Abstract Demand-Adaptive Systems (DAS) display features of both traditional fixed-line bus services and purely on-demand systems such as dial-a-ride, that is they offer demand-responsive services within the framework of traditional scheduled bus transportation. A DAS bus line serves, on one hand, a given set of compulsory stops according to a predefined schedule specifying the time windows associated with each, providing the traditional use of the transit line, without requiring any reservation. On the other hand, passengers may also issue requests for transportation between two desired, optional, stops, which induces detours in the vehicle routes. The design of a DAS line is a complex planning operation that requires to determine not only its design in terms of selecting the compulsory stops, but also its master schedule in terms of the time windows associated with the compulsory stops. Designing a DAS thus combines elements of strategic and tactical planning. In this paper we focus on determining a master-schedule for a single DAS line. We propose a mathematical description and a solution framework based on the estimation of a number of statistical parameters of the demand and the DAS line service. Results of numerical experiments are also given and analyzed
