# How to include material flow in job shop scheduling problem (as constraint?)?

I am reading about https://en.wikipedia.org/wiki/Job-shop_scheduling and https://en.wikipedia.org/wiki/Optimal_job_scheduling. Such scheduling is possible if we know the number (amount) of operations (intensity of operations). But what about the following situation: operation A receives A1, A2 amount of materials 1 and 2 and outputs AO3, AO4 amount of materials 3 and 4. Operation B recieves B1, B3 amount of materials 1 and 3 and outputs BO5 amount of material 5.

How we can incorporate in the job-shop scheduling problem the constraint, that the intensity of operation B depends on the availability of material 3 and hence the intensity of operation B is determined by the intensity of operation A which itself is dependent on the availability of materials 1, 2, the availability of respective machine and staff for operation A. And, of course, the inventory of materil 3 can also be available but with the respective costs.

What is the name (term, keyword) for general job-shop scheduling problem that incorporates the flow of materials as well?

• I don't understand what you mean by "intensity of operations" and by "operation X receives Y amount of materials". Does that mean that operation X requires some amount Y of a renewable or non-renewable resource? Oct 6 at 11:54
• Operation required 5.5 units of good 1 and 6.5 units of good 2 and it produces 2.2 units of good 3. Operation can not proceed if there is not enough goods 1 or 2 available. Such constraint means that we can not plan the high intensity of downstream operations if the upstream operations had not been in enough intensity.
– TomR
Oct 6 at 12:05
• TomR do you mean capacity instead of intensity? Oct 6 at 12:07
• @TomR I don't understand the second sentence. Based on the first one, are you looking for this kind of problem doi.org/10.1007/s10696-012-9152-5 ? Oct 6 at 12:13