Abstract
This paper is aimed at studying a two-machine flowshop scheduling where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. That is, when a job is processed completely on the first machine, a certain delay time is required before its processing on the second machine. If we would like to reduce the actual waiting time, the processing time of the job on the second machine increases. The objective is to minimize the makespan. When the processing time is reduced, it implies that the consumption of energy is reduced. It is beneficial to environmental sustainability. We show that the proposed problem is NP-hard in the strong sense. A 0-1 mixed integer programming and a heuristic algorithm with computational experiment are proposed. Some cases solved in polynomial time are also provided.
Highlights
We consider a two-machine flowshop scheduling problem where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine
If we can find a way to reduce the certain delay time at the cost of extra processing time added to the processing time of the job on the second machine, the whole processing time of all jobs may be reduced
If there is an advantage in terms of the makespan minimization, we can reduce the waiting time after the completion of cooking at the cost of an extra processing time of the chilling process
Summary
We consider a two-machine flowshop scheduling problem where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. Yang and Chern [23] further extended the problem studied by Sriskandarajah and Goyal [22] and considered a problem in which the processing time of a job on the second machine is linearly dependent on the waiting time if the waiting time is beyond a certain range. They proposed an integer program and a heuristic algorithm to solve the problem.
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