A train dispatching model based on fuzzy passenger demand forecasting during holidays

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1 Journa of Industria Engineering and Management JIEM, (1): Onine ISSN: Print ISSN: A train dispatching mode based on fuzzy passenger demand forecasting during hoidays Fei Dou 1,2, Jie Xu 2, Li Wang 1,2, Limin Jia 2 1 State Key Laboratory of Rai Traffic Contro and Safety, Beijing Jiaotong University, 2 Schoo of Traffic and Transportation Beijing Jiaotong University (China) @bjtu.edu.cn, jxu1@bjtu.edu.cn, wangi298@gmai.com, jiam@vip.sina.com Received: October 2012 Accepted: March 2013 Abstract: Purpose: The train dispatching is a crucia issue in the train operation adjustment when passenger fow outbursts. During hoidays, the train dispatching is to meet passenger demand to the greatest extent, and ensure safety, speediness and punctuaity of the train operation. In this paper, a fuzzy passenger demand forecasting mode is put up, then a train dispatching optimization mode is estabished based on passenger demand so as to evacuate stranded passengers effectivey during hoidays. Design/methodoogy/approach: First, the compex features and reguarity of passenger fow during hoidays are anayzed, and then a fuzzy passenger demand forecasting mode is put forward based on the fuzzy set theory and time series theory. Next, the bi-objective of the train dispatching optimization mode is to minimize the tota operation cost of the train dispatching and unserved passenger voume during hoidays. Finay, the vaidity of this mode is iustrated with a case concerned with the Beijing-Shanghai high-speed raiway in China. Findings: The case study shows that the fuzzy passenger demand forecasting mode can predict outcomes more precisey than ARIMA mode. Thus train dispatching optimization pan proves that a sma number of trains are abe to serve unserved passengers reasonaby and effectivey. Originaity/vaue: On the basis of the passenger demand predictive vaues, the train

2 dispatching optimization mode is estabished, which enabes train dispatching to meet passenger demand in condition that passenger fow outbursts, so as to maximize passenger demand by offering the optima operation pan. Keywords: raiway transportation, passenger demand forecasting, train dispatching, fuzzy ogica reationships, optimization mode 1. Introduction With the constant improvement of China's high-speed raiway network and the enhancement of connectivity within the area of the road network, inter-regiona passenger demand increases. The train can t ensure the safety and punctuaity of the train operation, aso unabe to meet the passenger demand. A arge number of passengers are stranded at the station or transfer to other modes of transport to trave. Especiay in the traditiona hoiday, the amount of trave passenger reached a peak vaue in a short period of time because of the sudden increase in passenger traffic and the uneven distribution. Some trains ack of staff and run without passengers, which causes great waste in transport capacity and increases the tota costs of consumption invisibe. It s very necessary to deveop detaied train dispatching program, distribute and transport passenger panned. Train dispatching is a muti-variabe, muti-constraint, arge-scae and muti-objective combination of optimization. In 1971, Amit and Godfarb appied mathematica programming methods to train scheduing probem. Experts and schoars studied extensivey train scheduing probem with mathematica programming theory (Dejax & Crainic, 1987; Beaujon & Turnquist,1991). Schoars did a arge number of vauabe researches in train depoyment method. For exampe, the concept of a passengers traveer time is proposed (Ghoseiri et a., 2004), which is the index to evauate passenger satisfaction. He aso estabished dua goa programming mode, whose target is to minimize a traveers time and energy consumption. Objective optimization mode (Higgins et a., 1996; Chen et a.2003), which coud minimize the tota train deays and operating costs, is estabished. The mixed integer programming mode (Kraay et a., 1991) to minimize train deay and tota energy consumption is proposed. The integer programming mode (Zhou & Zhong, 2005; Zhang & Jin, 2005) on considering the waiting time in train station and a the train trave time is estabished. Fuzzy expected vaue mode by fuzzy variabes (Yang et a., 2009), which goa is to minimize a passenger trave time and energy consumption, is estimated. It took tabu search agorithm to sove the train scheduing probem. And the objective function is the minimum rate of train deays. (Dong, Wang and Yan, 2005)

