Jinjiang Yuan

A note on the scheduling with two families of jobs

Baker and Smith [J. Scheduling, 6, 7–16, 2003] introduced a new model of scheduling in which there are two or more distinct families of jobs pursuing different objectives. Their contributions include two polynomial-time dynamic programming recursions, respectively, for the single machine scheduling with two families of jobs to minimize a positive combination of total weighted completion time, or maximum lateness, of the first family of jobs and maximum lateness of the second family of jobs. Unfortunately, these dynamic programming recursions are incorrect. In this paper, we solve the same problems by an O(n1n2(n1 + n2)) time algorithm.

Parallel-machine scheduling with deteriorating jobs and rejection

We consider several parallel-machine scheduling problems in which the processing time of a job is a (simple) linear increasing function of its starting time and jobs can be rejected by paying penalties. The objective is to minimize the scheduling cost of the accepted jobs plus the total penalty of the rejected jobs. Three variations of the scheduling cost are considered in this paper. The first is the makespan, the second is the total weighted completion time (for simple linear deterioration), and the third is the total completion time. For the former two problems, we propose two fully polynomial-time approximation schemes to solve them when the number of machines is fixed. For the last problem, we present an optimal O(n^2)-time dynamic programming algorithm when the deteriorating rates are equal for all jobs.

On-line scheduling on an unbounded parallel batch machine to minimize makespan of two families of jobs

AbstractWe study the on-line scheduling on an unbounded parallel batch machine to minimize makespan of two families of jobs. In this model, jobs arrive over time and jobs from different families cannot be scheduled in a common batch. We provide a best possible on-line algorithm for the problem with competitive ratio n

A best online algorithm for scheduling on two parallel batch machines

(sqrt{17}+3)/4approx1.7808

A best online algorithm for unbounded parallel-batch scheduling with restarts to minimize makespan

n.

Unbounded parallel-batch scheduling with family jobs and delivery coordination

We consider the online scheduling on two parallel batch machines with infinite batch size to minimize makespan, where jobs arrive over time. That is, all information of a job is not available until it is released. For this online scheduling problem, Nong et al. [Q.Q. Nong, T.C.E. Cheng, C.T. Ng, An improved online algorithm for scheduling on two unrestrictive parallel batch processing machines, Operations Research Letters, 36 (2008) 584-588] have provided an online algorithm with competitive ratio no greater than 2. We show that this bound is tight for the problem. Furthermore we give a new best possible online algorithm with a tighter structure.

Preemptive scheduling with simple linear deterioration on a single machine

We consider online scheduling with restarts in an unbounded parallel-batch processing system to minimize the makespan. By online we mean that jobs arrive over time and all the information on a job is unknown before its arrival time (release date) and restart means that a running batch may be interrupted, losing all the work done on it, and the jobs in the interrupted batch are released and become independently unscheduled jobs. It is known in the literature that the considered problem has no online algorithm with a competitive ratio less than

A note on the preemptive scheduling to minimize total completion time with release time and deadline constraints

(5-sqrt{5})/2

Online scheduling on a single machine with rejection under an agreeable condition to minimize the total completion time plus the total rejection cost

. We give an online algorithm for the considered problem with a competitive ratio

An on-line algorithm for the single machine unbounded parallel-batching scheduling with large delivery times

(5-sqrt{5})/2approx 1.382