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

Abstract

Abstract.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 tardy 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(n 5 ) 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(n 4 √ 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(n 3 ) is provided for the special case of the problem of minimizing total weighted number of early and tardy jobs with agreeable earliness-tardiness weights.

A survey on scheduling problems with due windows

“…Heuristic (Yoo & Martin-Vega, 2001) 9 (Janiak, Janiak, & Januszkiewicz, 2009) 10 (Janiak, Janiak, & Januszkiewicz, 2009) …”

Metaheuristics for scheduling on parallel machine to minimize weighted number of early and tardy jobs

“…Adamu and Abass (2010) proposed four greedy heuristics for the Pm|∑w j (U j + V j ) problem and extensive computational experiments was performed. Janiak et al (2009) gave an O(n 5 ) complexity for solving the problem (Pm|p j = 1 |∑w j (U j + V j ). They also consider a special case with agreeable earliness and tardiness weights where they gave O(n 3 ) complexity (Pm|p j = 1, r j , agreeable ET weights|∑w j (U j + V j )).…”

Measurement of noise in the Monte Carlo point sampling method

“…The simplicity of a typical cornell box itself causes that the image rendered using light-tracing algorithm with even less than 10 rays per pixel contains an imperceptible variance in the estimates. All images used in the experiment present the same scene renderd with the ligh-tracing algorithm with the resolution of 800x600 considering parallel processor scheduling algorithms [5].…”