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Holloway Consulting is a leading Construction Consulting Firm providing construction scheduling, delay analysis and contractor and owner claims services to U.S. and International clients, including law firms, public agencies, developers, owners, design professionals, construction managers, general and trade contractors.



Arrow Diagrams and I-J Network Methods

Although the bar chart method contains inherent disadvantages, it was used for many years simply because other planning and scheduling methods had not been developed. As the size, complexity and cost of projects grew, the need for more sophisticated planning and scheduling methods grew. As a result, the Program Evaluation and Review Technique, or PERT, was a statistical planning and scheduling method developed for the U.S. Navy in the mid-1950s. PERT was used most effectively on research and development projects, but did not enjoy wide use in the construction industry.

The development of CPM planning and scheduling methods and techniques, which are used extensively today in both project management and disputes, began in the mid to late 1950s, when the birth of the computer age opened the door for the development of CPM scheduling. By the late 1950s, E. I. duPont de Nemours and Company had developed the fundamentals of a critical path scheduling method to control projects through the use of computers. This new management tool was developed to catalog and present the essential information necessary to plan, schedule and control duPont’s construction and facility maintenance projects.

As originally developed, the foundation of CPM was the Arrow Diagram Method (ADM). The arrow diagram method is a model that depicts an arrangement of activities in a logical sequence of performance. Each arrow in the diagram is a separate activity that represents an item of work in the project. The tail of the arrow is the start of the activity and the head of the arrow is the finish of the activity. The arrow diagram identifies the activities that must be completed before a given activity can start and which activities can be performed during the same time period, or concurrently. An arrow diagram can be drawn with or without a time scale.

Arrow Diagrams Methods

In ADM, the point at which two or more activities converge is designated as an event or node. All activity arrows leading into an event or node must be completed before any activities leading out of the event or node can be started. To facilitate the unique identification of activities in an arrow diagram, the events or nodes are numbered. An activity’s identification is, therefore, comprised of two numbers – the starting node number and the ending node number. As the method of arrow diagramming evolved, the starting node was referred to as the “i” node and the ending node was referred to as the “j” node. This node numbering approach used with arrow diagrams is now commonly referred to as the “i-j” method.

I-J Network Methods

The development of the arrow diagramming method, or i-j scheduling method, overcame the basic weaknesses of bar charts; that is, the logical interrelationships between activities are shown, the earliest and latest start and finish dates for each activity are calculated (through mathematical techniques called the “forward” and “backward” pass), and the amount of slip or float available for activities is determined. The “float” for an activity is calculated as the difference between either the early start and late start or early finish and late finish. The term “critical path” is defined as the longest path through a network. The early and late start dates and early and late finish dates for any single activity on the critical path are the same. The float on critical path activities is calculated to be zero and any delays to the critical path would theoretically extend the projected completion date.

The concepts of critical path and activity float are the heart of CPM scheduling methods, and construction schedule delay claims and methods.

Call Steve Holloway – – at (303) 984-1941 to discuss your construction scheduling consulting needs.

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