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

Abstract

Abstract. In the paper we investigate four single processor scheduling problems, which deal with the process of the negotiation 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 formulated 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.

Scheduling problems with a common due window assignment: A survey

“…P O(n log n) (Janiak et al, 2009;Janiak and Marek, 2004) et al, 2001b) of problems with job-independent and job-dependent earliness/tardiness penalties. We have also analysed the research findings related to other mathematically complicated models.…”

“…were studied by Liman et al (1998) as well as Janiak and Marek (2009;, respectively. Optimal O(n log n) time algorithms were constructed for these problems.…”

A survey on scheduling problems with due windows

“…The abbreviation FPTAS in positions 8 and 9 denotes Fully Polynomial Time Approximation Scheme. Janiak, Janiak, and Marek (2009) investigated the single processor scheduling problem, in which the earliest due date was a decision variable and the latest due date was the sum of job processing time and some other decision variable: 1| e j = e, d j = d + p j | max{αE j , βT j , γ (d − e)}. They considered also another problem where the earliest due date was the sum of job processing time and a decision variable, and the latest due date was some other decision variable: 1| e j = e + p j , d j = d | max{αE j , βT j , γ (d − e)}.…”

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

“…In a scientific literature there have also been studied problems with due window assignment. For a literature review and some results see [7].…”