Activity list representation for a generalization of the resource-constrained project scheduling problem

Abstract

Most of the real life scheduling problems include several constraints in addition to the precedence and resource constraints considered in the resource-constrained project scheduling problem ( RCPSP ). In this paper, we define a generalization of the ( RCPSP ) with a wide class of additional constraints, including (but not limited to): a pair of activities must be separated by at least a given duration; a subset of activities cannot be processed simultaneously; an activity cannot start before a particular period; an activity cannot be scheduled in a particular time window; there are resource constraints with varying required and available quantities. We show that for this generalization the activity list and the activity set list representations can be used as efficiently as in the ( RCPSP ) and that by using these representations the optimal solution can always be reached. This allows most of the known solution procedures for ( RCPSP ) based on these representations to be extended for the generalized ( RCPSP ) by simply replacing the classical decoding procedure used for the ( RCPSP ) with the generalized version introduced here.