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OPTIMIZATION IN PUBLIC TRANSPORTATION José Fernando Román Guzmán 11/28/12

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The System: Transmilenio

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“Tables” TimeTablePosition TimeTablePosition 04:58:001505:00:002961 05:00:0015205:51:002941 05:55:0012305:55:152941 06:00:0012306:46:152961 06:53:0015206:47:302961 06:55:3015207:38:002941 07:50:3012307:39:152941 07:52:3012308:30:152961 08:45:3015208:35:152961 19:50:302941 19:51:002941 20:42:002961 servbuskilcomtimehlp 11798072040035612.96 2278745306601679.8

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The Problem Kilometers assign to each company is equal to the participation times the total kilometers of all the “tables”. Assign all of the “tables” to the seven companies according to their participation Minimize the hlp

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Restrictions Limited capacity in the parking lots Different type of buses Special requirement form the companies

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The Solution Linear Optimization using the simplex algorithm to find the real solution and then the branch and bound algorithm to find the integer solution Only one person is responsible for the assignation of whole system Reduction of the HLP(kilometers when the buses are not in service) of 25% TableCompanyInitial Parking lotFinal Parking lot 1j1k1k2 2j2k2k4 3j3k5k3

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References Web address (text): http://en.wikipedia.org/wiki/Drag_coefficienthttp://en.wikipedia.org/wiki/Drag_coefficient Web address (map): http://www.transmilenio.gov.co/WebSite/Default.aspx

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