ON THE POWER OF RANDOMIZATION FOR JO B SHOP SCHEDULING WITH k -UNITS LENGTH TASKS

In the job shop scheduling problem k - uni ts- Jm,therearem machines and each machine has an integer processing time of at mostk time units. Each job consists of a permutation of m tasks correspond-ing to all machines and thus all jobs have an identical dilation D .Thecontribution of this paper are the following results; (i) for d = o(√D )jobs and every fixed k , the makespan of an optimal schedule is at mostD + o( D ), which extends the result of [ 3]for k = 1; (ii) a randomizedon-line approximation algorithm for k - uni ts- Jmis presented. This isthe on-line algorithm with the best known competitive ratio against anoblivious adversary for d = o(√D )and k> 1; (iii) different process-ing times yield harder instances than identical processing times. Thereis no 5/3 competitive deterministic on-line algorithm for k - uni ts- Jm,whereas the competitive ratio of the randomized on-line algorithm of(ii) still tends to 1 for d = o(√D )