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Operational planning of public transit with economic and environmental goals: application to the Minneapolis–St. Paul bus system


This study develops a framework to optimize bus assignments and operating practices to routes considering both operating costs and environmental goals. The mixed-integer programming model is applied to the Metro Transit bus system in the Minneapolis–St. Paul metropolitan area. The model is used to derive representative solutions on the efficient frontiers between operating costs and emissions, and to demonstrate how economic factors such as fuel cost and service level affect the trade-offs between costs and environmental outcomes. An analysis of fleet composition shows that vehicle assignments can significantly affect the cost and emission performance of the fleet. We then use the model to evaluate the actual bus assignment schedule used by Metro Transit, and provide suggestions on how to reduce operating costs and emissions. The model is useful in supporting strategic decisions such as vehicle replacement and purchase, as well as operational planning.

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  1. 1.

    For transit planning problems that include light rail, scheduling variables may be used to assemble trains of specific sizes during particular planning periods.

  2. 2.

    The GAMS model used here is designed for analyses of a wide range of transit planning problems. For details, see Apland and Sun (2019).


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This work is part of the project “Enabling the Next Generation of Super Hybrid Transit Bus”, which was jointly funded by the Initiative for Renewable Energy and the Environment (Grant number RL-0013-13) and the Center for Transportation Studies, both at University of Minnesota, and Metro Transit—the public transportation operator in the Minneapolis–St. Paul Metropolitan Area. We would like to thank Janet Hopper, David Haas and Chuck Wurzinger at Metro Transit for providing extensive datasets. We are also very grateful for the advice and assistance from Steven Taff, William Northrop, David Kittelson, Win Watts, Andrew Kotz, Shashank Singh and Kieran McCabe at the University of Minnesota, and the anonymous reviewers.

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Correspondence to Bixuan Sun.

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Appendix 1: Equation used to calculate NOx and PM emission levels

$$\frac{{\text{g}}}{{{\text{mile}}}}{\text{ = N}} \times \left( {{\text{D}} - {\text{x}} \times \left( {{\text{D}} - {\text{B}}} \right)} \right) \times {{\eta }}_{{{\text{th}}}} \times \frac{{\text{1}}}{{{\text{MPG}}}}$$

where: N = gNOX/Bhp-hr—CARB emission standard for NOX, D = Bhp-hr/gal-Diesel—Diesel fuel energy content per gallon, B = Bhp-hr/gal-Biodiesel—Biodiesel fuel energy content per gallon, x = Volume fraction of biodiesel—The fraction varies by season. The summer level is 20%, while the winter level is 2.5%. MPG = Miles per gallon of fuel—Determined by total miles divided by total fuel, G = Gallons Fuel—From Fuel consumption, ηth = Thermal Efficiency— % of energy in fuel tuned into useful work.

Appendix 2: Weights and values of efficient solutions in Fig. 2, 3, 5 and 6

See Tables 7, 8, 9 and 10.

Table 7 Efficient combinations of operating cost and emission cost
Table 8 Efficient combinations of operating cost and NOx emissions
Table 9 Efficient combinations of operating cost and emission cost with low diesel fuel prices
Table 10 Efficient combinations of operating cost and emission cost with high demand for service

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Sun, B., Apland, J. Operational planning of public transit with economic and environmental goals: application to the Minneapolis–St. Paul bus system. Public Transp 11, 237–267 (2019).

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  • Transportation
  • Multi-criteria optimization
  • Mixed-integer programming
  • Operational planning
  • Operating costs
  • Environmental impacts