Evaluation of feeder bus systems with probabilistic time-varying demands and nonadditive time costs

Optimal fixed-route conventional bus (CBS) and flexible-route subscription bus (SBS) systems are compared. The average cost, including operator and user costs, is defined as the objective function to be minimized. The decision variables are route spacing and vehicle size in CBS, but service area and vehicle size in SBS. The systems serve probabilistic demand that varies over a 10-h operating period with high demand in the morning and afternoon peak hours. Passengers are assumed to have nonadditive value of time. Average cost per trip is calculated for a numerical example designed to compare the suitability of a particular service under various demand conditions. For this particular example, the CBS provides the lower-cost service. However, the operator can further reduce the cost of daily operation by providing the CBS service in periods of high demand and operating the SBS during off-peak periods. In general, the threshold value of demand at which one system is more cost-effective than another is readily calculated. A sensitivity analysis is conducted to show the effect of varying model parameters on the objective functions and the decision variables.