Approximating Scheduling Machines with Capacity Constraints

In the Scheduling Machines with Capacity Constraints problem, we are given k identical machines, each of which can process at most m i jobs. $M \leq \sum_{i = 1}^{k}{m_i}$ jobs are also given, job j has a non-negative processing time length t j *** 0. The task is to find a schedule such that the makespan is minimized and the capacity constraints are met. In this paper, we present a 3-approximation algorithm using an extension of Iterative Rounding Method introduced by Jain [4]. To the best of the authors' knowledge, this is the first attempt to apply Iterative Rounding Method to scheduling problem with capacity constraints.

[1]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[2]  L. G. H. Cijan.  A polynomial algorithm in linear programming , 1979 .

[3]  Jiawei Zhang,et al.  An approximation algorithm for scheduling two parallel machines with capacity constraints , 2003, Discrete Applied Mathematics.

[4]  Evripidis Bampis,et al.  A FPTAS for Approximating the Unrelated Parallel Machines Scheduling Problem with Costs , 2001, ESA.

[5]  Gerhard J. Woeginger,et al.  A comment on scheduling two parallel machines with capacity constraints , 2005, Discret. Optim..

[6]  Li-Hui Tsai,et al.  Asymptotic Analysis of an Algorithm for Balanced Parallel Processor Scheduling , 1992, SIAM J. Comput..

[7]  Kamal Jain.  A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem , 2001, Comb..

[8]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Yinyu Ye,et al.  On the Budgeted Max-cut Problem and Its Application to the Capacitated Two-parallel Machine Scheduling , 2001 .

[10]  Dennis F. X. Mathaisel,et al.  Airline Scheduling: An Overview , 1985, Transp. Sci..

[11]  Martin Gairing,et al.  A faster combinatorial approximation algorithm for scheduling unrelated parallel machines , 2005, Theor. Comput. Sci..