3 Study of train dispatching issues was not abe to meet passenger demand, so we must firsty forecast and assess passenger demand. Existing short-term raiway passenger demand forecasting contained the reevant mode predictions method and time mode prediction method. Some researchers estabished mode for passenger demand forecast on considering the transport competition, OD partition, the eve of socio-economic deveopment, nationa income and other factors. The mode contained neura network mode, Logit mode (Peter, Aura & Tommaso, 1996), mutipe regression mode and the MD mode (Butkevicius, Mindaugas, Vadas & Skirmantas, 2004; Fabio, 2006). Time mode prediction methods incuded passenger demand forecasting method based on time series anaysis, the gray mode (Chen, 2008), ARIMA mode and BP neura network mode (Guo, Qiao, 2008; Wang, 2006). This paper anayzed the hoiday passenger fow characteristics based on passenger data from Beijing South Raiway Station to Langfang station during 2011 Nationa Day hoidays. Then estabished the passenger change rate of fuzzy ogica reationship based on fuzzy theory and time series theory, and proposed fuzzy passenger demand forecasting mode. A bi-objective programming mode is estabished and the goa is to minimize the tota operation cost of the train dispatching and unserved passenger voume. In this mode, passenger demand is known, the constraints are station capacity restrictions, section capacity restrictions, the required number of trains restrictions and train set configuration restrictions. Thus, an interior-penaty method is used to sove this difficut probem. This paper took the Beijing-Shanghai high-speed raiway for exampe. The resuts showed that the train dispatching optimization mode is reasonabe and effective, and better abe to meet the actua passenger demand. The structure of this paper is as foowing Figure 1. Figure 1. The structure of a train dispatching mode based on fuzzy passenger demand forecasting during hoidays

4 2. Anaysis of passenger fow features during hoidays Hoidays are the main reason for sudden arge passenger fow and raiway passenger is increased substantiay. Passenger fow characteristics associated with time are mainy noninear fuctuation and quasi-periodic fuctuation of short-term passenger, as is shown in Figure 2. Figure 2. Change trend of passenger fow 2.1. Noninear fuctuation of passenger fow Sudden arge passenger fow during hoidays, which is imbaance, has the characteristics of instant sudden, passenger structura compexity and unidirectiona. During hoidays, start and end points of passenger are cear, which resut in the increase of passenger fow is singedirection in a certain period. The passenger fow during hoidays is mainy consist of civi servants, businessman, tourism, students and workers. The passengers arriva and eaving time mainy focus on two periods, before and after the hoidays beginning and ending. The passenger voume wi reach the peak in a short time and the peak time is outstanding. Therefore, the raiway passenger fow during hoidays is impacted by a variety of factors, and passenger fow change rate in short time is noninear fuctuation Quasi-periodic fuctuation of passenger fow The running speed of high-speed train is acceerating graduay, which shorten the distance between cities indirecty. The high-speed raiway passenger fow is growing year by year during the hoiday, daiy morning and evening peak traffic is arge and fat peak period passenger fow is gente. The passenger fow quasi-periodic fuctuations are significant

5 3. Fuzzy passenger demand forecast Variabe Description t: Passenger fow periods, i.e., one hour. p(t): The passenger fow in period t. pt (): The passenger fow predictive vaue in period t. n: The number of period in historica passenger fow. v(t): The change rate from p(t) to p(t+1). p max : The maximum vaue of the historica passenger fow. p min : The minimum vaue of the historica passenger fow. u i : The rate range of different changes in passenger fow. u i: The intermediate vaues of passenger fow change rate range u i. k i : The number of the passenger fow change rate beongs to passenger fow change rate range u i. M: The ast period in a of passenger fow periods Reguarity of passenger fow The passenger fow between the two stations in high-speed passenger raiway ine is statistica by a certain period of time. The history passenger fow in different periods is p(1), p(2), p(t-1),p(t),p(t+1), p(n-1), p(n). Take into account the passenger fow change rates between adjacent periods, which are denoted by v(1), v(2), v(t-1),v(t),v(t+1), v(n-2), p(n-1). Then anayze the passenger fow change rate, summarize up the reguarity of the changes in passenger fow of the adjacent period. In order to express passenger fow trend in adjacent period ceary and more accuratey, passenger fow change rate is normaized. Define standardized passenger fow change rate is v( t) ( p( t 1) p( t)) ( p p ) [ 1,1]. (1) max min When p(t+1)-p(t)<0, the passenger fow descends from period t to t+1. When p(t+1)-p(t)=0, the passenger fow doesn t change from period t to t

