An exact approach for single machine subproblems in shifting bottleneck procedures for job shops with total weighted tardiness objective

0377-2217/$ see front matter 2011 Elsevier B.V. A doi:10.1016/j.ejor.2011.10.020 ⇑ Corresponding author. Tel.: +43 732 2468 9466. E-mail address: [email protected] (R. Braune). In this paper, we propose an exact solution method for single machine scheduling problems typically arising from bottleneck-based decomposition of weighted tardiness job shops. The encountered subproblems are characterized by delayed precedence constraints, multiple local due dates per operation and an objective function that is given by a weighted sum of maximum tardiness values. The key concept for solving these subproblems to optimality is a dominance rule whose underlying concepts have been newly developed to cope with the given structural properties. Furthermore, a simple lower bound and a dedicated constraint programming technique are presented. The efficiency of the proposed method is demonstrated by means of single machine problems collected during a run of a shifting bottleneck procedure for job shops in different size and due date tightness configurations. 2011 Elsevier B.V. All rights reserved.