Scheduling with Limited Processor Availability
International Handbook on Information Systems
In scheduling theory the basic model assumes that all machines are continuously available for processing throughout the planning horizon. This assumption might be justified in some cases but it does not apply if certain maintenance requirements, breakdowns or other constraints that cause the machines not to be available for processing have to be considered. In this chapter we discuss results related to deterministic scheduling problems where machines are not continuously available for
... . Examples of such constraints can be found in many areas. Limited availabilities of machines may result from pre-schedules which exist mainly because most of the real world resources planning problems are dynamic. A natural approach to cope with a dynamic environment is to trigger a new planning horizon when the changes in the data justify it. However, due to many necessities, as process preparation for instance, it is mandatory to take results of earlier plans as fixed which obviously limits availability of resources for any subsequent plan. Consider e.g. ERP (Enterprise Resource Planning) production planning systems when a rolling horizon approach is used for customer order assignment on a tactical level. Here consecutive time periods overlap where planning decisions taken in earlier periods constrain those for later periods. Because of this arrangement orders related to earlier periods are also assigned to time intervals of later periods causing the resources not to be available during these intervals for orders arriving after the planning decisions have been taken. The same kind of problem may be repeated on the operational level of production scheduling. Here processing of some jobs is fixed in terms of starting and finishing times and machine assignment. When new jobs are released to the shop floor there are already jobs assigned to time intervals and machines while the new ones have to be processed within the remaining free processing intervals. Another application of limited machine availability comes from operating systems for mono-and multi-processors, where subprograms with higher priority will interfere with the current program executed. A similar problem arises in multi-user computer systems where the load changes during the usage. In big massively parallel systems it is convenient to change the partition of the processors among different types of users according to their requirements for the machine. Fluctuations related to the processing capacity can be modeled by intervals of different processor availability. Numerous other examples exist where the investigation of limited machine availability is of great importance and the prac-This paper is based on O. Braun, J, Breit, G.