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Pro c ess O p timization F r ame w ork s 163

The algorithm generating the optimal schedule depends on the
storage policy to be considered: nonintermediate storage (NIS), finite
intermediate storage (FIS), or unlimited intermediate storage (UIS).
In this chapter we assume a NIS policy, so an equipment unit
becomes available only after finishing a task and transferring its
intermediate product to the subsequent task in the recipe. On an
S-graph representing a schedule under NIS policy, an arc leads from
the node subsequent in the recipe to the node of the task to be
performed next by the same equipment unit. For example, equipment
E1 first performs task 6, then moves to task 1 and finally to task 7,
which is represented by arcs drawn from node 11 (subsequent to
task 6) to node 1 and from node 2 (subsequent to node 1) to node 7 in
Figure 7.11.
The advantage of the S-graph framework over conventional
Mathematical Programming lies in its ability to exploit the problem’s
structure to effect a drastic reduction on computational intensity
without requiring unknown information, such as the number of time
points. (Visit www.s-graph.com for further information.)