Projects of various forms have been carried out for millennia. Ancient Egyptians put up the pyramids some 4500 years ago while the eminent Chinese military general Sun Tzu wrote extensively on strategy and planning some 2500 years ago. The 19 th century witnessed the construction of transcontinental railways. These projects, despite their enormity and complexity, never led to the crystallization of science of management. It was not until the second half of the twentieth century that project management emerged as a distinct area of inquiry (Weaver, 2007) . Since its inception in 1958, modern project management has swiftly evolved as researchers and practitioners have developed numerous techniques, tools, and processes that have enabled them to contribute to the emergence of the field while simultaneously enhancing their performance and understanding. The development of the Critical Path Method (CPM) and Precedence Diagramming Method (PDM) have been seminal milestones for the field. The latter, with its activity –on node network and other precedence relationships, arguably offers a more flexible and easier network approach for modeling large projects than the former (Hajdu, 2015) .
PDM, also known as Activity on Node (AON) method, is a technique of graphical representation that shows the scheduling of or interdependencies between various projects (Weist, 1981) . Goksu and Catovic (2014) describe the diagramming method as a common technique used to show the critical chain network diagram and the critical path network diagram. PDM plots the work or task to be completed and connects them with arrows that show dependencies (Weist, 1981) . There are mandatory dependencies in any work or process. For instance, in the construction of a building, the obvious starting point is the laying of the foundation and, therefore, building a wall cannot precede this stage. With the appreciation of mandatory dependencies, project managers and their teams can then decide on discretionary dependencies. These should, however, be defined on the basis of previous experience or best practice within a particular area. Once the dependencies have been developed, they can be mapped into a precedence diagram.
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A team drawing a precedence diagram first needs to settle on which tasks will be completed after the other, which can be undertaken simultaneously and which tasks are not dependent on others at all and, therefore, can be undertaken independently. It is, in fact, a common technique to work backward during the construction of a precedence diagram (Hajdu, 2015) . The Precedence Diagramming Method (PDM) commonly consists of rectangles, which are known as nodes, and project activities that are contained in the rectangles. These nodes are connected to one another using arrows to demonstrate dependencies. Diagrams constructed through the precedence diagramming method are, therefore, known as Activity on Nodes (AOD) diagrams.
Developing a precedence diagram can be a complicated affair especially for complex and large projects. This is especially the case given the enormity of money, people, material, and equipment that may be required. Planners, therefore, need adequate information to buttress this exercise. In particular, planners require information on the duration (DUR) that each project will take, the earliest start time (EST) an activity can commence without undue interference on preceding activities, and the last start time (LST), which refers to the lastest a task can start without interference on a subsequent task. Additionally, planners need information on the earliest finish time (EFT) and the latest finish time (LFT). The LFT refers to the latest a task can finish without interference with the commencement of the subsequent activity. Finally, planners need information on the float time of a task. This is the time available for the performance of a task less the required time (Isaac & Hajdu, 2016) . Critical activities are those whose float is zero. That is to say EST=LST. In many instances, the duration of a project is not based on the discretion of the manager. Senior management or project funders often set deadlines. In such instances, it is crucially important that a near accurate approximation is made to address the varying concerns.
In general, PDM consists of predecessors, successors, and four logical relationships or what is termed as dependencies. A predecessor can be viewed as that activity that comes, logically, before the dependent activity. A successor, on the other hand, is the dependent activity that naturally flows from another scheduled activity (Weaver, 2007) . Having made references to predecessors and successors, attention will now be shifted to these dependencies: Finish to Start (FS), Finish to Finish (FF), Start to Start (SS) and Start to Finish (SF).
Finish to Start
In this particular dependency, the start of the second activity is contingent upon the completion of the first. It is the most used dependency in diagramming techniques. For example, painting a wall presupposes the existence of or completion of construction exercise.
Finish to Finish
In this dependency, completion of the second activity cannot take place without the completion of the first activity. Put differently, both activities end simultaneously. For instance, when coding a program for a client, one cannot finish the coding process without getting the complete requirements from the client. Both activities here end simultaneously.
Start to Start
Here, the start of the second activity can only take place if the first has been started. Both activities take place simultaneously.
