Amortized efficiency of list update and paging rules
Communications of the ACM
The competitiveness of on-line assignments
Journal of Algorithms
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
Online parallel machines scheduling with two hierarchies
Theoretical Computer Science
Online scheduling of two job types on a set of multipurpose machines with unit processing times
Computers and Operations Research
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
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In this paper we study the optimality of the TLS algorithm for solving the online scheduling problem of minimizing the makespan on a set of m multipurpose machines, where there are two different job types and each job type can only be processed on a unique subset of machines. The literature shows that the TLS algorithm is optimal for the special cases where either m=2 or where all processing times are restricted to unity. We show that the TLS algorithm is optimal also for the special cases where the job processing times are either job type or machine set dependent. For both cases, the optimality of the TLS algorithm is proven by showing that its competitive ratio matches the lower bound for any processing set and processing time parameters.