Abstract
This paper considers a problem of semi-online scheduling jobs on two identical parallel machines with objective to minimize the makespan. We assume there is an unavailable period [B,F] on one machine and the largest job processing time P max is known in advance. After comparing B with P max we consider three cases, and we show a lower bound of the problem are 3/2, 4/3 and \((\sqrt{5}+1)/2\) , respectively. We further present an optimal algorithm and prove its competitive ratio reaches the lower bound.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
He Y, Zhang G (1999) Semi on-line scheduling on two identical machines. J Comput 62:179–187
Hwang HC, Chang SY (1998) Parallel machines scheduling with machine shutdowns. Comput Math Appl 36:21–31
Lee CY (1996) Machine scheduling with an availability constraint. J Glob Optim 9:363–382
Schmidt G (2000) Scheduling with limited machine availability. Eur J Oper Res 121:1–15
Tan Z, He Y (2002) Optimal online algorithm for scheduling on two identical machines with machine availability constraints. Inf Proc Lett 83:323–329
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H., Su, C. An optimal semi-online algorithm for 2-machine scheduling with an availability constraint. J Comb Optim 22, 153–165 (2011). https://doi.org/10.1007/s10878-009-9280-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-009-9280-3