Wyniki wyszukiwania - BazTech

1

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

EN

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.

2

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

EN

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.

3

Single processor scheduling problems with various models of a due window assignment

Janiak A., Janiak W.A., Marek M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2009

|

Vol. 57, nr 1

95-101

EN

In the paper we investigate four single processor scheduling problems, which deal with the process of the negotia-tion between a producer and a customer about delivery time of final products. This process is modeled by a due window, which is a generalization of well known classical due date and describes a time interval, in which a job should be finished. Due window assignment is a new approach, which has been investigated in the scientific literature for a few years. In this paper we consider various models of due window assignment. To solve the formu-lated problems we have to find such a schedule of jobs and such an assignment of due windows to each job, which minimizes a given criterion dependent on the maximum or total earliness and tardiness of jobs and due window parameters. One of the main results is the mirror image of the solutions of the considered problems and other problems presented in the scientific literature. The wide survey of the literature is also given.

4

Algorithms for parallel processor scheduling with distinct due windows and unit-time jobs

Janiak A., Janiak W.A., Januszkiewicz R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2009

|

Vol. 57, nr 3

209-215

EN

We have studied problems of scheduling n unit-time jobs on m identical parallel processors, in which for each job a distinct due window is given in advance. If a job is completed within its due window, then it incurs no penalty. Otherwise, it incurs a job-dependent earliness or tardiness cost. The objective is to find a job schedule such that the total weighted earliness and tardiness, maximum weighted earliness and tardiness or total weighted number of early and lardy jobs is minimized. Properties of optimal solutions of these problems are established. We proved that optimal solutions for these problems can be found in O(n5) time in case of minimization of the total weighted earliness and tardiness and the total weighted number of early and tardy jobs and in O (n4 n log n) time in case of minimization of the maximum weighted earliness and tardiness. The established solution methods are extended to solve the problems with arbitrary integer release dates. A dedicated algorithm with time complexity O(n3) is provided for the special case of the problem of minimizing total weighted number of early and tardy jobs with agreeable earliness-tardiness weights.