An Improved Immune Genetic Algorithm for Solving the Flexible Job Shop Scheduling Problem with Batch Processing

Table 1

Mathematical symbols and their definitions.

Mathematics symbol	Symbol definition and interpretation
	Total number of jobs
	Total number of machines
Ω	Total machine set
	Machine serial number,
	Job serial number, 。
	Total number of operations of the job
	Operation sequence,
	Optional processing machine set for the operation h of the job j
	Number of optional processing machines for the operation h of the job
	Operations h of the job
	Operations of the job j is processed on machine i
	Processing time of the operations h of the job on machine
	Processing start time of the operations of the job
	Completion time of the operations of the job
	A positive number large enough
	Due date of the job
	Completion time of each job
	Batch processing time of the job
	Size of the job
	Arrival time of the job to the buffer of the batch processing machine
	Batch processing machine capacity
	Set of jobs in batch
	Sets of all batches
	Available time of batch , the maximum arrival time of all jobs in batch b
	Start time of batch
	Processing time of batch , the maximum processing time of all jobs in batch
	Completion time of batch