An on-line scheduling problem of parallel machines with common maintenance time

AbstractIn this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio $4 - \tfrac{1} {m} $. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is $\tfrac{{10}} {3} $.

[1]  Ramaswamy Chandrasekaran,et al.  Improved Bounds for the Online Scheduling Problem , 2003, SIAM J. Comput..

[2]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[3]  Yong He.  The optimal on-line parallel machine scheduling , 2000 .

[4]  Ernst W. Mayr,et al.  On-line scheduling of parallel jobs with runtime restrictions , 1998, Theor. Comput. Sci..

[5]  Apa Arjen Vestjens.  On-line machine scheduling , 1997 .

[6]  Gerhard J. Woeginger,et al.  A polynomial-time approximation scheme for maximizing the minimum machine completion time , 1997, Oper. Res. Lett..

[7]  Joseph Y.-T. Leung,et al.  Makespan minimization in online scheduling with machine eligibility , 2010, 4OR.

[8]  Yong He,et al.  Optimal online algorithm for scheduling on two identical machines with machine availability constraints , 2002, Inf. Process. Lett..

[9]  György Turán,et al.  On the performance of on-line algorithms for partition problems , 1989, Acta Cybern..

[10]  H.-C. Hwang,et al.  Parallel Machines Scheduling with Machine Shutdowns , 1998 .

[11]  Kangbok Lee,et al.  The effect of machine availability on the worst-case performance of LPT , 2005, Discret. Appl. Math..

[12]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[13]  Susanne Albers.  Better Bounds for Online Scheduling , 1999, SIAM J. Comput..

[14]  Qi Feng,et al.  A Semi-on-Line Scheduling Problem of Two Parallel Machines with Common Maintenance Time , 2012, Asia Pac. J. Oper. Res..

[15]  Chris N. Potts,et al.  On-line scheduling of a single machine to minimize total weighted completion time , 2002, SODA '02.

[16]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[17]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..

[18]  Han Hoogeveen,et al.  A Best Possible Deterministic On-Line Algorithm for Minimizing Maximum Delivery Time on a Single Machine , 2000, SIAM J. Discret. Math..