6 When p(t+1)-p(t)>0, the passenger fow increasing from period t to t+1. In order to refect the reguarity of the passenger fow trend ceary and express varying degrees of passenger fow change respectivey, we divide passenger fow change rate into eight intervas appying Zadeh's fuzzy set theory(zadeh, 1999). Define the universe of discourse U={u 1,u 2,u 3,u 4,u 5,u 6,u 7,u 8 }, and partition it into equa ength intervas u 1 =[-1,-0.75], u 2 =[-0.75,-0.5], u 3 =[-0.5,-0.25], u 4 =[-0.25,0], u 5 =[0,0.25], u 6 =[0.25,0.5], u 7 =[0.5,0.75], u 8 =[0.75,1]. Define each fuzzy set A i based on the re-divided intervas, fuzzy set A i denotes a inguistic vaue of the passenger fow represented by a fuzzy set, 1<i<8. A 1 denotes that passenger fow decrease is too arge, A 2 denotes that passenger fow decrease is arger, A 3 denotes that passenger fow decrease is micro-arge, A 4 denotes that passenger fow decrease is ess, A 5 denotes that passenger fow increase is ess, A 6 denotes that passenger fow increase is micro-arge, A 7 denotes that passenger fow increase is arger, A 8 denotes that passenger fow decrease is too arge. Determine the membership function of fuzzy subset A i using assign method, namey: when i 1, 1, xu1 A1( x) 0.5, x u2 0, x u u 1 2 1, xui ;when i 2,,7, Ai ( x) 0.5, x ui 1 ui 1 0, x ui ui ui 1 1 ; when i 8, 1, xu8 A8( x) 0.5, x u7. 0, x u7 u8 Define fuzzy subset A i as foows: , A2, u u u u u u u u A1 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u A3, A4, u u u u u u u u u u u u u u u u A5, A6, u u u u u u u u u u u u u u u u A7, A8. u u u u u u u u u u u u u u u u

7 Estabish fuzzy ogica reationships based on the fuzzed passenger fow change rates: A j A p, A p A q,, A s A t A q A p, A p A s,, A s A r A j A p denotes that if the fuzzed passenger fow rate from period t-1 to t is A j, the fuzzed passenger fow rate from period t to t+1 wi be A p. For exampe, information of passenger fow is shown in Tabe 1. Date Time period Passenger fow Change vaue of passenger fow Change rate Fuzzy set 8:00-9: A 5 9:00-10: A 3 10:00-11: A 5 11:00-12: A :00-13: A 8 13:00-14: A 2 14:00-15: A 3 15:00-16: A 5 16:00-17: A 4 17:00-18: A 6 18:00-19: A 5 Tabe 1. Information of passenger fow Foowing the above exampe, the fuzzy passenger fow change rate for 8:00-9:00 is A 5, and for 9:00-10:00 is A 3. Hence, we can estabish a fuzzy ogica reationship is A 5 A 3. Simiary, from Tabe 1, we can get fuzzy ogica reationships are A 5 A 3, A 3 A 5, A 5 A 4, A 4 A 8, etc. Therefore, the fuzzy ogica reationships of the passenger fow change rate are shown in Tabe 2. A 5A 3 A 3A 5 A 5A 4 A 4A 8 A 8A 2 A2A 3 A 3A 5 A 5A 4 A 4A 6 A 6A 5 Tabe 2. Fuzzy ogica reationships From Tabe 2, fuzzy passenger fow change rate is A 5 in previous period, in the foowing period fuzzy passenger fow change rate are A 3, A 4, and A 4, just as A 5 A 3, A 5 A 4 and A 5 A

