Multisystem Optimization for an Integrated Production Scheduling with Resource Saving Problem in Textile Printing and Dyeing

Table 1

The symbols and notations used in the proposed model.

Indices
I	Job
J	Procedure
k	Machine
n	Number of jobs
m	Number of procedures
	Number of parallel machines
Variables
	= 1 if the jth procedure of the ith job is processed on the kth machine
	Job sequence
Parameters
	Production cost of the jth procedure of the ith job on the kth machine
	Unit processing cost of the jth procedure of the ith job on the kth machine
	Finishing time of the ith job through all procedures
	Finishing time of the ith job through the jth procedures
	Processing time of the jth procedure of the ith job on the kth machine
	Set-up time of the kth machine when the (j-1)th procedure changes to the jth procedure for the ith job
	Standby time of the kth machine when the (j-1)th procedure changes to the jth procedure for the ith job
	Unit processing power of the jth procedure of the ith job on the jth machine
	Unit set-up power of the kth machine when the (j-1)th procedure changes to the jth procedure for the ith job
	Unit standby power of the kth machine when the (j-1)th procedure changes to the jth procedure for the ith job
	Auxiliary unit power of the kth machine during the jth procedure
	Unit water wastage of the kth machine when processing the jth procedure of the ith job
	Unit water wastage of the kth machine in the set-up stage of the jth procedure