The problea of scheduling under liaited resources istreated by using two approaches. The first approach is themathematical approach. It is found that the shearingdemerits of the mathematical procedures are theformidability of formulation, and the limitation on theproblem size. The second is the heuristic approach. It isfound that each heuristic method is a ”tailor m.ad.e” and itperforms well under a certain conditions. So, the heuristicmethods are categorised according to Gome networkcharcteristic measures. A heuristic algorithm is suggestedwhich is designed to reduce the time of solution andprocreate the best solution. A case study is solved usingthe proposed heuristic algorithm. The case study isaconstruction project of a port on the Nile. The two modesof executing the activities (continuous and intermiltentmodes) are considered in the computerised algorithm.