1. Classification Track Assignment in Rail Hump Yard Haodong Li a and Mingzhou Jin b a Beijing Jiaotong University b The University of Tennessee November 11, 2014

2. Introduction Literature Review Classification Track Assignment Model Algorithm Numerical Experiments Conclusions 2 Outline

3. Receiving Area: inbound trains received and inspected; Hump: classification of inbound trains; Classification Area: railcars rearranged and waiting for connection; Departure Area: outbound trains inspected and ready for departure 3 1. Introduction Illustration of a Hump Yard (Boysen 2012) Receiving AreaHump Classification Area Departure Area

4. Hump operations (HO) 4 1. Introduction The process of humping railcars to the classification tracks, also called roll-in operation The process of pulling all the railcars on a classification track back to the hump, then decouple again to the classification tracks. Also called pull-out operation. Rehump operations (RO) Assemble railcars that on classification tracks, and then pullout as an outbound train to the departure area by yard engines. Pullback operations (PO)

5. 5 1. Introduction PO Classification Track Assignment decides how to build each outbound train on different classification tracks with limited capacity (length).

6. 6 2. Literature Review Kraft (1993) and Wang (1997) proposed mixed integer models to optimize the block-to-track assignment and hump sequence together. Those models are too complicated to be solved within an acceptable amount of time. How to solve this problem easier Classification track assignment Hump(Assemble) sequencing

7. 7 2. Literature Review Few literatures on classification track assignment Bohlin et al. (2011, 2011, 2012) present integer programming models on the classification track allocation in classification yard with mixed tracks. The objectives are to minimize the penalty cost of violation of available mixed track capacity, and the extra roll-in operations due to railcars mixing Assumptions restrict its application 1.each departing train takes one track 2.each track can only occupied by one train 3.mixed tracks are pulled back periodically or at fixed time

8. 8 3. Classification Track Assignment Model Assumptions 1. Railcars connection, hump sequence of inbound trains and assembly sequence of outbound trains are given. 2. No particular order of railcars within the outbound train Find an assignment of classification tracks to outbound trains, with the objective to minimize the number of mixed track and lead-use. Goals

9. 9 3. Classification Track Assignment Model Assumptions 1. Railcars connection, hump sequence of inbound trains and assembly sequence of outbound trains are given. Hump time of inbound trains Assemble time of outbound trains Time points(t) The status of classification tracks changes only at those time points

10. 10 3. Classification Track Assignment Model Assumptions

11. 11 3. Classification Track Assignment Model Four types of classification tracks (Lin & Cheng, 2009) 1.Clean tracks; 2.Clear tracks; 3.Mixed tracks; 4.Dirty tracks. Mixed tracks Possibly increase the pullback operations Dirty tracks Increase the rehumps Minimize

12. 12 3. Classification Track Assignment Model Parameters

13. 13 3. Classification Track Assignment Model

14. 14 (1) s.t.(2) (3) (4) (5) (6) (7) 3. Classification Track Assignment Model

15. Generate first solution by assigning one classification to each rail cut randomly. Infeasible solution is penalized. 15 4. Tabu Search Algorithm Initialization Termination Condition Neighborhood Search Update the Tabu List Update the Current Solution End No Yes Update the Best Solution Fig. 1. Framework of the tabu search algorithm

16. Change the assigned track of any rail cut to generate a neighbor. 16 4. Tabu Search Algorithm Initialization Termination Condition Neighborhood Search Update the Tabu List Update the Current Solution End No Yes Update the Best Solution Fig. 1. Framework of the tabu search algorithm

17. Tabu object: the change of track assignment of any rail cut. 17 4. Tabu Search Algorithm Initialization Termination Condition Neighborhood Search Update the Tabu List Update the Current Solution End No Yes Update the Best Solution Fig. 1. Framework of the tabu search algorithm

18. They are inbound trains which denoted by A1-A12 with 65 rail cuts, and 12 outbound trains. All the un-departed railcars are treated as outbound trains according their destination. So, there are 5 dummy trains, that is 17 outbound trains in this plan horizon totally. 18 5. Numerical Experiments

19. 19 5. Numerical Experiments Table 1 Sequence of Classification and Assembly Inbound trains Outbound trains SequenceTrainStart timeEnd timeSequenceTrainStart timeEnd time 1A29:409:551B19:5510:10 2A19:5510:102B310:1010:25 3A310:1010:253B210:2510:40 4A410:2510:404B410:4010:55 5A610:4010:555B510:5511:10 6A510:5511:106B611:1011:25 7A711:1011:257B711:2511:40 8A811:2511:408B811:4011:55 9A911:4011:559B911:5512:10 10A1211:5512:1010B1012:1012:25 11A1112:1012:2511B1112:2512:40 12A1012:2512:4012B1212:5313:08

