We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j is given by two machine indexes aj and bj; i.e., job j can only be scheduled on machines aj, aj + 1, ..., bj. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2 - 1 / m. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively.
All Science Journal Classification (ASJC) codes
- Information Systems and Management
- Management Science and Operations Research
- Modeling and Simulation