# Job shop problem: capacity constraint and variable if production in time t

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Hi all,

I am creating a job shop scheduling model in AIMMS for my MSc thesis. The model plans jobs j of production orders i backwards from their due date. The main (nonnegative) decision variables are:

• StartTime(i,j) = the start time of production order i job j
• EndTime(i,j) = the end time of production order i job j

The only thing I still need to add is that capacity may not be exceeded. I have the following information:

• Capacity(j) = total capacity of job j in one time bucket

Now I need some counter / variable looking like:

• x(i,j,t) = the amount processed of operation i, job j in time bucket t. Where time bucket 1 = [0,1], time bucket 2 = [1,2] et cetera.

See the figure below for my current data, I want to retrieve the following x(i,j,t) values:

• x(1,COAT,1) = 0.5 (from 0 to 0.5)
• x(1,PRO,1) = 0.5 (from 0.5 to 1)
• x(1,PRO,2) = 0.7 (from 1 to 1.7)
• x(1,PW,2) = 0.3 (from 1.7 to 2)
• x(1,PW,3) = 0.5 (from 2 to 2.5)

Does someone have an idea on constraints to retrieve the values for x(i,j,t) as shown in the example?