The planning of on-demand services requires the formation of vehicle schedules consisting of service trips and empty trips. This paper presents an algorithm for building vehicle schedules that uses time-dependent demand matrices (= service trips) as input and determines time-dependent empty trip matrices and the number of required vehicles as a result. The presented approach is intended for long-term, strategic transport planning. For this purpose, it provides planners with an estimate of vehicle fleet size and distance travelled by on-demand services. The algorithm can be applied to integer and non-integer demand matrices and is therefore particularly suitable for macroscopic travel demand models. Two case studies illustrate potential applications of the algorithm and feature that on-demand services can be considered in macroscopic travel demand models.