# How to write a job shop problem with these constraints in alpha|beta|gamma notation?

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.)

• What is "alpha|beta|gamma" notation? I've never heard of it. Please provide a reference to a textbook or published paper that defines it. Jul 8, 2021 at 16:38
• en.wikipedia.org/wiki/Optimal_job_scheduling Jul 8, 2021 at 18:32
• @WanderingLogic: from the wikipedia article, here is the link to the paper: mat.uab.es/~alseda/MasterOpt/79_03_scheduling_survey.pdf Jul 8, 2021 at 20:30
• @YuvalFilmus: thank you, that is what I mean. Jul 8, 2021 at 20:30