Lingfa Lu

Single machine scheduling with release dates and rejection

In this paper, we consider the single machine scheduling problem with release dates and rejection. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem is NP-hard in the ordinary sense. Then we provide two pseudo-polynomial-time algorithms. Consequently, two special cases can be solved in polynomial-time. Finally, a 2-approximation algorithm and a fully polynomial-time approximation scheme are given for the problem.

Single-machine scheduling under the job rejection constraint

In this paper, we consider single-machine scheduling problems under the job rejection constraint. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. However, the total rejection penalty of the rejected jobs cannot exceed a given upper bound. The objective is to find a schedule such that a given criterion f is minimized, where f is a non-decreasing function on the completion times of the accepted jobs. We analyze the computational complexities of the problems for distinct objective functions and present pseudo-polynomial-time algorithms. In addition, we provide a fully polynomial-time approximation scheme for the makespan problem with release dates. For other objective functions related to due dates, we point out that there is no approximation algorithm with a bounded approximation ratio.

The single machine batching problem with identical family setup times to minimize maximum lateness is strongly NP-hard

Abstract In this paper, we consider the single machine batching problem with family setup times to minimize maximum lateness. Recently, Cheng et al. [T.C.E. Cheng, C.T. Ng, J.J. Yuan, The single machine batching problem with family setup times to minimize maximum lateness is strongly NP-hard, Journal of Scheduling 6 (2003) 483–490] proved that this problem is strongly NP-hard. This answers a long-standing open problem posed by J. Bruno and P. Downey [Complexity of task sequencing with deadlines, setup times and changeover costs, SIAM Journal on Computing 7 (1978) 393–404]. By a modification of the proof in Cheng et al. (2003), we show that this problem is still strongly NP-hard when the family setup times are identical.

RESCHEDULING WITH RELEASE DATES TO MINIMIZE TOTAL SEQUENCE DISRUPTION UNDER A LIMIT ON THE MAKESPAN

In this paper, we consider the rescheduling problem for jobs on a single machine with release dates to minimize total sequence disruption under a limit on the makespan. We show that the considered problem can be solved in polynomial time. Consequently, the rescheduling problem for jobs on a single machine with release dates to minimize makespan under a limit on the total sequence disruption can also be solved in polynomial time.

Single Machine Scheduling With Job Delivery To Minimize Makespan

In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio

Single machine unbounded parallel-batch scheduling with forbidden intervals

\frac{5}{3}

Integrated production and delivery scheduling on a serial batch machine to minimize the makespan

, and pointed out that no heuristic can have a worst-case performance ratio less than

Two-machine open-shop scheduling with rejection to minimize the makespan

\frac{3}{2}

Preemptive scheduling on identical machines with delivery coordination to minimize the maximum delivery completion time

unless P = NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio

Two-stage scheduling on identical machines with assignable delivery times to minimize the maximum delivery completion time

\frac{3}{2}