Hybrid solution method for resource-constrained project scheduling problem using a new schedule generator

Abstract

A number of exact scheduling schemes incorporating various solution procedures such as branch and bound and dynamic programming exist for solving the well-known resource-constrained project scheduling problem. In this paper, we report on an efficient hybrid method which prominently depends on a branch and bound with a look-ahead mechanism as well as a genetic algorithm coupled with a new schedule generation scheme called tri-directional schedule generator. Minimal delay set, core time, and left shift are among the pruning rules used to prune inferior nodes of the enumeration tree. The proposed method has been verified and validated using a standard set of test problems with 30–120 activities requiring between one and six resource types each. The capability and applicability of the proposed method are demonstrated using standard problem instances.

Appendix

Proof of Lemma By the definition of core time and sets $C\prime{(x)_i}\;;\,\left( {\,i = 1,\, \ldots, \,q} \right),$ since for every set $\,C\prime{(x)_i}\;;\,\,\left( {i = 1,\, \ldots, \,q} \right),$, there are not enough resources for amount of l_i in which $\,{l_i} = \left| {\mathop{ \cap }\limits_{{j \in C\prime{{(x)}_i}}} \left[ {L{S_j}\,,\,E{F_j}} \right]\,} \right|\,$; therefore, the lower bound LB(x) must be increase at least by l_i, hence the lower bound must be increase at least by

$$ L = Max\left\{ {\,{l_i}\,\,|\,\,\,i = 1,\,...,\,q\,} \right\}. $$