Power of Preemption for Minimizing Total Completion Time on Uniform Parallel Machines

Power of Preemption on Uniform Parallel Machines

For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2 − 1/m is tight. If the makespan of the optimal preemptive schedule is defined by...

A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 2 (1 + √ 2)-approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximat...

Minimizing Total Weighted Completion Time on Uniform Machines with Unbounded Batch∗

In this paper, we consider the scheduling problem of minimizing total weighted completion time on uniform machines with unbounded batch. Each of the machine Ml (l = 1, ⋅ ⋅ ⋅ ,m) has a speed sl and can process up to B(≥ n) jobs simultaneously as a batch. The processing time of a batch denoted by P(B) is given by the processing time of the longest job in it, and the running time of the batch on m...

Fuzzy Programming for Parallel Machines Scheduling: Minimizing Weighted Tardiness/Earliness and Flow Time through Genetic Algorithm

Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. One type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical model for...

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time