A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

• Published in: Annals of operations research Vol. 338; no. 1; pp. 429 - 452
• Main Authors: Cohen, Ilan Reuven, Cohen, Izack, Zaks, Iyar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2024; Springer Nature B.V
• Subjects: Algorithms; Approximation; Business and Management; Cloud computing; Combinatorics; Completion time; Heuristic methods; Integer programming; Mixed integer; Operations Research/Decision Theory; Optimization; Original Research; Polynomials; Scheduling; Theory of Computation; Parallel machines; Cloud computing; Approximation algorithms; Scheduling; Capacitated machines
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-023-05613-x

We consider the weighted completion time minimization problem for capacitated parallel machines, which is a fundamental problem in modern cloud computing environments. In our setting, the processed jobs may be of varying duration, require different resources, and be of unequal importance (weight). Each server (machine) can process multiple concurrent jobs up to its capacity. We study heuristic approaches with provable approximation guarantees and offer an algorithm that prioritizes the jobs with the smallest volume-by-weight ratio. We bound the algorithm’s approximation ratio using a decreasing function of the ratio between the highest resource demand of any job and the server’s capacity. Thereafter, we create a hybrid, constant approximation algorithm for two or more machines. We also develop a constant approximation algorithm for the case of a single machine. Via a numerical study and a mixed-integer linear program of the problem, we demonstrate the performance of the suggested algorithm with respect to the optimal solutions and alternative scheduling methods. We show that the suggested scheduling method can be applied to both offline and online problems that may arise in real-world settings. This research is the first, to the best of our knowledge, to propose a polynomial-time algorithm with a constant approximation ratio for minimizing the weighted sum of job completion times for capacitated parallel machines.