Single machine scheduling with chain: structured precedence constraints and separation time windows

We consider a single machine scheduling problem which we studied to improve the efficiency of an automated medical laboratory. In this problem, there are not only chain structured precedence constraints, but also minimal and maximal times separating successive jobs in the same chain (separation time windows). The criterion to be minimized is the makespan. Potential applications are not restricted to medical analysis. This problem often arises in systems where chemical processes are involved. Therefore the problem studied in this paper is important in practice. We prove that the problem is nonpolynomial (NP)-complete. As a consequence, we propose three heuristics for large size problems and a branch and bound based algorithm for small size problems. Computational results are reported.