RRM) (Chorus et al., 2008). There have been many studes mplemented ths modelng technque for transportaton related choce decson. For example route choce, travel nformaton acquston choce, parkng lot, shoppng locaton (Chorus, 2010; 2012), automoble fuel choce (Hensher et al. 2013), wllngness to

2 pay for advanced transportaton servces, and salary and travel tme trade off (Hess et al., 2014). Accordng to Chorus et al. (2014), there were 43 emprcal studes that compare RUM and RRM from Regardng ther model ft, 15 tmes RRM outperforms RUM and 15 tmes the other way around. Other 13 emprcal studes show nether of these two modelng approaches outperforms each other. Addng to that lst s the study by Belgawan et al. (2017) where they compare the performance of RUM and RRM on seven Swss data sets. They found that RRM outperforms RUM n sx cases. Note that most emprcal studes compared RUM and RRM regardng ther model ft. Few exceptons compared the applcaton of the model such as the value of travel tme savngs (VTTS), and demand elastctes. Therefore, the am of ths study s to compare between RUM and RRM approaches for the case of Sarbagta. We would lke to fnd whch modelng approaches s best used for the area so that t can be used by the government to mplement a new polcy regardng publc transportaton system. We also present the VTTS and demand elastctes obtaned from those two models as consderaton for a new transport polcy. Another contrbuton of ths research s to add new RRM case study to the exstng body of RRM research whch to our knowledge there has not been any dscusson regardng the comparson of RUM and RRM for Indonesa case, specfcally Bal area. In Secton 2 we dscuss the hstory of RRM and ts mplementaton, whle n Secton 3 we descrbe how we collect the data and the descrptve statstcs of the data. In secton 4 we dscuss the modelng technque and model comparson. Followed by secton 5 where we compare the VTTS and demand elastctes. Fnally, we conclude our study n secton MODELLING APPROACHES 2.1 Random Regret Model Random regret mnmzaton was frst ntroduced by Chorus et al. (2008) for a model of travel choce. Accordng to Chorus et al. (2008) n RRM, ndvdual bases hs/her choce between alternatves wshng to avod a stuaton where a non-chosen alternatve turns out to be more attractve than the chosen one, whch causes regret. Thus, the ndvdual when choosng between alternatves s assumed to mnmze antcpated regret as opposed to maxmzng hs/her utlty. Chorus (2010) stated that ths frst RRM approach has two lmtatons. Therefore, he mprovsed the technque to allevate those lmtatons wth the new RRM-approach. In RRM framework, the regret assocated wth alternatve s obtaned by the followng formula (Chorus, 2010): where, RR n RR n R n n j k ln 1 exp k kjn kn n : random (or total) regret for an alternatve for person n R n : observed regret for an alternatve for person n n : unobserved regret for an alternatve for person n : alternatve specfc constant k : estmable parameter assocated wth generc attrbute k kn, kjn : values assocated wth an attrbute k for, respectvely, person n choosng alternatve over alternatve j. Smlar to RUM formulaton of choce probabltes (McFadden, 1974), the RRM framework assumes the error term n Eq. 1 be dentcally and ndependently dstrbuted (..d) 2 (1)

3 Extreme Value Type I-dstrbuted wth a varance of formulaton of choce probabltes s as follow: P n j 1 J exp Rn exp R jn 2 /6. In the RRM settng, the (2) The result from MNL and RRM models can be used to calculate the value of travel tme savngs (VTTS) and demand elastctes. 2.2 Value of Travel Tme Savngs The value of travel tme savngs (VTTS) measures how much money (e.g. Indonesan Rupah - IDR) a person s wllng to pay for a reducton of travel tme unt (e.g. hour). To measure the VTTS for MNL model we can use the formula below. VTTS MNL n V / T 60 n n T 60 (3) Vn / Cn C Where V n represents systematc utlty for an alternatve for person n, T n represents travel tme for the person choosng an alternatve, and represent the cost for the person choosng an alternatve. The parameters of tme and cost are represented by and respectvely. We use the formula taken from Chorus (2012) to measure the VTTS for RRM, as shown below. T n C VTTS RRM n n R 60 R n n n / TT / TC n n 60 j j C T C n exp T T exp C Note that, n contrast to RUM, RRM s a context-dependent model, whch means the performance of other alternatves nfluences the VTTS for a chosen alternatve. Therefore, as shown n Eq.4, VTTS measures wll change when the number of avalable alternatves n the choce set ncreases/decreases. Changes n the attrbutes of chosen alternatve as well as non-chosen alternatves wll also nfluence the VTTS. The dervaton of the formula to measure VTTS for RRM can be seen n Belgawan et al. (2017) 2.3 Demand elastctes Drect elastcty shows the relatonshp between a percentage change n the magntude of the attrbute and the percentage change n the probablty of choosng an alternatve based on the respected attrbute. The formula to measure the dsaggregate drect pont elastctes for RUM model s shown below (Ben-Akva and Lerman, 1985) P C jq jq T q C q 1 1 n kn En kn ( 1 Pn ) k kn (5) kn Pn (4) Hensher et al. (2013) derved for the frst tme an equaton to measure the elastcty of RRM Eq.6 below. The dervaton of the formula can also be seen n Belgawan et al. (2017). 3

