Using Constraint Programming and Simulation for Execution Monitoring and On-Line Rescheduling with Uncertainty

Abstract

Modern scheduling techniques must take into account incomplete information and/or potential changes in the environment, i.e. uncertainty. The central issue is to design robust scheduling techniques, aimed at guaranteeing the feasibility and the quality of the executed schedule. Several ways to get a more robust schedule have already been investigated. One way among others is to keep one and only one fixed schedule to execute, but reschedule when it appears the quality of the currently executing schedule degrades. This approach is relevant as far as rescheduling is fast enough w.r.t. the scheduling execution, i.e. when the dynamics of the system are low. The problem we tackle is on-line rescheduling with temporal uncertainty: activity durations are uncertain and activity end times must be observed during execution. In this paper we assume we have a representation of the uncertainty on each activity duration in the form of probability distributions which are used in the simulation of schedule execution. We use the simulations to monitor the execution of the schedule and in particular to estimate the quality of the schedule and the end times of the activities. Given an initial schedule, execution starts and we must decide when to reschedule. We propose and explore a non-monotonic technique where each time we reschedule we can completely change the existing schedule except for those activities that have already started or finished execution. This paper addresses the basis on which the decision to reschedule is made by investigating three simple measures of the data provided by simulation that are called the rescheduling criteria. We have chosen to use constraint programming for scheduling the initial problem and rescheduling when necessary. We illustrate our approach on job-shop problems with uncertain durations. The first experimental results are promising since on-line rescheduling improves schedule quality with a little additional computational effort whatever the rescheduling criterion used. In addition, these techniques can easily be extended to solve more complex problems and simulation permits us to quickly obtain good approximations whatever type of uncertainties and probability distributions are considered. Future work will focus on developing these scheduling methods to better tune the different parameters and implementing a monotonic approach where a partial schedule is built until some horizon and never questioned.