New approximation algorithms for flow shop total completion time problem

This article addresses the flow shop scheduling problem to minimize the sum of the completion times. On the basis of the properties in job sequencing, the triangular shortest processing time (TSPT) first and dynamic triangular shortest processing time first heuristics are designed to solve the static and dynamic versions of this problem, respectively. Moreover, an improvement scheme is provided for these heuristics to enhance the quality of the original solutions. For further numerical evaluation of the heuristics, two new lower bounds with performance guarantees are presented for the two versions of the problem. At the end of the article, a series of numerical experiments is conducted to demonstrate the effectiveness of the algorithms.