4 J Rq R jq E n kq P jq kq kq j J j1 kq (6) In ths paper, we are comparng the model ft, VTTS and demand elastctes of standard RUM model (MNL) wth the RRM (Chorus, 2010) to see whch model s sutable for the Sarbagta case. 3. DATA COLLECTION AND DESCRIPTION The data was collected n 22 nd 25 th of January 2016 n Sarbagta by SUTIP (Sustanable Urban Transportaton Improvement Project) part of GIZ (Deutsche Gesellschaft für Internatonale Zusammenarbet) project n Indonesa wth total respondents of 526 respondents (Prayudyanto et al. 2016). The survey was conducted by dstrbutng the questonnare proportonally based on populaton n each regon n Sarbagta area. By proportonally, t means that we weghted our sample wth the Bal populaton based on 2010 populaton census (Statstcs of Bal Provnce, 2016). The characterstcs of our respondents can be seen n Table 1 below. We present the gender, age, and ncome proporton of our 526 sample. In the rght column, we present the gender and age proporton of 3,890,754 Bal populaton from 2010 populaton census. Table 1. Sample Descrptve Analyss Varable Value Sample Populaton Male 50.00% 50.41% Female 50.00% 49.59% Age % 40.27% % 26.37% % 19.16% % 7.63% % 6.57% Income (n IDR per month*) Less than IDR 1,000 K 34.62% NA IDR 1,000 K - 2,000 K 28.54% NA IDR 2,000 K - 6,000 K 30.16% NA IDR 6,000 K - 10,000 K 5.87% NA More than IDR 10,000 K 0.81% NA *At the tme of the survey, USD 1 = IDR 13,600. We have almost equal gender proporton n our sample whch s smlar to the populaton. The bggest part of our respondents belongs to undergraduate students age (1-24), almost smlar to the populaton proporton where the bggest part of the populaton s also under 25. Snce the proporton of age category of our sample s not smlar to the populaton proporton, we calculate the weght usng post-stratfed weghts. The weght calculaton s necessary to calculate the aggregate drect pont elastctes n Secton 5. The proporton of monthly ncome s almost equal for the three lowest categores, whle we have a small percentage of hgher ncome. In the survey, each of the respondents s gven sets of scenaros where they need to choose between four alternatves modes: Trans Sarbagta Bus Rapd Transt (BRT), feeder, car, and motorcycle. Each of the alternatve s gven some attrbutes. For BRT and Feeder, the attrbutes are travel tme (n mnute), travel cost (n IDR 1K), watng tme (n mnute), and walkng dstance to the shelter (n meter). Whle for car and motorcycle the attrbutes are 4

5 travel tme (n mnute), travel cost (n IDR 1K), parkng cost (n IDR 1K), and the ease of parkng (bnary response; 1=easy, 0=otherwse). Each scenaro has dfferent attrbute characterstcs whch can be seen n Fgure 1. Fgure 1. Examples of scenaros for stated mode choce experments Ths survey conssts of sx blocks whch desgned usng orthogonal fractonal factoral Hensher et. al. (2005). There are three dfferent categorcal scenaros n each block, whch based on dstance; short (less than 5 km), medum (between 5 km and 15 km), and long (more than 15 km). There are ten stated preference (SP) experments for each respondent n one categorcal dstance, therefore, n total, each respondent faces 30 SP experments and for all blocks, we have180 combnaton of dfferent attrbutes. There are 526 respondents that we use n our analyss. There are some respondents that dd not complete the questonnare, thus, n total, we have 4,928 observatons for short-dstance, 4,528 for medum-dstance, and 4,599 for long-dstance. Detaled attrbutes and values n each alternatve s shown n Table 2. 5

