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I have a job shop scheduling problem with the following characteristics. How would I write that in alpha|beta|gamma notation (see 1,2)? I know some of the parts, but not all. I add my suggestions in code blocks.

alpha:

  • Job shop J
  • number of machines is part of the input m

beta:

  • batch processing b with job compatibilities ? and capacity constraints ? (i.e., a machine can process multiple jobs, if they belong to the same family and the machines capacity suffices. Each job has a fixed resource allocation which is the same on every machine.)
  • release times r_j
  • non-uniform setup times, depending on the schedule ?
  • transportation delays between machines, depending on the job and the machine t_{j,k}

gamma:

  • minimizing total completion times sum(C_j)

Further: Is it true, that the job-shop implies a strict ordering of the jobs, so a precedence relation is implicit, or should i note that as well? In my problem, the jobs have to be processed by machines in the given order. (Btw.: The "direction" defines the compatibility.)

Example:

  • Job 1: machines {1, 2, 3, 4}, comp. class A
  • Job 2: machines {3, 4, 5}, comp. class A
  • Job 3: machines {6, 5, 4, 3}, comp. class B

(Edit: Add links to sources about the notation.)

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