Sequential operations on different machines
Fig 1. Sequential operations on different machines
Sequential operations on different machines
The above figure shows an example of two machines being scheduled, machine k and machine h against a time base of abritrary units. We assume that two operations (j and j-1) need to be carried out sequentially. In this general case operation j on machine k cannot begin until operation j-1 on machine h is complete.
We can formally describe this from an integer programming point of view by stating that:
... which enforces the sequentiality.
Within the constraints that machine k and h belong to a set of machines, whose size is m:
... and the job i, which is part of a set of n jobs:
This gives the overall, formal expression:
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