Optimal Incremental and Anytime Scheduling

We discuss the use of constraint programming for a class of reactive applications that concurrently monitor and control their environment. Programs dealing with such problems have to be incremental and anytime, in the sense that sensor information is accumulated incrementally and control decisions have to be made on request while the program is running. We present as a real-life example the scheduling of networked repro-graphic machines. Given a speciied output document, the scheduler's task is to determine the input times of sheets and images. The pages of the document are received incrementally, and while the scheduler tries to look ahead to nd optimal schedules, it usually does not have time to wait until the entire document is known. While concurrent constraint languages seem well suited for such re-active applications, existing implementations do not support the combination of optimal control and deferred commitment. In this paper, we propose and analyze the use of projected optimization to handle this problem. We also explain its implementation in AKL(FD) and CLP(FD) and discuss experimental results.