Parallel machine scheduling to minimize the makespan with sequence dependent deteriorating effects

A new unrelated parallel machine scheduling problem with deteriorating 26 effect and the objective of makespan minimization is presented in this paper. The 27 deterioration of each machine (and therefore of the job processing times) is a function of the 28 sequence of jobs that have been processed by the machine and not (as considered in the 29 literature) by the time at which each job is assigned to the machine or by the number of jobs 30 already processed by the machine. It is showed that for a single machine the problem can be 31 solved in polynomial time, whereas the problem is NP-hard when the number of machines is 32 greater or equal than two. For the last case, a set of list scheduling algorithms and simulated 33 annealing meta-heuristics are designed and the effectiveness of these approaches is evaluated 34 by solving a large number of benchmark instances. 35