This work considers the three main optimization variants of the Simple Assembly Line Balancing problem (SALBP): SALBP-1, SALBP-2 and SALBP-E. These problems have origin in typical industrial production processes, where, to obtain a final product, partially ordered operations must be processed in workstations connected by a transportation equipment. Each version determines a different objective to be optimized: SALBP-1 focuses on minimizing the number of workstations while maintaining a certain production rate, SALBP-2 tries to maximize the production rate with a bounded number of workstations, and SALBP-E attempts to maximize the line efficiency. These problems are NP-hard and have been largely studied in the literature, however, the results on their approximability are scarce. This work approaches SALBP-1, SALBP-2 and SALBP-E, proving an equivalence on approximating in polynomial time SALBP-2 and a generalization of SALBP-E, and proposing very efficient polynomial time 2-approximation algorithms for each one of these three versions of SALBP.

这项工作考虑了简单装配线平衡问题 ( SALBP )的三个主要优化变体：SALBP-1、SALBP-2和SALBP-E。这些问题起源于典型的工业生产过程，在这些过程中，为了获得最终产品，必须在由运输设备连接的工作站中处理部分有序的操作。每个版本都确定了不同的优化目标：SALBP-1侧重于在保持一定生产率的同时最小化工作站数量，SALBP-2试图在有限数量的工作站上最大化生产率，而SALBP-E试图最大限度地提高生产线效率。这些问题是NP难题，并且在文献中已经进行了大量研究，但是，关于它们的近似性的结果很少。这项工作接近SALBP-1、SALBP-2和SALBP-E，证明了在多项式时间内逼近 SALBP-2的等价性和SALBP-E的推广，并为这三个中的每一个提出了非常有效的多项式时间 2 逼近算法SALBP 的版本。