(159bb) A Continuous-Time Linear Programming Formulation for the Resource-Constrained Project Scheduling Problem with Production and Consumption of Resources

We study an extension of the resource-constrained project scheduling problem RCPSP by so-called storage resources which are produced or consumed by the execution of the project activities. For each storage resource, an initial stock is given. The problem consists in determining a project schedule with minimal duration such that at no point in time, the capacity of any renewable resource is exceeded; furthermore, the stock of each storage resource must always be non-negative. Typical examples for storage resources are a project budget or some intermediate materials. We propose a novel formulation of this problem as a continuous-time mixed-integer linear program. In an experimental analysis based on several test sets from the literature, it has turned out that for instances with a relatively long planning horizon, the novel model exhibits a better performance than all state-of-the-art models.