Time-cost analysis (CPM-COST). Algorithm versus optimization model

The author of this paper analyses examples of network diagrams presenting different projects. The target consists in compressing the project schedule to a time desired and minimizing direct costs. On the basis of these case studies the author shows how both, i.e., 1) the algorithm based on the critical path method with a time-cost analysis and 2) the optimization models, generate each iteration to finally determine the best solution. However, the results obtained are different. In this connection, the steps of the algorithm are demonstrated in order to proof that some of its assumptions are not entirely defined in a proper way. It turns out that the project accelerating 1) by shortening each critical path by exactly one unit and 2) by selecting the cheapest combination of critical activities, may not necessarily lead to the optimal solution. At the end of the paper two modified assumptions are proposed.