Nonsimultaneous Machine Research Articles

Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines

An unrelated-parallel-machine scheduling model with job rejection option was studied. In this model, all jobs are available at time zero but some machines are not available at time zero. Each job is either accepted and processed once without interruption, or is rejected at a penalty cost. To minimize the makespan of all accepted jobs plus the total cost of rejecting and processing jobs, we provide a heuristic with worst-case ratio bound of 2.

Scheduling with Deteriorating Jobs and Non-Simultaneous Machine Available Times

In this paper, We deal with the scheduling problems with simple linear deterioration function on unrelated parallel-machine and identical parallel-machine. We assume that all the jobs (tasks) are available at time zero, but all machines (processors) may not be available simultaneously at time zero. The objective functions are to minimize the total logarithm of completion time, the total logarithm of machine load, the total absolute differences in logarithm completion times and the total absolute differences in logarithm waiting times respectively. We provide the polynomial-time algorithms to solve the problems under the proposed model respectively.

Parallel machines scheduling with simple linear job deterioration and non-simultaneous machine available times

In this note, we deal with the parallel-machine scheduling of deteriorating jobs where the actual processing of a job is a simple linear function of the job’s starting time. The jobs are available at time zero but the machines may not be available simultaneously at time zero. For the problem to minimize the logarithm of makespan, we present heuristic algorithms and analyze their worst-case error bounds.

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.

Ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times

This paper considers ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times. Two objects of minimizing the latest job completion time and minimizing the latest machine completion time are studied. For the first objective, we present the optimal algorithms for m = 2, 3, 4 machine cases. For m ≥ 5, we propose an algorithm with competitive ratio 2 - 1/( m - 1) while the lower bound is 5 3 . For the second objective, the optimal algorithm is also given. Furthermore, for a special case, an algorithm with significantly improved competitive ratio is given.

A note on “parallel machine scheduling with non-simultaneous machine available time”

The purpose of this note is to point out that if there are some machines that do not process any job and hence is inactive in the planning horizon then the lower bound of makespan provided by Lee (1991) in the above mentioned paper may not be a valid one. Furthermore, the error bound of applying the Longest Processing Time (LPT) algorithm to the problem can be tightened if the number of active machines is smaller than the total number of machines.

The multifit algorithm for set partitioning containing kernels

This paper investigates the set partitioning containing kernels. This problem can also be considered as the identical machine scheduling problem with nonsimultaneous machine release times. That the algorithm MULTIFIT has a worst case bound of 6/5 is proved. Through combining MULTIFIT and LPT, an algorithm MULTILPT with a worst case bound of 7/6 has been obtained.

The exact bound of Lee's MLPT

Lee provided a modified version of LPT algorithm to deal with the problem Parallel Machines Scheduling with Nonsimultaneous Machine Available Times, and got an upper bound of built4 3 for its worst-case performance ratio. An open question is then proposed to obtain the exact value of this ratio, which is determined in this paper. The instance which achieves the ratio is also demonstrated.

Parallel machine scheduling to maximize the minimum load with nonsimultaneous machine available times

We consider a generalized version of the classical parallel machine scheduling problem, in which the m machines are available at time a j⩾0, j=1,2,…,m . The objective function is to maximize the minimum machine completion time. Using the conventional weighting function technique, previously, a lower bound of 5 8 has been shown for the worst-case performance ratio of the famous Longest Processing Timing (LPT) approximation. In this paper, we develop a new method, called matching, and show that the worst-case performance ratio of LPT is exactly (2 m−1)/(3 m−2). We also give an instance to indicate the tightness of this ratio.

Exact bounds of the modified lpt algorithms applying to parallel machines scheduling with nonsimultaneous machine available times

In this paper, we consider Parallel Machines Scheduling with nonsimultaneous machine available time. We give the exact worst case performance bound of MLPT proposed by Lee. Furthermore, two other modified LPT algorithms are discussed. The paper is ended by numerical experiments of these algorithms.

Parallel machines scheduling with nonsimultaneous machine available time

In this paper we consider the problem of scheduling n independent jobs on m identical machines in order to minimize the makespan, the total finishing time. The jobs are available at time zero, but some machines may not be available at time zero. This problem is a generalization of the classical multiprocessor scheduling problem, where all machines are available simultaneously at time zero. We first show that the makespan obtained by applying the longest processing time (LPT) algorithm to our generalized problem is always within ( 3 2 − 1 2 m) M ∗ and the bound is tight. We then provide a modified LPT (MLPT) algorithm and show that the makespan obtained by MLPT is bounded by 4 3 M ∗.