Determination of the optimum trip schedules is an important problem for public transportation systems. It is complex task to assign optimum number of vehicles and determine the trip schedules for a public transport systems which consist of many routes. In the case of taking infrequent trip schedules, the existing passenger demand is not satisfied. Therefore waiting times are increased in the bus stops. In contrary, with more frequent intervals, unutilized capacity and higher operational costs are expected. Also, intense traffic density and environmental pollution are associated with the frequent trips. The optimum trip frequencies of the passenger demands varies during the hours of a day and is important for passenger satisfaction and operation efficiency of the system. Trip scheduling and vehicle assignment studies take attention in the current literature assisted with different optimization techniques and artificial intelligence method. In this study, only 10 different bus routes which is operated privately, were considered in the city center of Antalya and the Linear Goal Programming (LGP) was used to determine the optimum number of vehicles operated on the routes. The study results showed that the existing system performance can be preserved by reducing the frequency of specific trips and LGP is stated as an efficient algorithm for determining the optimum trip frequencies and number of vehicles in a public transportation systems.