20. 20 5. Numerical Experiments Table 2 Cuts Information of Inbound Trains Cut IDDirection Railcar Number Length Cut IDDirection Railcar Number Length A0 1146.4 A3 1813437.4 22001921619.2 3344.420466.6 446 2122030.0 5500 A4 2234044.0 66002341013.0 770024544.8 A1 813040.025644.8 921013.02641215.6 107 12.027744.8 11544.8 A5 2814056.0 1211821.62922633.8 A2 1334048.030789.6 14446.4 A6 3131416.8 1551015.43252024.0 1632026.033446.4 17667.8 Cut IDDirection Railcar Number Length Cut IDDirection Railcar Number Length A6 34344.4 A9 5041213.2 3551819.85121617.6 3661421.0 A10 5232026.0 A7 3732224.253688.8 38546.45472431.2 3971213.25542026.0 404812.0 A11 5613033.0 4132024.057669.6 427810.45821012.0 A8 4323048.05952022.0 4472024.060169.6 45544.4 A12 61622.4 4621018.06243437.4 4771013.06351213.2 A9 4812032.064366.6 4922631.26542224.2

21. 21 5. Numerical Experiments Table 3 Railcars connection plan TrainMakeup B1A0/4/6, A2/13/40, A2/16/20 B2A3/18/34, A3/19/16, A3/21/20 B3A0/1/4, A1/8/30, A1/9/10, A1/12/18 B4A0/3/4, A4/22/40, A4/23/10, A4/26/12 B5A2/15/10, A2/17/6, A4/24/4, A4/25/4, A6/32/20, A6/36/14 B6A5/28/40, A5/29/26 B7A6/31/14, A7/37/22, A7/40/8, A7/41/20 B8A1/10/10, A5/30/8, A7/39/12, A7/42/8, A8/44/20, A8/47/10 B9A8/43/30, A9/49/26 B10A3/20/6, A9/50/12, A12/62/34, A12/65/22 B11A9/48/20, A11/56/30, A11/60/6 B12A6/35/18, A7/38/4, A10/53/8, A11/57/6, A11/59/20, A12/63/12 B13(3)A6/34/4, A8/46/10, A9/51/16, A11/58/10, A12/64/6 B14(4)A2/14/4, A6/33/4, A10/52/30, A10/55/20 B15(5)A1/11/4, A8/45/4, B16(6)A12/61/2, B17(7)A4/27/7, A10/54/24,

22. 22 4. Tabu Search Algorithm Value of objective function Fig. 2. Convergence process of the algorithm

23. 23 4. Tabu Search Algorithm IBM ILOG CPLEXTabu search Value of objective function 8 tracksout of memory34 9 tracks27 10 tracks22 11 tracks18 12 tracks17 Run time （ s ） 8 tracksout of memory23.12 9 tracks456.9211.04 10 tracks211.4711.56 11 tracks49.2911.79 12 tracks13.5412.67

24. 24 5. Numerical Experiments No dirty track Results of different scenarios—10 classification tracks The capacity of tracks are （ 70 ， 70 ， 70 ， 70 ， 70 ， 75 ， 75 ， 70 ， 70 ， 70 ）

25. 25 5. Numerical Experiments 1 dirty track Results of different scenarios—9 classification tracks The capacity of tracks are （ 70 ， 70 ， 70 ， 70 ， 75 ， 75 ， 70 ， 70 ， 70 ）

26. 26 5. Numerical Experiments 1 dirty track Results of different scenarios—smaller capacity of 10 classification tracks （ 45 ， 50 ， 50 ， 60 ， 70 ， 75 ， 75 ， 70 ， 70 ， 70 ）

27. 27 5. Numerical Experiments No dirty track Results of different scenarios—priority assignment Block 1,2 assigned to track 1 to 3; block 3,4 assigned to track 4 to 6; block 5 to 7 assigned to track 7 to 10

28. A classification track assignment model for rail hump yard dispatching is proposed; The model was verified by a numerical experiment, which seems to be a good starting point for further research for the dispatching plans in rail hump yards. More sophisticated algorithms are necessary to obtain better solutions 28 Conclusions

29. Thanks! 29