Continuous filling and emptying of storage systems in constraint-based scheduling

In constraint-based scheduling, storage systems are modeled by a class of resources called reservoirs. Activities can either produce a quantity of product to be stored in the reservoir or consume it, removing the quantity from the reservoir. Most of the models presented in the literature assume that the production and the consumption is instantaneous but it can be a very bad approximation for some problems, for example those dealing with tanks of fluid. This paper introduces the continuous reservoir model in which the activity fills or empties the reservoir at a constant rate from its start time to its end time. This model is generalized to deal with additional constraints, such that leaks or overflows, that cannot be modeled by activities. Timetabling, a classical technique for the propagation of resource constraints in constraint-based scheduling, is adapted and extended to this new model.