A class of scheduling problem with chains constrains and processing times constrained by a resource

In this paper, a class of single machine resource constrained scheduling problem is investigated. In this model, it is assumed that the jobs are subject to parallel chains precedence constrains. The objective is total weighted completion times. Two versions of problem are addressed. In the first one the chains canpsilat be interrupted, whereas in the second one the chains can be interrupted. For both cases, polynomial algorithms are presented, respectively. We also give an example to illustrate the feasibility of the algorithm.