Purpose

Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage.

Design/methodology/approach

Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution.

Findings

Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time.

Originality/value

Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

中文翻译：

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数学模型和两个有效的分支定界算法，解决装配车间的调度问题

目的

包括加工车间和组装阶段的两阶段生产系统广泛用于各种制造业。这两个阶段通常是独立研究的，可能不会导致理想的结果。本文旨在处理一个包括生产车间和装配阶段的两阶段生产系统。

设计/方法/方法

提出了一些基于分支定界（B＆B）方法的精确方法，以最大程度地缩短产品的总完成时间。由于B＆B方法通常很耗时，因此针对该问题开发了三个有效的下限，并且使用可变邻域搜索为每个分支中的解决方案提供适当的上限。另外，为了创建分支并搜索新节点，应用了两种策略，包括最佳优先搜索和深度优先搜索（DFS）。所提出算法的另一个特征是通过释放优先约束来减少搜索空间。在这种情况下，该问题等效于并行机调度问题，并且删除了不考虑优先级约束的冗余分支。因此，

发现

一些数值示例用于评估所提出方法的性能。与数学模型（混合整数线性规划）的比较结果验证了所提方法的性能准确性和效率。此外，计算结果表明DFS策略在CPU时间方面具有优势。

创意/价值

对于包括车间然后组装阶段的两阶段生产系统的调度问题的研究，传统上提出了解决问题的近似方法和元启发式算法。这是第一项介绍基于（B＆B）方法的精确方法的研究。