A Decomposition Algorithm for Sequencing with General Precedence Constraints

Many important unconstrained job sequencing problems for which optimal algorithms exist satisfy the adjacent job interchange property. In recent years, a more general property, the adjacent sequence interchange property, has been identified and shown to be a sufficient condition for the existence of efficient algorithms for sequencing problems with series-parallel precedence constraints. In this paper, additional properties are defined which are sufficient to prove the existence of decomposition algorithms for general precedence structures. These results are applicable to several problems, including the two-machine maximum flow time problem, the maximum cumulative cost problem, the least cost fault detection problem, and the total weighted exponential completion time problem, and represent an extension of Sidney's results on the weighted completion time problem.