Sequential operations on the same machine
![Fig 2. Sequential operations on the same machine Image of: Fig 2. Sequential operations on the same machine](assets/hilite_graphics/rhfeb07g02.png)
Fig 2. Sequential operations on the same machine
Sequential operations on the same machine
The above figure shows an example of two operations q and j of two different jobs p and i, being sequentially scheduled for one machine, machine k. In this general case job i operation j (ij) cannot begin on this machine until job p operation q (pq) is complete.
As for Figure 1, we can formally describe this from an integer programming point of view by stating that:
![Equation 05 Equation 05](assets/hilite_graphics/rhfeb07_eqn_g05.png)
... which enforces the sequentiality.
Within the constraints that machine k belongs to a set of machines, whose size is m:
![Equation 06 Equation 06](assets/hilite_graphics/rhfeb07_eqn_g06.png)
... and the jobs both i and p, belong to a set of n jobs:
![Equation 07 Equation 07](assets/hilite_graphics/rhfeb07_eqn_g07.png)
This gives the overall, formal expression:
![Equation 08 Equation 08](assets/hilite_graphics/rhfeb07_eqn_g08.png)
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