8 3.2. Fuzzy passenger demand forecasting mode The estabishment of fuzzy passenger demand forecasting mode is based on fuzzy ogica reationships and time series theory, and the steps are as foows: Step1: Start with period =n+1 to predict passenger fow. Step2: Use Eq.(1) to cacuate the passenger fow change rate v(n-1) in period n-1 to n, and fuzzy passenger fow change rate is A i. We can find the next fuzzy passenger fow change rate A j according to fuzzy ogica reationships. k i is the number of the passenger fow change rate A j which beongs to passenger fow change rate range u. i Step3: Cacuate the passenger fow change rate in period =n+1, which is k1u 1 k2u 2 k3u 3 k4u 4 k5u 5 k6u 6 k7u 7 k8u 8 v ( 1). 8 k i1 i Step4: Cacuate predictive vaue p( ) p( 1) p( 1) v( 1), and add predictive vaue to the data of passenger fow, repeat Step2 to Step3 with regard to =+1 unti =M. Step5: Cacuate the root mean squared error (RMSE) between the actua vaues and predictive vaues, which is 1 RMSE p i p i M M 2 [ ( ) ( )]. n i n Anaysis of mode effectiveness The 800 passenger fow data are the passenger fow between Beijing and Tianjin in Beijing- Shanghai high-speed raiway, and haf an hour is an interva between 8:00 and 18:00 from September 21, 2011 to October 30, passenger fow data of first 36 days is historica passenger fow data, 80 passenger fow data of ast 4 days is test data. A the computer programs are written in Matab 7.1. The predictive vaues and actua vaues are shown in Figure

9 Figure 3. Comparison of predictive vaue and rea vaue Furthermore, the resuts show that the fuzzy passenger demand forecasting mode has a better prediction vaue, compared with ARIMA mode. Three statistics are used to compare, they are mean absoute error (MAE), mean absoute percentage error (MAPE) and root mean square error (RSME), as is shown in Tabe 3. Prediction mode MAE MAPE RMSE ARIMA Fuzzy passenger demand forecast Tabe 3 The comparison of prediction mode 4. Train dispatching optimization mode The whoe procedure of the mode incuding minimize the tota operation cost of the train dispatching and unserved passenger voume. If the operation pan doesn t satisfy the passenger demand, operation pan woud be dispatched for passenger fow assignment, in order to attain the passenger demand Notation Input data : The train type. T: The panned operating period, i.e., one day. F : The variabe operating cost for train running one kiometer. F : The variabe operating cost for train empty running one kiometer

10 L ij : The distance between stations i and j. N i,j : The required number of train between stations i and j. u : The seat capacity of train. U ij : The unserved passengers voume between stations i and j. C k ij: The carrying capacity between stations i and j on the raiway ine k. D: The fixed overhead cost for one train. C t : The carrying capacity of station t for the panned operating period T. C k : The carrying capacity of section k for the panned operating period T. Decision variabes X i,j, : The number of train between stations i and j. y i,j, : The number of the empty running train between stations i and j. x t i,j,: The number of train stops at station t between stations i and j. y t i,j,: The number of the empty running train stops at station t between stations i and j. x k i,j,: The number of train runs in section k between stations i and j. y k i,j,: The number of the empty running train runs in section k between stations i and j Objective function Train set configuration is to meet the demand of passenger fow outburst. In this case, the minimum tota operation cost of the train dispatching and unserved passenger voume are the objective functions to meet the passenger demand. Minimize the tota operation cost, which incudes the fixed overhead cost, variabe operating cost for running and variabe operating cost for the train empty running.. min z ( D( x y ) F L x F L y ) 1 i, j, i, j, ij i, j, ij i, j, i j j Minimize the unserved passengers voume for successfuy to meet the passenger demand.. min z ( P u x ) 2 i, j, i, j, i j j 4.3. Constraint conditions The required number of trains restrictions: ( xi, j, yi, j, ) Ni, j, i j