6 Table 2. Attrbute and values of the alternatves n stated choce survey Alternatves Attrbute Values BRT Travel tme (mnutes) Travel cost (IDR 000) Watng tme (mnutes) Walkng dstance to shelter (meter) Feeder Car Motor cycle Travel tme (mnutes) Travel cost (IDR 000) Watng tme (mnutes) Walkng dstance to shelter (meter) Travel tme (mnutes) Travel cost (IDR 000) Parkng Cost (IDR 000) The ease of parkng Travel tme (mnutes) Travel cost (IDR 000) Parkng Cost (IDR 000) The ease of parkng 4. MODEL ESTIMATION 5, 10, 15, 30, 45, 60, 75, 105 2, 3, 5,7,9 5, 10, 15, 20 50, 100, 150, 200 5, 10, 15, 30, 45, 60, 75, , 3, 5, 6, 7, 9, 12 5, 10, 15, 20 50, 100, 150, 200 5, 10, 15, 20, 30, 45, 60, 75, 90, 105 2, 4, 5, 6, 8, 10, 15, 20, 25 2, 4, 5, 8, (easy) 5, 10, 15, 30, 45, 60, 75 1, 2, 3, 4, 6, 9, 12, 15 2, 4, 6, (easy) 4.1 Model Specfcaton RRM s a context-dependent model, whch means choosng an alternatve s nfluenced by the presence of other alternatves n term of ther attrbute values, therefore for ths study, we only use a parsmonous model formulaton wth only generc attrbutes travel tme and cost. The generc attrbute s an attrbute that s avalable across all alternatves. Those generc attrbutes are suffcent to measure the VTTS and demand elastctes. In ths secton, we present the utlty functon for the MNL and RRM. The estmaton s maxmum lkelhood usng PythonBogeme (Berlare, 2016). The general utlty functon for MNL model s as follow: V T C (7) T C where, V k T C : utlty for BRT (=1), feeder (=2), car (=3), motorcycle (=4) : alternatve specfc constant (ASC) assocated wth (fxed at 0 for =1) : estmable parameter assocated wth attrbute : travel tme for alternatve : cost for alternatve k For the classcal RRM, the general regret functon s as follows: R j ln 1 exp T T j T ln1 exp C C j C j (8) where, R j : regret for alternatve : the chosen alternatve : the competng alternatve 6

7 4.2 Model Estmaton We present the result of the MNL and RRM n Table 3. The reference choce s Trans Sarbagta. As mentoned n Secton 3, we dvded our observatons nto three categores accordng to the dstance. For the RUM case, we can see that almost all parameters are sgnfcant wth a negatve sgn. In the case of RRM, all the parameters are sgnfcant, wth all attrbutes have a negatve value, and the ASCs have a postve value. Table 3. Model comparson between MNL and RRM RRM MNL Short RRM Short MNL Medum Varables Medum MNL Long RRM Long Est. t-test Est. t-test Est. t-test Est. t-test Est. t-test Est. t-test Travel tme * * * * * * Cost * * * * * * ASC Feeder * * * * * * ASC Car * * * * * * ASC Motorcycle * * * * * * Observatons Fnal-LL Rho-square AIC BIC *p value <0.01. All of the parameter estmate (tme and cost) are sgnfcant (p value < 0.01) wth expected sgn. Note that the nterpretaton of MNL result s dfferent than the nterpretaton of RRM results. For example, n short dstance MNL, ncreasng of a unt of one attrbute, travel tme, decrease 0.04 unt of utlty assocated wth mode alternatve, smlar nterpretaton also apples to travel cost. However, for the RRM parameter estmate, an ncrease n travel tme refers to the potental decrease n regret assocated wth comparng a chosen mode alternatve wth other non-chosen mode alternatves. Therefore we cannot just compare the magntude of parameter estmate of an attrbute between MNL and RRM. For drect comparson of the nfluence of an attrbute, we need to compare the elastctes (n Secton 5), whch gve the percent change n the choce probablty of an alternatve as a result of a percent change n one of ts attrbutes. Negatve ASCs n MNL case tells us that ceters parbus BRT s preferred compare to other modes. Smlarly, postve ASCs for RRM ndcates that those modes gve more regret than choosng BRT. Overall we can say that BRT s the most preferred mode for all dstance categores whle car s the least preferred mode for short and medum dstance. Interestngly car s more preferred for the case of long dstance compare to feeder and motorcycle whch make sense. Regardng model ft, we can compare log-lkelhood, Rho-squared as well as Akake Crteron (AIC) and Bayesan Crteron (BIC). From the fnal-ll, we can see that MNL s better than RRM. From the Rho-square, MNL s slghtly better than RRM for the short and medum dstance. From the AIC comparson, t appears that MNL s better than RRM for the medum dstance. For nternal valdaton, we performed out-of sample model estmaton and formulaton, where we choose 2/3 of the sample for estmaton and smulate the model on the rest of 1/3 sample. For all dstance categores, MNL outperforms RRM. 7

