Abstract：Research purposes: Based on generalizing the influential factors of passenger train departure time range，as well as introducing the determination methods of the needful passenger train stock number，this paper deeply analyzes the relationship between passenger train departure time range and needful number of passenger train stock． Then，the optimal model of passenger train departure range with least numbers of passenger train stock is established，while the solving algorithm of traditional method combining heuristic algorithm is put forward，which can provide decision － making basis for determining optimized passenger train plan．
Research conclusions: ( 1) The needful number of the passenger train stock is an important index of passenger train plan，and it will influence the operation cost and efficiency of railway passenger transportation to a great extent． The passenger train departure time range is an important factor to determining the needful number of passenger train stock．( 2) The optimized passenger train departure range with least number of train stocks can be got by establishing optimization model taking the minimal overall time of staying in departure station and turn － back station as objective． It has a certain real significance to optimize passenger train plan．
张玉召，张红伟，文娟娟. 车底需要数最少的旅客列车始发范围优化模型[J]. 铁道工程学报, 2011, 28(4): 111-114.
ZHANG Yu － zhao，ZHANG Hong －Wei，WEN Juan － juan. Optimal Model of Passenger Trains Departure Time Range with Least Passenger Train Stock Number. 铁道工程学报, 2011, 28(4): 111-114.
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2011, Vol. 28 
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