Optimization Models for Improving Bus Transit Services
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To provide efficient public transportation services in areas with high demand variability over time, it may be desirable to switch vehicles between different types of services such as conventional services (with fixed routes and schedules) for high demand periods and flexible route services during low demand periods. Thus, this dissertation analyzes and compares conventional, flexible, and variable type bus service alternatives. Optimization formulations and numerical results show how the demand variability over time and other factors affect the relative effectiveness of such services. A model for connecting one terminal and one local region is solved with analytic optimization. Then, models are extended to consider multiple regions as well as multiple periods. Numerical results of problems for multiple regions and multiple periods are also discussed. Secondly, a problem of integration of bus transit services (i.e., conventional and flexible services) with mixed fleets of buses is explored. A hybrid method combining a genetic algorithm and analytic optimization is used. Numerical analyses confirm that the total system cost can be reduced by integrating bus services with mixed fleets and switching service types and vehicles over time among regions in order to better fit actual demand densities. The solution optimality and the sensitivity of results to several important parameters are also explored. Thirdly, transit ridership may be sensitive to fares, travel times, waiting times, and access times. Thus, elastic demands are considered in the formulations to maximize the system welfare for conventional and flexible services. Numerical examples find that with the input parameters assumed here, conventional services produce greater system welfare (consumer surplus + producer surplus) than flexible services. Numerical analysis finds that conventional and flexible services produce quite acceptable trips with the zero subsidies, compared to various financially constrained (subsidized) cases. For both conventional and flexible services, it is also found that total actual trips increase as subsidies increase. When the cost is fully subsidized, conventional services produce 79.2% of potential trips and flexible services produce 81.9% of potential trips. Several methods are applied to find solutions for nonlinear mixed integer formulations. Their advantages and disadvantages are also discussed in the conclusions section.