An analysis method in project management using primal–dual relationships

In the analysis of network models, project evaluation and review technique (PERT) and critical path method (CPM) are the methods which have been widely applied to industrial project planning and control in practice. PERT, which is a large scale model, analyzes the project using a standard forward–backward analysis method. Further, quantitative models have been developed for shortening total project time by determining appropriate activities for crashing with a minimum cost. In this study, to solve the project planning and control problems, a new method of analysis is introduced with the help of the LP model using primal–dual relationships. This method, tested on middle scale problems, has proved to be more efficient in terms of mathematical calculations than traditional PERT–CPM solutions, simplex solutions to LP formulation and Out-of-Kilter method. The method of analysis proposed has been applied to a holiday village project with a 370 bed capacity. The result is a minimum cost program with the total project time of 10 months.