J.J. Yuan

Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs

We consider the feasibility model of multi-agent scheduling on a single machine, where each agents objective function is to minimize the total weighted number of tardy jobs. We show that the problem is strongly NP-complete in general. When the number of agents is fixed, we first show that the problem can be solved in pseudo-polynomial time for integral weights, and can be solved in polynomial time for unit weights; then we present a fully polynomial-time approximation scheme for the problem.

Multi-agent scheduling on a single machine with max-form criteria

We consider multi-agent scheduling on a single machine, where the objective functions of the agents are of the max-form. For the feasibility model, we show that the problem can be solved in polynomial time even when the jobs are subject to precedence restrictions. For the minimality model, we show that the problem is strongly NP-hard in general, but can be solved in pseudo-polynomial-time when the number of agents is a given constant. We then identify some special cases of the minimality model that can be solved in polynomial-time.

A note on the complexity of the problem of two-agent scheduling on a single machine

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agents objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.

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

In this paper, we consider the single machine batching problem with family setup times to minimize maximum lateness. While the problem was proved to be binary NP-hard in 1978, whether the problem is strongly NP-hard is a long-standing open question. We show that this problem is strongly NP-hard.

Single machine batch scheduling problem with family setup times and release dates to minimize makespan

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an

Two-agent single-machine scheduling with release dates and preemption to minimize the maximum lateness

O(n (\frac{n}{m}+1)^m)

A Stronger Complexity Result for the Single Machine Multi-Operation Jobs Scheduling Problem to Minimize the Number of Tardy Jobs

time dynamic programming algorithm and an