Optimum zone structure during peak periods for existing urban rail lines

The problem of optimizing the service along an existing two-track rail line by adopting a zone-stop schedule during the peak periods is investigated. A dynamic programming technique is employed to determine the number of zones, the stations that belong to each zone, the headway between trains to the same zone and the fleet size. The general objective of the analysis is to minimize the total transportation cost, defined as the sum of the costs of time to the passengers and the relevant rail capital and operating costs. The optimization problem is subject to several constraints including avoidance of train conflicts, limitations on the value of the headway and an available fleet size. The applicability of the model is demonstrated through a numerical example using field data.