Guoqiang Fan

Two-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizes

We schedule the jobs from two agents on a single parallel-batching machine with equal processing time and non-identical job sizes. The objective is to minimize the makespan of the first agent subject to an upper bound on the makespan of the other agent. We show that there is no polynomial-time approximation algorithm for solving this problem with a finite worst-case ratio, unless P=NP. Then, we propose an effective algorithm LB to obtain a lower bound of the optimal solution, and two algorithms, namely, reserved-space heuristic (RSH) and dynamic-mix heuristic (DMH), to solve the two-agent scheduling problem. Finally, we evaluate the performance of the proposed algorithms with a set of computational experiments. The results show that Algorithm LB works well and tends to perform better with the increase of the number of jobs. Furthermore, our results demonstrate that RSH and DMH work well on different cases. Specifically, when the optimal makespan on the first agent exceeds the upper bound of the makespan of the other agent, RSH outperforms or equals DMH, otherwise DMH is not less favorable than RSH.

Heuristics for Non-dominated Sets of Two-Agent Scheduling on a Single Parallel-Batching Machine

We study a bi-objective problem of scheduling the jobs from two agents on a single parallel-batching machine with the objective of minimizing the makespans of the both agents. All jobs have an equal processing time and non-identical job sizes. We define a boundary of Pareto-optimal set and then present two metrics to evaluate the quality of a non-dominated set. Based on two different strategies, two heuristics are proposed to generate non-dominated sets. Furthermore, we compare the performance of the heuristics with the widely used non-dominated sorting genetic algorithm (NSGA-II), and evaluate the quality of the obtained non-dominated set based on the proposed metrics. The results show that the proposed heuristics outperform NSGA-II, and the obtained non-dominated set is very close to the Pareto-optimal set.