Optimal scheduling Subject

Unlike continuous systems, batch operations do not run under steady-state conditions, and their performance varies with time. As discussed in Chapter 2, the important issues with batch systems are the optimal scheduling of different equipment to produce a variety of products and the determination of optimal cycle times for batch processes. Therefore, the optimization of batch operations often involves determining the best processing time for a certain operation, the best time at which a certain action should take place, or the best distribution of actions over a period of time. The optimization of batch processes is, in itself, a very broad topic and certainly beyond the scope of this section of this chapter. Rather than try to address the many interesting problems in this field, the approach here is to illustrate several inportant concepts through the use of exanples. The interested reader is encouraged to read further into this subject [7-101. 

What follows mainly focuses on the detailed scheduling of the jobs. Given a collection of jobs that have to be processed in a given machine environment, the problem is to schedule the jobs, subject to given constraints, in such a way that one or more performance criteria are optimized. Various forms of uncertainties, such as random job-processing times, machines subject to breakdown, and rush orders, may have to be dealt with. 

The controlflow/dataflow graphs are rearranged and optimized. Using a percolation algorithm, the vertices are scheduled into specific states, subject to data dependencies, resource limits, and other constraints. 

First, Park s flocking Scheme Synthesis ackage (CSSP) is used to find the operations on the critical path and the optimal number of steps in the critical path, and fimctional units are allocated and bound to those operations. Then, the freedom (mobility) of each operation is computed (the difference between the time when the input values are needed and the time when the results are needed, less the delay for the operation), and the operations with the smallest freedom are scheduled first. If necessary, additional functional units are added subject to the cost constraints and the freedoms are recalculated. If additional functional units cmi not be added, additional time steps are added to the critical path (subject to Ihe time constraints) and the allocation begins again. 

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