Lower bounds for single machine subproblems occurring in weighted tardiness oriented shifting bottleneck procedures

In this paper, we propose lower bounds for single machine scheduling problems which occur during a run of a shifting bottleneck procedure for total weighted tardiness job shops. The specific structure of this kind of problem and its objective function in particular prevent an immediate transfer or an adaption of existing lower bounds from “conventional” single machine problems with tardiness related objectives. Hence it has been necessary to develop bounding approaches which are to some extent conceptually new. Potential application scenarios range from exact subproblem solution methods or machine prioritization criteria in a shifting bottleneck procedure to branch-and-bound algorithms for job shops with total weighted tardiness objective. In order to provide a significant evaluation of the proposed lower bounds regarding their effectiveness and efficiency, we tested them based on problem instances which actually have been generated in a shifting bottleneck procedure applied to benchmark job shop problems.