11 Station capacity restrictions: t t ( xi, j, yi, j, ) Ct. i j j Section capacity restrictions: k k ( xi, j, yi, j, ) Ck. i j j Train set configuration restrictions: if the round-trip trains are no-oad, it can t satisfy the condition of passenger fow outburst between stations i and j. y y i j. i, j, j, i, =0, 4.4. Mode of the train dispatching optimization min z ( D( x y ) F L x F L y ) 1 i, j, i, j, ij i, j, ij i, j, i j j min z ( P u x ) 2 i, j, i, j, i j j st.. ( xi, j, yi, j, ) Ni, j, i j i j j i j j ( x y ) C t t i, j, i, j, t ( x y ) C k k i, j, i, j, k y y i j i, j, j, i, =0, x, x, x 0 t k i, j, i, j, i, j, y, y, y 0 t k i, j, i, j, i, j, The train dispatching optimization mode is a noninear compementarity constraints program. An interior-penaty method (Dou, 2011; Fetcher et a., 2004; Hu & Raph, 2004) is used to sove this difficut probem. 5. Case study In Tabe 4, the data is the passenger fow between Beijing and Jinan in Beijing-Shanghai highspeed raiway, an hour is an interva between 8:00 and 20:00 from September 27, 2011 to October 10, A the computer programs are written in Matab 7.1. The passenger fow predictive vaues are shown as Figure

12 Date Time period Passenger fow Change vaue of passenger fow Change rate Fuzzy set 8:00-9: A 5 9:00-10: A 3 10:00-11: A 5 11:00-12: A 4 12:00-13: A :00-14: A 2 14:00-15: A 3 15:00-16: A 5 16:00-17: A 4 17:00-18: A 6 18:00-19: A 5 19:00-20: A :00-9: A 5 9:00-10: A 3 18:00-19: A 5 19:00-20: A :00-9: A 6 9:00-10: A 3 18:00-19: A 5 19:00-20: Tabe 4. Information of the historica passenger fow data Figure 4. Passenger demand forecasting vaue The passenger fow from Beijing to Jinan is Simiary, the passenger demand forecasting vaues are shown in Tabe 5. capacity station station Beijing Langfang Tianjin Jinan Beijing Langfang Tianjin Jinan Tabe 5. Passenger demand forecasting vaue

13 Assume that the fixed overhead cost for one train is yuan. There is ony one type train, and this type of train u 1 can accommodate 1200 passengers. In addition, the required number of train between stations i and j is N 12=N 21 =2, N 13 =N 31 =4, N 14 =N 41 =3, N 23 =N 32 =3, N 24 =N 42 =2, N 34 =N 43 =3, the carrying capacity of section between station i and station j is shown in Tabe 6.(unit: train). The carrying capacity of station is shown in Tabe 7.(unit: train). capacity station station Beijing Langfang Tianjin Jinan Beijing Langfang Tianjin Jinan Tabe 6. Section capacity station Beijing Langfang Tianjin Jinan capacity Tabe 7. Station capacity In the process of train dispatching between stations i and j, the variabe operating cost F L ij for running is shown in Tabe 8. (unit: yuan). cost station station Beijing Langfang Tianjin Jinan Beijing Langfang Tianjin Jinan Tabe 8. Variabe operating cost for running In the process of train dispatching between stations i and j, the variabe operating cost F L ij for empty running is shown in Tabe 9. (unit: yuan). cost station station Beijing Langfang Tianjin Jinan Beijing Langfang Tianjin Jinan Tabe 9. Variabe operating cost for empty running We can cacuate the minimum tota cost of the train dispatching is 2.17 miion yuan, and there are not round-trip and no-oading trains from the resut. The train dispatching scheme achieved maximum utiization. Line pan of BJ station-jn station in high-speed raiway can aso be got, as is shown in figure