8 5. MODELS APPLICATION 5.1 Value of Travel Tme Savngs We present the mean value and standard devaton of the value of travel tme savngs for three dstance categores for RRM model n Table 4. MNL s not a context-dependent model. Therefore the VTTS of an alternatve s not nfluenced by the performance of other alternatves n contrast to RRM. It s qute nterestng that overall the VTTS of medum dstance s lower than the short dstance VTTS. The VTTS for long dstance s the hghest whch makes sense. Normally we would expect that the VTTS for car s hgher than publc transport. However, t appears that t s not the case for Bal. Table 4. Value of travel tme savngs (n IDR/hour*) Short dstance Medum dstance Long dstance Alternatves RRM RRM RRM MNL MNL MNL Mean Std. D Mean Std. D Mean Std. D BRT 15,414 1,760 14, ,680 2,360 Feeder 15,102 1,931 14, ,817 2,347 15,358 12,786 18,421 Car 14,877 1,717 12, ,202 2,224 Motorcycle 16,728 1,845 13, ,133 2,131 *At the tme of the survey, USD 1 = IDR 13,600. To gve a better depcton of the VTTSs dstrbuton, we plot the VTTS by alternatve modes for short, medum and long dstance n Fgure 2, Fgure 3, and Fgure 4. On the x-axs, we present the alternatves modes. At the y-axs, we present the VTTS n IDR 1,000 per hour. The reference lne attaches to the y-axs represents the MNL VTTS for that dstance category. For short dstance travel, we can see that the medan value RRM of BRT, feeder, and car are below the MNL lne. For the medum and long dstance travel, the medan value RRM of BRT and feeder are above the MNL lne. Fgure 2. Value of travel tme savngs for short dstance travel RRM (IDR 1,000/hour) 8

9 Fgure 3. Value of travel tme savngs for medum dstance travel RRM (IDR 1,000/hour) Fgure 4. Value of travel tme savngs for long dstance travel RRM (IDR 1,000/hour) 5.2 Demand Elastctes To compare elastctes between models, we have to calculate the aggregate drect pont elastctes for each model. The measurement formula, presented n Atasoy et al. (2013), s shown below: w P N W s n n EnX nxkn kn N s n1 w n np 1 n E (9) Where wn represents the sample weght for an ndvdual populaton N and from sample N s from E s the dsaggregate elastcty of demand of ndvdual n for nxkn varatons n the attrbute X kn. We weghted each observaton on our data sets accordng to the representaton of ts age and gender category n Bal populaton data set (Statstcs of Bal Provnce, 2016) as dscussed n Secton 2. We present the aggregate drect pont elastctes for travel tme and cost for three dstances category for MNL and RRM n Table 5. Travel tme and cost for all models are relatvely nelastc except for feeder travel tme and car travel tme n the long dstance category. The percentage dfferences for short dstance travel are substantally hgh, hgher 9 n

