In this paper, we study the two-machine no-wait flow shop scheduling problem with two competing agents. The objective is to minimize the overall completion time of one agent subject to an upper bound on the makespan of the second agent. We proved the \(\mathcal {NP}\)-hardness for three special cases: (1) each agent has exactly two operations. (2) the jobs of one agent require processing only on one machine, (3) the no-wait constraint is only required for the jobs of one agent. We exhibited polynomial time algorithms for other restricted cases. We also proposed a mathematical programming model and a branch and bound scheme as solving approaches for small-scale problems. For large instances, we present a tabu search meta-heuristic algorithm. An intensive experimental study is conducted to illustrate the effectiveness of the proposed exact and approximation algorithms.

在本文中，我们研究了具有两个竞争代理的两机无等待流水车间调度问题。目的是使一种药剂的总完成时间减至最小，该时间取决于第二种药剂的有效期的上限。我们证明了\（\ mathcal {NP} \）-在三种特殊情况下的硬度：（1）每个代理正好有两个操作。（2）一个代理程序的工作仅需要在一台计算机上进行处理，（3）仅一个代理程序的工作需要无等待约束。我们展示了针对其他受限情况的多项式时间算法。我们还提出了数学规划模型和分支定界方案作为解决小规模问题的方法。对于大型实例，我们提出一种禁忌搜索元启发式算法。进行了深入的实验研究，以说明所提出的精确算法和近似算法的有效性。