14 BJ LF TJ JN Figure 5. Line pan of BJ station-jn station in high-speed raiway 6. Concusions The train dispatching optimization mode is a arge-scae combinatoria optimization probem, there are many factors and the reationship between the factors is compex. Fuzzy set theory, portfoio optimization and train operation adjustment theory are appied in this paper. First, fuzzy passenger demand forecasting mode is estabished to predictive passenger during hoidays. The resuts showed that the fuzzy passenger forecasts predict is more accurate than ARIMA mode. Then, train depoyment theory in sudden arge passenger fow is studied on considering the tota operation cost of the train dispatching, unserved passenger voume, the required number of trains, station capacity, section capacity and train set configuration. Finay, train dispatching optimization mode is estabished, the vaidity of this mode is iustrated with a case study. With the increase in passenger fow during hoidays, train dispatching is infuenced by more factors and there are more constraints to consider. Further discussion is need for mode and more detaied anaysis of the raiway ine is sti need in the case. Acknowedgement This work has been supported by the Nationa Natura Science Foundation of China (Grant: ), the Nationa Key Technoogy R&D Program (Grant: 2009BAG12A10), the Research Fund of the State Key Laboratory of Rai Traffic Contro and Safety (Grant: RCS2008ZZ003, RCS2009ZT002), and the Research Fund of Beijing Jiaotong University (Grant: 2011YJS035). References Beaujon, G.J., & Turnquist, M.A. (1991). A mode for feet sizing and vehice aocation. Transportation Science, 25, Butkevicius, J., Mindaugas, M., Vadas, I., & Skirmantas, M. (2004). Anaysis and forecast of the dynamics of passenger transportation by pubic and transport. Transport, 19,

15 Chen, J.L. (2008). Raiway passenger traffic voume forecasting from Chongqing to Chengdu based on grey theory. China New Technoogies and Products, 4, Chen, Y.R., Peng, Q.Y., & Jiang, Y.S. (2003). Research on a mode for adjusting train diagram on doube track raiway with satisfactory optimization. Journa of the China Raiway Society, 25(3), Dejax, P.J., & Crainic, T.G. (1987). A review of empty fows and feet management modes in freight transportation. Transportation Science, 21(4), Dong, S.Q., Wang, J.Y., & Yan, H.F. (2005). Tabu search for train operation adjustment on doube-track ine. China Raiway Science, 26(4), Dou, F. (2011). Study on train depoyment mode and agorithms during hoidays. Beijing Jiaotong University. Fabio, S. (2006). An integrated forecasting and reguation framework for ight rai transit systems. Journa of Inteigent Transportation Systems, 7, Fetcher, R., & Leyffer, S. (2004). Soving mathematica program with compementarity constraints as noninear programs. Optimization Methods and Software, 19(1), Ghoseiri, K., Szidarovszky, F., & Asgharpour, M.J. (2004). A muti-objective train scheduing mode and soution. Transportation Research Part B, 38(10), Guo, W., & Qiao, Y.Z. (2008). The forecasting research of raiway passenger capacity based on neura network optimized by GA. Journa of Shandong University of Technoogy, 5, Higgins, A., Kozan, E., & Ferreira, L. (1996).Optima scheduing of trains on a singe ine track. Transportation Research Part B, 30(2), Hu, X.M., & Raph, D. (2004). Convergence of a penaty method for mathematica programming with compementarity constraints. Journa of Optimization Theory and Appications, 123(2), Kraay, D., Harker, P.T., & Chen, B. (1991). Optima pacing of trains in freight rairoads: Mode formuation and soution. Operations Research, 39(1),

16 Peter, N., Aura, R., & Tommaso, T. (1996). Modeing inter-urban transport fows in itay a comparison between neura network anaysis and ogit anaysis. Transport Research, 6, Wang, F. (2006). Research of short-term passenger transportation voume forecasting methods. Beijing Jiaotong University. Yang, L.X., Li, K.P., & Gao, Z.Y. (2009). Train timetabe probem on a singe-ine raiway with fuzzy passenger demand. IEEE Transactions on Fuzzy Systems, 17(3), Zadeh, L.A. (1999). Fuzzy sets as a basis for a theory of possibiity. Fuzzy Sets and Fuzzy Systems, 100, Zhang, Y.S., & Jin, W.D. (2005). Mode and agorithm for train operation adjustment on singetrack raiways based on genetic agorithm. Journa of Southwest Jiaotong University, 40(2), Zhou, X.S., & Zhong, M. (2005). Bicriteria train scheduing for high-speed passenger rairoad panning appications. European Journa of Operationa Research, 167(3), Journa of Industria Engineering and Management, 2013 ( E artícuo está con Reconocimiento-NoComercia 3.0 de Creative Commons. Puede copiaro, distribuiro y comunicaro púbicamente siempre que cite a su autor y a Intangibe Capita. No o utiice para fines comerciaes. La icencia competa se puede consutar en