Abstract
We study a problem of scheduling a set of n jobs with unit processing times on a set of m multipurpose machines in which the objective is to minimize the makespan. It is assumed that there are two different job types, where each job type can be processed on a unique subset of machines. We provide an optimal offline algorithm to solve the problem in constant time and an online algorithm with a competitive ratio that equals the lower bound. We show that the worst competitive ratio is obtained for an inclusive job-machine structure in which the first job type can be processed on any of the m machines while the second job type can be processed only on a subset of m/2 machines. Moreover, we show that our online algorithm is 1-competitive if the machines are not flexible, i.e., each machine can process only a single job type.
| Original language | English |
|---|---|
| Pages (from-to) | 405-412 |
| Number of pages | 8 |
| Journal | Computers and Operations Research |
| Volume | 39 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:This research was partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev.
Funding
This research was partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev.
| Funders | Funder number |
|---|---|
| Ben-Gurion University of the Negev |
Keywords
- Competitive ratio
- Eligibility constraint
- Multipurpose machine scheduling
- Online scheduling