Start to finish
Here, the second activity can only be completed if the first has been started.
Part of the popularity that PDM enjoys lies in its extensive employment of CPM techniques. CPM essential technique is to develop a model of project scheduling that takes into consideration the list of activities necessary to complete the project (commonly known as work breakdown structure), the duration for each activity’s completion, and the essential dependencies between various activities. In particular, CPM computes the longest path of set activities to their completion as well as the earliest and latest that each task can start and finish without lengthening the project. It also determines the critical tasks on the longest project. Thus, through CPM effective management, shortening of the planned critical path may be undertaken through pruning critical path activities, crashing the critical path (reducing the critical path’s duration by adding resources) or fast-tracking. According to Gosku and Catovic (2014), the CPM approach can be put into three phases.
Phase 1
Entails breaking the project into operational units for implementation. The sequential relationships of these operations are also established with attention to the possibility for overlap and the date each operation is earmarked for commencement.
Phase II
This level pays attention to the time each operation will consume. The specific aims are things like the earliest possible start date, earliest finish, and latest start and finish dates. These may be revised upon completion of phase three.
Phase III
Entails establishing the time-cost relationship with the view of determining the most favorable balance between the two. After the completion of this task, the planner may proceed to double check for missed relationships and subsequently, create a start node followed by an arrow from it to the first activity of the node. In many ways, therefore, Precedence Diagramming Method borrows heavily from the Critical Path Method. Nonetheless, as it has been noted earlier, it is more elaborate, flexible and easier thanks to its combination of the merits of these earlier techniques.
Importance of Precedence Diagramming Method
The primary benefit of PDM is that it demonstrates activity dependencies-the scheduling- and can be an important communication tool on stakeholders. This is especially important when project managers are seeking to manage stakeholder expectation, for instance, on the date of project completion. The PDM thus demonstrates that estimations are not the product of vague and erroneous generalizations but rather the product of rigorous processes. It is important to underscore that this is one of the main reasons that lead to the creation of PDM: CPM use from the mid-1950s to the 1970s in the construction industry was riddled with waterfall and wagon wheel dependency errors (Isaac & Hajdu, 2016) . It was upon this basis that the Navy contracted Stanford Professor John Fondahl to develop CPM computation models that would address the issue of dummy dependencies. At a time when finish to start relationships were most rampant, Dr. Fondahl reversed the classical Activity on Arrow diagramming method to develop the Activity-on Node diagramming method. Of course, as computer capabilities have developed especially between 1980 and 2000, many more attributes such as multiple calendars, lag and lead time dependencies, and multiple resources on activities have been added to the basic PDM framework (Hajdu, 2015) .
However, despite PDM developing into a relatively complicated framework that can incorporate a range of factors in the scheduling process, there are those who feel it remains inadequate. A serious challenge lies in its complexity (Weist, 1981) . Young persons with limited scheduling experience may have huge difficulties in undertaking schedule development and monitoring. Nevertheless, this complexity may not necessarily lead to a detailed and logical scheduling plan. If anything, such complex tools at times merely create the illusion accuracy (Weaver, 2007) . This is especially important given that the principal issue that bedevils schedule planning is inadequately planning the details of contract execution and failing to document plans in a manner that is clear and understandable. One missed dependency in precedence diagramming method is also likely to invalidate the entire results. In light of these pitfalls associated with precedence programming method, more so for the novice, Isaac & Hajdu (2016) have suggested the need for improvements while others scholars have suggested looking for alternative approaches like the Arrow Diagramming Method.
References
Goksu, A., & Catovic, S. (2014). Implementation Of Critical Path Method And Project Evaluation And Review Technique. International Burch University .
Hajdu, M. (2015). History and Some Latest Developments of Precedence. Szent Istvan University .
Isaac, S., & Hajdu, M. (2016). The Possibilities for Better Project Tracking based on the New Developments of the Precedence Diagramming Method. Procedia Engineering, 164 , 75-81.
Weaver, P. (2007). The Origins of Modern Project Management. Fourth Annual PMI College of Scheduling Conference .
Weist, J. (1981). Precedence Diagramming Method: some unusual characteristics and their implications for project managers. Journal of Operations Management, 3 (1), 121-130.
