Certain maintenance procedures fail to perform prior to a pre-specified deadline and need extra time for successful accomplishment. Processing times under this specific deterioriation are represented by a step function. We study the problem of makespan minimization of step-wise deteriorating jobs. We introduce compact integer programming formulations. We then focus on heuristic methods, since even the case of single machine single-step deterioration is NP-complete. These methods are extended to settings of multi-machine and multi-step deterioration. Our numerical tests indicate that the proposed algorithms are highly accurate and efficient in the context of a numerical study discussed in this paper.
Bibliographical noteFunding Information:
Acknowledgements--The author is grateful to Ziv Katalan and Avital Lann for their helpful comments. This research was supported in part by the Recanati fund of The School of Business, The Hebrew University, Jerusalem.