Planning, scheduling and uncertainty in the sequence of future events

Scheduling in the factory setting ie compounded by computational comple:Aty and temporal uncertainty. Together, these two factors guarantee that the proceee of constructing an optimal schedule will be very costly and the chances of e:eecuting that schedule are vef11 slight. Temporal uncertainty in the e:eecution time environment can be oflset by 1everal methode: eliminate uncertainty by careful engineering, reduce uncertainty by using more powerful sensor•, restore certainty whenever it ie lost, quantify and circumscribe the remaining uncertainty. UnfortunatelfiJ the•e methode focus erzclusively on the eourcee of uncertainty and fail to appl'IJ lmowledge of the ta8Q which are to be tcheduled. A complete solution mutt teek to adapt the schedule of activities to be performed according to the evolving state of the world. The ezample of vision directed ueembl'IJ ie presented which illultratee that the principle of lea•t commitment, in the creation of a plan, in the representation of a 1chedule, and in the e:eecution of a schedule, enable• a robot to operate intelligently and efliciently, even in the presence of considerable uncertainty in the sequence of future event•. 1McDonnell Dough1.s Research Laboratories Artificial Intelligence Technology Group Dept 225/Bldg 305/Level 2E POB 516, St. Louis, MO, USA 63166 2 Arttnctal Intelltgence Center FMC Corporation 1185 Coleman Avenue Santa Clara, CA, USA 95052 1. Statement of the Problem The problem of sequencing and scheduling is to determine, in advance, when some set of events and activities should occur. The events and activities may be subject to some order­ ing constraints; the time of occurrence or the duration of some activities may be fixed; there may be some cost ass ociated with the time that an activity is performed or with the rate with which it progresses. The times selected for these events and activities must conform to the constraints, expected times and durations, and must generally minimize the associated costs. In problems which are over constrained, the selected times must at least conform to a rational relaxation of the given constraints. Scheduling in the factory setting is com­ pounded by two factors1. The first is comple:Aty. Most scheduling problems are NP­ hard. The number of potential schedules grows exponentially with the number of activities to be scheduled and the number of resources to be utilized. It is simply impossible to itemize and evaluate every possible schedule in order to find the best .schedule. At the same time, there is no known method for finding the best schedule which does not exhaustively consider (at least implicitly) every possible schedule. The second factor ls uncertainty. Any schedule constructed in advance is based solely upon assumptions about the ordering, the times of occurrence and the durations of the activities. *This research was conducted under the McDonnell Douglas Independent Research and Development Program.