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This study considers the planned gate and runway assignment problem for minimizing carbon emissions and costs during the aircraft taxiing stage. The distances between multiple gates and runways, the fuel consumption of different types of aircraft, the location of terminal buildings belonging to the airline, the size of parking aprons for aircraft, and runway lengths for different types of aircraft are all considered. We propose the following two objectives: the minimization of carbon emissions and the minimization of carbon emission costs for airport and for airlines, respectively. A case study based on operations of Taiwan's Taoyuan International Airport is performed. Analytical results indicate that our assignments can achieve an 8.93% reduction of carbon emissions and 10.33% reduction of carbon emission costs compared with the current assignments. [ABSTRACT FROM AUTHOR]