Critical Path analysis is commonly considered to be a technique for planning and scheduling of projects. The planning phase is usually identified with the construction of the project graph, during which time specific decisions are made on the method of performing jobs as well as their technological ordering. At the same time standard times are assigned to these jobs. At the completion of the planning stage it is possible, using the conventional Cpm calculations, to schedule the starting time of each job in the project. Unless several different plans are evaluated in this way, or unless the technique of job crashing is used, there is no interaction between the planning and the scheduling phase of the usual Cpm analysis.

We shall show in this paper that if an overall optimum is to be obtained a much greater degree of interaction is essential, and shall give methods for solving the more general problem. Thus if there are a number of competing methods of performing some of the jobs, each method having a different cost, a different time duration and different, technological dependencies, we shall include all these in the project graph, rather than making the decisions in advance. Then in the scheduling phase, we shall consider the effects of all alternate methods of performing a task on the total cost of completing the project and choose those alternatives which minimize this cost. We may apply the same method to the control of projects being carried out. Thus decisions 1, previously optimal, may be changed during the execution of the project due to certain jobs being delayed.

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