Minimizing the total flow time and the tardiness in a two-machine flow shop

This paper is concerned wit the two-criteria problem in a two-machine flow shop. The objective was to find a job sequence that minimized both the total flow time and the tardiness. Several dominant properties for the precedence relationship between jobs are proposed and a lower bound on the flow time and tardiness value for a subproblem is derived. The computational results of a branch-and-bound algorithm are also reported.