Hierarchical Production Planning and Real-Time Control for Parallel Batch Machines in a Flow Shop with Incompatible Jobs

Box 1

Periodic rolling scheduling heuristic.

Step 1: Set the number of control cycles. Calculate the capacitiesof the quenching stage and the tempering stage in each control

cycle, respectively.

Step 2: Read the jobs which need to be scheduled in the current control cycle. The jobs include which left from last control cycle

and which arrive in the current control cycle.

Step 3: Put the jobs in batches according to non-decreasing order of due-dates. Only the jobs with the same product type can be put

in the same batch.If the machine capacity is exceeded when a job is added to a batch, close the batch and place the job

in a new batch.

Step 4: Calculate the demands of the quenching stage and the tempering stage, respectively. If the demands are not greater than the

capacitiesat both stages respectively, put the jobs into the buffer and go to step 6; else go to step 5.

Step 5: Find out the lightest batch and remove it from the demand. Assuming the start time of the jobs in this batch is the earliest

time of the next control cycle. If the amount of tardiness by subcontracting is less than when left to the next control cycle,

the job will be subcontracting; Else, the job will be left to next control cycle. Go to step 4.

Step 6: If all the control cycles are scheduled, end scheduling; Else, advance to next control cycle and go to step 2.