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This paper presents the optimization problem of three different on-demand transit systems operated by vehicles of different sizes. This problem is aimed at minimizing the total cost of the system, which consists of the temporal cost experienced by users and the operating cost incurred by transit agencies. A compact set of estimations of the user performance and operating cost is provided, based on geometric probability. The optimization procedure allows the cost comparison of different semi-flexible services. Transit systems operated by cars (shared taxicabs) with flexible layouts are preferable for low demand densities (less than 92 pax/km²-h). For very high demand (higher than 200 pax/km²-h), bus systems with fixed layout and variable stop locations present the lowest total cost per passenger. In an intermediate domain, taxi and semi-flexible services compete among each other. The estimation of unit operating …