Heuristics for the Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup times

Algorithm 3

ESPRA algorithm.

	Step 1: Set the partial sequence OP^∗ = 0.
	Step 2: Calculate the matrix ESST, where each entity of ESST is calculated by equation (13)
	Step 3: Jobs are sorted by the ascending order of the corresponding summed idle energy consumption cost based on the setup time in ESST to obtain the sequence of jobs .
	Step 4: According to , identify the pairs of jobs as fictitious jobs, and calculate their running energy consumption cost based on processing time by equation (14).
	Step 5: Sort the fictitious jobs by the decreasing order of their running energy consumption cost and obtain the sequence of fictitious jobs .
	Step 6: Take the first two fictitious jobs of and allocate them on the machines at each stage with the EST rule with a better sequence which has less total energy consumption cost. Insert the sequence of the two fictitious jobs in to OP^∗ and delete them from .
	Step 7: Consider the next fictitious job of .
	Step 8: Insert the fictitious job into all positions of the partial sequence OP^∗ and find the sequence with the less total energy consumption cost. Delete this fictitious job form .
	Step 9: Set OP^∗ = .
	Step 10: If , go to Step 11, else go to Step 7.
	Step 11: Return the total energy consumption cost.