In this paper, a mathematical programming based model is described to assist with the schedule of services for a set of auxiliary bus lines that operate alleviating a disruption of the regular transportation system during a given time period. In contrast to other models, considered static, service schedules are set taking into account demand fluctuations that may happen in that time period. Passenger flows are represented with a multi-commodity structure and disseminate through paths on a diachronic capacitated network which lead them to their destination in the shortest time taking into account the available capacities of the bus units. The model permits to accommodate the schedules of the auxiliary bus lines in order to enhance transfers and to minimize total travel time. The model assumes that operational times at bus stops are constant and that buses do not queue at stops. The solution method can be considered an heuristic that combines searches along subgradient's projected directions with a pattern search based method for constrained optimization.

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