In this paper, we develop branch-and-bound algorithms for objectives such as sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, for an \(m-\)machine no-wait (continuous) flowshop. We believe that there has been no prior work on exact algorithms for this problem setup with a variety of objective functions. For the interest of space, we confine our discussion to a subset of certain combination of these objectives and the extension to other objective combinations is quite straight-forward. We explore the active nodes of a branch-and-bound tree by deriving an assignment-matrix based lower bound, that ensures one-to-one correspondence of a job with its due date and weight. This idea is based on our earlier paper on general \(m-\)machine permutation flowshop (Madhushini et al. in J Oper Res Soc 60(7):991–1004, 2009) and here we exploit the intricate features of a no-wait flowshop to develop efficient lower bounds. Finally, we conclude our paper with the numerical evaluation of our branch-and-bound algorithms.

在本文中，我们针对\（m- \）机器无等待（连续）流水车间，针对诸如加权流时间，加权拖延性和加权作业提前期之类的目标，开发了分支定界算法。我们认为，针对具有各种目标函数的问题设置，没有针对精确算法的先前工作。为了节省空间，我们将讨论限制在这些目标的某些组合的子集中，并且将其他目标组合的扩展非常简单。我们通过派生基于赋值矩阵的下限来探索分支定界树的活动节点，以确保作业与其到期日期和权重一一对应。这个想法是基于我们先前关于一般\（m- \）的论文机器置换流水车间（Madhushini等人在J Oper Res Soc 60（7）：991–1004，2009）中使用了无等待流水车间的复杂功能来开发有效的下界。最后，我们以分支定界算法的数值评估结束本文。