10 than the medum and long dstance. The travel tme and cost elastctes for RRM are greater than RUM for short dstance. As for the medum and long dstance, the travel tme elastctes for RRM are greater than RUM for BRT, feeder, and car. For motorcycle travel tme elastctes and all cost elastctes for medum and long dstance, MNL elastctes are hgher than RRM. For the nterpretaton of the elastctes, we can take one example, for short dstance MNL, a 10% ncrease n the travel tme of BRT makes, on average ceters parbus, a 1.4% reducton n the probablty of choosng BRT. At the same tme, 10% ncrease n BRT travel tme n the context of RRM takes nto account the travel tme assocated wth other three alternatve modes. A 10% ncrease n BRT travel tme, results n 3.3% reducton n the probablty of choosng BRT, whch explctly accounts for the dfference n travel tme n the set of avalable alternatves. The dfference s 135.7% wth RRM beng hgher than MNL, suggestng that the possblty of the wrong choce s taken, may have been made amplfes the behavoral responses. For medum and long dstance, changes n travel tme of BRT, feeder, and car mght gve a substantal mpact on the reducton/ncrease of probablty of choosng those modes. Polcy to reduce travel tme of BRT and feeder mght ncrease the probablty of choosng those modes for medum and long dstance travel. Therefore, accelerate development of the rest planned corrdors, as (Governor of Bal regulaton, 2010) stated that there are 17 corrdors are planned, mght be hghly mportant to support all commutng actvtes n Sarbagta area. Alternatvely, polcy maker could also thnk about the mplementaton of road prcng or congeston chargng to reduce the probablty to use car snce the cost of car for long dstance s nearly elastc. However, t should be proofed by future research. Travel tme Cost Table 5. Travel tme and cost elastctes Short dstance Medum dstance Long dstance Alternatves % df- % df- % df- MNL RRM MNL RRM MNL RRM ference ference ference BRT Feeder Car Motorcycle BRT Feeder Car Motorcycle CONCLUSION In ths paper, we try to compare the wdely used modelng technque MNL whch belong to the Random Utlty Maxmzaton framework wth the recently ntroduced Random Regret Mnmzaton framework. To check the senstvty to dstance, at the tme of the survey our respondents were gven ten scenaros for each of three dstance category, short (below 5 km), medum (5-15km), and long dstance (more than 15 km). We perform MNL and RRM for each of those dstance categores wth only two generc attrbutes travel tme and cost. We compare model ft, the value of travel tme savngs and demand elastctes of those two models. Comparng fnal-ll, MNL outperforms RRM n all dstance category. Regardng the VTTS, usng only generc attrbutes, travel tme and cost, RRM can gve rcher nterpretaton compare to MNL. For MNL we obtan one VTTS for all alternatve modes, whle for RRM we can obtan VTTS for all alternatves. We found an nterestng result that the VTTS for car overall s lower than BRT/feeder. The VTTS results obtaned for these 10

11 modelng approaches can be used for polcy makers to do cost beneft analyss for the transportaton related project. As for the demand elastctes, we found that for short dstance travel, the drect elastctes for travel tme and cost are nearly nelastc, that means the ncrease on both attrbutes mght not resultng n substantal reducton for the probablty of choosng the partcular mode. However, we found that n the medum and long dstance categores, travel tme s nearly elastc (elastc for feeder and car long dstance), whle cost s nearly nelastc for car. That means the mplementaton of a polcy to reduce BRT and feeder travel tme mght gve a substantal ncrease n the probablty to choose those modes, at the same tme, polcy to ncrease car cost mght gve a substantal reducton n the probablty to choose a car. Ths research s the frst one to compare RUM and RRM for Indonesan context. There are several lmtatons to ths study. We realze that low model fts that we obtan mght be because we only use generc attrbutes. We dd not utlze other non-generc attrbutes such as watng tme, walkng dstance to shelter, parkng cost and easness of parkng. We also do not use nteracton varable wth soco-demographc. Regardng the data collecton, we realze that stated preference survey (SP) tend to gve the lower VTTS than revealed preference survey (RP) snce the travel tme and cost used n the calculaton are hypothetcal tme and cost whch strongly depends on the expermental desgn (Brownstone and Small, 2005). Therefore, further research n the framework of RRM, possbly usng RP data, s necessary so that RRM can also be mplemented n Indonesa n general as an alternatve to RUM modelng technque. ACKNOWLEDGEMENTS The authors wsh to acknowledge SUTIP (Sustanable Urban Transportaton Improvement Project) part of GIZ (Deutsche Gesellschaft für Internatonale Zusammenarbet) for allowng us to use survey data n ths study. REFERENCES Atasoy, B., Glerum, A., Berlare, M. (2013) Atttudes towards mode choce n Swtzerland. dsp The Plannng Revew, 49, Belgawan, P. F., Schmd, B., Dubernet, I., Axhausen, K. W. (2017) Comparson between RUM, RRM varants, and RAM: Swss SP and RP data sets. 17 th Swss Transport Research Conference (STRC 2017), Monte Verta, Ascona, May Ben-Akva, M., Lerman, S. R. (1985) Dscrete Choce Analyss: Theory and Applcaton to Travel Demand. MIT Press, Cambrdge, MA. Berlare, M. (2016) PythonBogeme: a short ntroducton. Report TRANSP-OR Seres on Bogeme, Transport and Moblty Laboratory, School of Archtecture, Cvl and Envronmental Engneerng, Ecole Polytechnque Fédérale de Lausanne, Lausanne, Swtzerland. Brownstone, D., Small, K. A. (2005) Valung tme and relablty: assessng the evdence from road prcng demonstratons. Transportaton Research Part A: Polcy and Practce, 39, Chorus, C. G. (2010) A new model of random regret mnmzaton. European Journal of Transport and Infrastructure Research, 10(2), Chorus, C. G. (2012) Random Regret Mnmzaton: An Overvew of Model Propertes and Emprcal Evdence. Transport Revews, 32(1),

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