Optimum Time-Cost Trade-Off Strategies on Critical Path Method for Project Management

Approach of Crashing Critical Activities (CCA) was originally developed along with the Critical Path Method (CPM) for planning and controlling large scale projects in the late 50s. The objective of crashing critical activities in CPM is to find which activities should be crashed with the use of additional resources if the duration of the project must be shortened. Crashing in CPM means crashing one time unit from critical activity that has smallest cost slope while ensuring that the critical path is still the longest path in the project network. This procedure is repeated until the project has been shortened sufficiently or the cost to shorten the project exceeds the benefits to the derived. Due to this complexity we develop some new procedures in this thesis, which enable us to solve the above problems alternatively. The procedures composed of an approach of Stretching Noncritical Activities (SNA) and the approach of Stretching Noncritical and Critical Activities (SNCA). The general methodology of SNA assumes many situations in CPM in which the owners or project managers are crashing all activities in the project simultaneously to directly find the shortest possible duration for the project completion. Later it is possible to reduce the extra cost of the project by stretching noncritical activities without extending the project duration. The general methodology of SNCA is considered a complementary to SNA, it supposes various circumstances may be forced the owners or project managers to extend the completion of the project or reduce the total cost by stretching critical activities to meet the desired project completion time. When critical activity is stretched and the shortest possible of project completion is extended, other paths may also become noncritical, therefore, the noncritical activities can be stretched again until all the slack in the different noncritical paths is used up. In addition, we have built some of Linear Programming models that have been of great value in analyzing project time-cost trade-offs problems. These models provide us the analysis of results that obtained from solving these models to give us some flexibility in planning and scheduling. Computational results are presented for the problems under study. We demonstrate that our algorithms produce consistently good results for all versions of time-cost trade-off problems. In order to illustrate the usefulness of our approaches, we elaborate our algorithms on six cases of the well-known time-cost trade-off problem. These problems are designed to cope with more realistic setting: time-cost constraints. Proposed approaches provide greater opportunity for project managers in determining the appropriate strategy at the outset of project implementation.

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