A Multi-Period, Multiple Objective, Mixed Integer Programming, GAMS Model for Transit System Planning

This paper provides a detailed overview of a general mathematical programming model of transit system operations. The model is designed to address a wide range of transit planning and policy problems while considering a variety of managerial and public policy objectives. As a decision support tool for system managers, the model will provide optimal vehicle assignments and schedules given the available resources, market conditions and the demand for services. Strategic planning problems may be supported also, for example by solving the model with alternative fleet configurations, levels of service, market conditions and public policies. Policy analysts may use the model to predict how public policies might impact transit system management including costs of operation, necessary changes to fleet composition and other transit management issues. The model will derive optimal plans considering two or more performance measures and may be used to determine efficient trade-offs between alternative goals. Performance measures or objectives may be general, or time and/or location specific when appropriate. Integer variables are used to characterize discrete decisions such as the assignment of vehicles to routes over a set of operating periods and may include “deadheading” costs between depots and routes. Operating activities allow for the deployed vehicles to be used under various operating practices that may have different resource requirements, service contributions and/or performance measure consequences. An example analysis of bus scheduling using data from the Minneapolis-St Paul Metro Transit System is presented. In that study, daily bus scheduling plans are found considering total operating cost, CO2, NOX and particulate emissions, and a measure of emissions cost. The model is constructed using GAMS – the Generalized Algebraic Modeling System software -and is designed to be used by researchers, analysts and managers familiar with GAMS to analyze a wide range of transit problems. The GAMS code for the model, including that for the Metro Transit study and associated data files, are available from the authors by request. 1 Jeffrey Apland is a Professor in the Department of Applied Economics and Bixuan Sun is a Post-Doctoral Associate in the Humphrey School of Public Affairs, at the University of Minnesota.

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