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Scheduling problems with a common due window assignment: a survey

Janiak A., Kwiatkowski T., Lichtenstein M.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 1

231--241

In this article a survey of studies on scheduling problems with a common due window assignment and earliness/tardiness penalty functions is presented. A due window is a generalization of the classical due date and describes a time interval in which a job should be finished. If a job is completed before or after the due window, it incurs an earliness or a tardiness penalty, respectively. In this survey we separately analyse the classical models with job-independent and job-dependent earliness/tardiness penalty functions and some other more complicated models. We describe the computational complexity of the problems and the main features of the approaches developed to solve them. Particular attention is paid to practical applications of the analysed models. As turns out, some complicated models combining classical scheduling problems with, e.g., learning and aging effects have no reasonable practical justification in the literature.

Scheduling and due-date assignment problems with job rejection

Mosheiov G., Sarig A.

Foundations of Computing and Decision Sciences

2009

Vol. 34, No. 3

193-208

Scheduling with rejection reflects a very common scenario, where the scheduler may decide not to process a job if it is not profitable. We study the option of rejection in several popular and well-known scheduling and due-date assignment problems. A number of settings are considered: due-date and due-window assignment problems with job-independent costs, a due-date assignment problem with job-dependent weights and unit jobs, minimum total weighted earliness and tardiness cost with job-dependent and symmetric weights (known as TWET), and several classical scheduling problems (minimum makespan, flow-time, earliness-tardiness) with position-dependent processing times. All problems (excluding TWET) are shown to have a polynomial time solution. For the (NP-hard) TWET, a pseudo-polynomial time dynamic programming algorithm is introduced and tested numerically.