By the mid Twentieth century, projects were managed on an ad hoc basis using mostly Gantt Charts, and informal techniques and tools.

During that time, the Manhattan project was initiated and its complexity was only possible because of project management methods.

The Manhattan project was the codename given to the Allied effort to develop the first nuclear weapons during World War II.

It involved over thirty different project sites in the US and Canada, and thousands of personnel from US, Canada and UK.

Born out of a small research program that began in 1939,

the Manhattan Project would eventually employ 130,000 people and cost a total of nearly 2 billion USD

and result in the creation of multiple production and research sites operated in secret.

The project succeeded in developing and detonating three nuclear weapons in 1945. 

The 1950s marked the beginning of the modern Project Management era.

Two mathematical project scheduling models were developed: 

The Program Evaluation and Review Technique or PERT, developed by Booz-Allen & Hamilton

as part of the United States Navy's (in conjunction with the Lockheed Corporation) Polaris missile submarine program.

Pert is basically a method for analyzing the tasks involved for completing a given project,

especially the time needed to complete each task, and identifying the minimum time needed to complete the total project (Figure 1.4). 

The Critical Path Method (CPM) developed in a joint venture by both DuPont Corporation

and Remington Rand Corporation for managing plant maintenance projects.

The critical path determines the oat, or schedule flexibility, for each activity by calculating the earliest start date,

earliest finish date, latest start date, and latest finish date for each activity.

The critical path is generally the longest full path on the project.

Any activity with a oat time that equals zero is considered a critical path task.

CPM can help you figure out how long your complex project will take to complete and which activities are critical;

meaning they have to be done on time or else the whole project will take longer.

These mathematical techniques quickly spread into many private enterprises.