Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions

On the NP-hardness of scheduling with time restrictions

“…For any real x, no unit time interval [x, x + 1) is allowed to intersect more than B jobs. The problem has been shown to be NP-hard when B is part of the input and left as an open question whether it remains NP-hard or not if B is fixed [1,5,7]. This paper contributes to answering this question that we prove the problem is NP-hard even when B = 2.…”

“…Braun, Chung and Graham [1] showed that any reasonable schedule T must have C T ≤ (2 − 1 B−1 )C * + 3 if B ≥ 3 and C T ≤ 4 3 C * + 1 if B = 2, where C T and C * denote the makespan of T and the optimal schedule respectively. In [5], it is further improved to C T ≤ (2 − 1 B−1 )C * + B B−1 for any B ≥ 3. If we produce the schedule T by the LPT algorithm (in which jobs are arranged by non-increasing order of their execution times), then it is shown that C T ≤ (2 − 2 B )C * + 1 for any B ≥ 2 and the bound is best possible [5].…”

Editorial “Project Management and Scheduling”

“…Additionally, two regularly submitted papers on the subject by Esmaeilbeigi et al (2016) and Braun et al (2016) were added. The 10 papers arch the entire field from new approaches for well-known studied problems as in Schnell and Hartl (2016) to modeling of complex industry scheduling problems as in Schulze et al (2016), approaches and insights for new project organizations such as public private partnership presented in De Clerck and Demeulemeester (2016) to, finally, the treatment of classical machine scheduling problems as in Braun et al (2016) More detailed, this special issue contains the following contributions.…”

“…The 10 papers arch the entire field from new approaches for well-known studied problems as in Schnell and Hartl (2016) to modeling of complex industry scheduling problems as in Schulze et al (2016), approaches and insights for new project organizations such as public private partnership presented in De Clerck and Demeulemeester (2016) to, finally, the treatment of classical machine scheduling problems as in Braun et al (2016) More detailed, this special issue contains the following contributions. Schnell and Hartl (2016) propose exact approaches using branch-and-bound with principles from constraint programming and boolean satisfiability for solving the multi-mode resource-constrained project scheduling problem with generalized precedence relations to optimality.…”

“…Finally, Braun et al (2016) consider single machine scheduling with time restrictions, present an improved bound for list scheduling and analyze the worst-case behavior of LPT ordered jobs.…”