Two-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizes - Wang, Jun-Qiang; Fan, Guo-Qiang; Zhang, Yingqian; Zhang, Cheng-Wu; Leung, Joseph Y.-T. (European journal of operational research, 2017)
•We schedule two agents on a single p-batching machine with non-identical job sizes.•We minimize the makespan of one agent under a bounded makespan of the other agent.•We show that no polynomial-time algorithm with a finite bound exists, unless P = NP.•We propose an effective algorithm to obtain a lower bound of the optimal solution.•We propose two heuristics and illustrate the effectiveness by computational studies. [Display omitted] 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.