Moutaz Fakhry, Yuri Granik, et al.
SPIE Photomask Technology + EUV Lithography 2011
Scheduling problems with preemption are considered, where each operation can be interrupted and resumed later without any penalty. We investigate some basic properties of their optimal solutions. When does an optimal schedule exist (provided that there are feasible schedules)? When does it have a finite/polynomial number of interruptions? Do they occur at integral/rational points only? These theoretical questions are also of practical interest, since structural properties can be used to reduce the search space in a practical scheduling application. In this paper we answer some of these basic questions for a rather general scheduling model (including, as the special cases, the classicalmodels such as parallelmachine scheduling, shop scheduling, and resource constrained project scheduling) and for a large variety of the objective functions including nearly all known. For some two special cases of objective functions (including, however, all classical ones), we prove the existence of an optimal solution with a special "rational structure." An important consequence of this property is that the decision versions of these optimization scheduling problems belong to class NP. © 2010 Pleiades Publishing, Ltd.
Moutaz Fakhry, Yuri Granik, et al.
SPIE Photomask Technology + EUV Lithography 2011
Jianke Yang, Robin Walters, et al.
ICML 2023
A. Gupta, R. Gross, et al.
SPIE Advances in Semiconductors and Superconductors 1990
F.M. Schellenberg, M. Levenson, et al.
BACUS Symposium on Photomask Technology and Management 1991