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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 processing.

The scheduling model we consider now is more complicated than the previous ones, because any task, besides processors, may require for its processing some additional scarce resources. Resources, depending on their nature, may be classified into types and categories. The classification into takes into account only the functions resources fulfill: resources of the same type are assumed to fulfill the same functions. The classification into will concern two points of view. First, we differentiate three categories of resources from the viewpoint of resource constraints. We will call a resource , if only its total usage, i.e. temporary availability at every moment, is constrained. A resource is called , if only its total consumption, i.e. integral availability up to any given moment, is constrained (in other words this resource once used by some task cannot be assigned to any other task). A resource is called , if both total usage and total consumption are constrained. Secondly, we distinguish two resource categories from the viewpoint of resource divisibility: discrete (i.e. discretely-divisible) and (i.e. continuously-divisible) resources. In other words, by a discrete resource we will understand a resource which can be allocated to tasks in discrete amounts from a given finite set of possible allocations, which in particular may consist of one element only. Continuous resources, on the other hand, can be allocated in arbitrary, a priori unknown, amounts from given intervals.

Constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades. The basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables, domains and constraints describing a specific problem instance.

An important application area for machine scheduling theory comes from Flexible Manufacturing Systems (s). This relatively new technology was introduced to improve the efficiency of a job shop while retaining its flexibility. An FMS can be defined as an integrated manufacturing system consisting of flexible machines equipped with tool magazines and linked by a material handling system, where all system components are under computer control [BY86a]. Existing FMSs mainly differ by the installed hardware concerning machine types, tool changing devices and material handling systems. Instances of machine types are dedicated machines or parallel multi-purpose ones. Tool changing devices can be designed to render automatic online tool transportation and assignment to the machines’ magazines while the system is running. Li other cases tool changes are only possible if the operations of the system are stopped. Most of the existing FMSs have automatic part transportation capabilities.

Within all activities of production management, is a major part covering planning and control functions. By we mean all activities which are necessary to carry out production. The two main decisions to be taken in this field are production and production . Production scheduling is a common activity of these two areas because scheduling is needed not only on the planning level as mainly treated in the preceding chapters but also on the control level. From the different aspects of production scheduling problems we can distinguish or () and or online-control (). Predictive production scheduling serves to provide guidance in achieving global coherence in the process of local decision making. Reactive production scheduling is concerned with revising predictive schedules when un-expected events force changes. OFP generates the requirements for ONC, and ONC creates feedback to OFP.