Speed-robust scheduling: sand, bricks, and rocks - Centre de Calcul de l'IN2P3 Accéder directement au contenu
Article Dans Une Revue Math.Programming Année : 2023

Speed-robust scheduling: sand, bricks, and rocks

Franziska Eberle
  • Fonction : Auteur
Ruben Hoeksma
  • Fonction : Auteur
Nicole Megow
  • Fonction : Auteur
Lukas Nölke
  • Fonction : Auteur
Kevin Schewior
  • Fonction : Auteur
Bertrand Simon

Résumé

The speed-robust scheduling problem is a two-stage problem where, given m machines, jobs must be grouped into at most m bags while the processing speeds of the machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm's makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor 2 - 1/m for the most general setting and improve this to 1.8 for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to e/e - 1 approximate to 1.58. The particular machine environment in which all machines have either speed 0 or 1 was studied before by Stein and Zhong (ACM Trans Algorithms 16(1):1-20, 2020. https://doi.org/10.114/3340320) . For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of 1+root 2/2 approximate to 1.207. It lays the foundation for an algorithm matching the lower bound of 4/3 for equal-size jobs.

Dates et versions

hal-03719706 , version 1 (11-07-2022)

Identifiants

Citer

Franziska Eberle, Ruben Hoeksma, Nicole Megow, Lukas Nölke, Kevin Schewior, et al.. Speed-robust scheduling: sand, bricks, and rocks. Math.Programming, 2023, 197 (2), pp.1009-1048. ⟨10.1007/s10107-022-01829-0⟩. ⟨hal-03719706⟩
27 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More