Network Planning in Project Management

Abstract

Planning is a big part of project management, and the success of it is highly dependent on this process. The method Network planning will be used to reduce possible complexity of a project and smoothen the execution of the project planning. A project of a large scale that require coordination of multiple activities is a challenging task for a project manager. Succeeding a project is about simple forms of working and organizing regardless the size of the project . The method will therefore be used as an integration approach where the different activities are separated to get an overview of the process. Understanding the dependencies of the project and setting up millstones is also ideal to motivate the employees involved in the project.

Project networking is investigating a project as sets of interconnected activities with the purpose of assisting in planning, managing, and controlling projects . This article will mainly focus on the most well know network planning techniques: the Critical path method (CPM) and the Program evaluation and review technique (PERT). CPM and PERT was developed in the 1950’s and has since then been used widely in operation research . The goal of the tool is to manage a project, meeting its deadlines with a minimum total cost. The tools will help organising the project, getting an overview of the activities and estimate the total length of the project. There can be multiple paths to the end of the project, but those tools can help the manager find the most effective one. Initially the methods will need three types of information to describe the project: activity, precedence, and time . This will be elaborated in the article followed by a description of the tool, an example of how to use the tool, other alternative planning tools and the limitations of the tool.

This article will elaborate the theory behind network/graphs and the focus on the comparison of different planning tools that are not focused on network planning specifically. The article is based on a project managers point of view and what that person may consider and wonder about when planning a project.

Introduction

In order to manage the complexity of a socio-technical system, such as a project, it is important to consider the following three steps; separating, integrating and adapting. Running a project can be overwhelming and no person is specialised in every little step, therefore it is important to divided the project into different activities. It is then essential for the project that these activities complement each other and contributes to the overall purpose of the project. Lastly the project needs to continuously evolve and respond to changes. The goal of every project is a smooth project execution where deadlines are meet, rework is avoided and every person involved is engaged in the success . To meet this goals and increase the effectiveness, the planning of the project must executed with high priority and professionalism. Network planning is a tool used in project, program and portefolio management in the planning process. The tool is great to give an overview and coordinate the activities in the given project in order to help project managers. Today it is set up as a software package in order to deal with the data and the progress. The two tools that will be described and elaborated in this article is the Critical Path Method (CPM) and the Program Evaluation and Review technique (PERT), which were originally independently developed, but today widely used as two tools merged into one . The tools work great together combining the techniques from both. This is also the case for most softwares, that it uses both tools in one with the purpose of scheduling and monitoring the project planning. In general network planning can study many different kind of problems such as project scheduling, risk analysis, cost minimization or Net Present Value maximization depends on the information that is needed from the project manager. Any delays within a project results in increased costs, which is highly avoidable.

The method is supported by the ISO 25000 standards that suggest three main processes for developing the schedule after identifying the activities. First is sequence activities, then estimate activity duration and develop schedule . In order to use those step in network theory for planning a project, they are set up in the following way.

• Activity information: the project must be broken down into individual activities

• Precedence relationships: find immediate predecessor(s) for each activity

• Time information: know/estimate the duration of each activity

A project should convey this information to describe the project and make the schedule . The estimation technique that is used in this method is similar to a bottom-up estimate, which is the reverser of the top-down estimate. A bottom-up estimate focus on estimating the duration of each activity before combining them all into the overall estimate of the project.

Network Theory

The first section will describe the terminology of network planning where two important definitions are described in order for better understanding of the method.

Graph Theory

A graph that consists of multiple nodes and arcs, are considered a network. This means that a network consists of nodes that are connected through arcs. In this article the exploration of networks will be centered around project planning, which means that the nodes correspond to the events in the project. The arcs correspond to the connection between the activities and can either be directed or undirected. When an arc is directed, for example for A to B, it means that the network can only go from A to B and not from B to A. An example of a network is illustrated below.

Figure 1. Small example with 7 nodes

Spanning Tree

Consider a network with a number of nodes n and no initially arcs. By adding one arc at a time between the nodes, a tree will appear. The first arc can be between any of the nodes in the network, but along the way, an arc cannot be placed if it creates a cycle. A network of nodes connected through arcs are referred to as a spanning tree. A network therefore differs between being cyclic or acyclic and a spanning three is acyclic.

A network will always have one or more start node(s) and a finish node/node(s). A project network can be split into two, depending on whether the activity is on the node or on the arc. Those two types are referred to Activity-on-arc (AOA) and Activity-on-node (AON). For the AOA, the node is separating the activities and therefor the arcs show the precedence relationship between the activities on the nodes. The AON is used in the CPM/PERT method, since it is remarkable more simple to construct, understand and revise than the AOA. Therefor this article will forward going only focus on AON, and therefor only activities. In the AOA method, it differs between events and activities, which is elaborated in an article presented in the Annotated Bibliography section.

CPM/PERT

The CPM/PERT method is an ideal method to get an overview of a project planning process and help answering multiple questions that a project manager may have for the process. The procedure described in this section is from . The method is a combination of the of the well known OR techniques Critical Path Method (CPM) and the Program Evaluation and Review technique (PERT). The PERT will graphically visualize the project timeline with all the individual tasks from start to completion of the project. It is used to estimate the duration of each activity, evaluating the the time that is needed in order to complete the project within the scope of the projects lifetime. The method uses the network terminology, where activities are visualized as nodes and arcs describing the precedence relationship between the activities indicating the flow of the whole project .

The critical path can answer how long time the project will take to complete and what the bottlenecks are to be aware of in order to prevent delays of the whole project. The CPM will establish the time length of the project, summing over all the durations of the activities. In a project network from a starting node to an end node, multiple paths can be set up if the activities can be done in sequence with a predecessors and no overlap. Therefor some activities have to wait for other activities to finish before it can start. Those can be activities that are on another path. The path with the longest total duration time is the critical path and therefor the longest duration time that the project can take assuming no delays occur. This is also the bottleneck activities of the project where delays most be avoided so that the whole project can be completed in time. The activities in the critical path therefor deserves the most attention, since this is very important for the project.

Scheduling the project

Earliest start- and finish time

The next question that the the project manager may ask is, when all the individual activities at earliest can start and finish? The first step of the procedure is therefor to address when every activity in the process can start and end if no delays occur. Those are defined as earliest starting time (ES) and earliest finish time (EF), where EF is equal to ES plus the estimated duration for the given activity. For convenience, the times are estimated in time periods instead of dates. This article will be based on weeks, but it could also be months or years. A small example is illustrated in figure 2.

How to find ES

Figure 2. Small example with 4 nodes

The first activity will always start at time period 0. Let's call the first activity A with a duration of 10 weeks. Then ES_A=0 and EF_A=0+10=10. For the next two nodes, lets call them B and C with duration 2 and 5 weeks, then ES_B=10 and EF_B=10+2=12 and ES_C=10 and EF_C=10+5=15. For the last node/activity of this small example, let's call it D with a duration of 7 weeks, the activity will have 2 predecessors and cannot start before both of them are done. Therefor the earliest starting time for C will be 15 weeks instead of 12. This means that ES_D=15 and EF_D=15+7=22. Now ES and EF is known for all nodes. The small example is illustrated in the figure 3. If a node/activity has a single predecessor, then ES for the activity is equal to EF for the predecessor. If the activity has two predecessors then ES is equal to the latest finished predecessors ES. In figure 2 is the small example from before visualized with ES and EF. Notice that this example has two possible paths where the first one has a total time length of 19 and the second one has a total time length of 22.

$Start \rightarrow A \rightarrow B \rightarrow D \rightarrow Finish$

$Start \rightarrow A \rightarrow C \rightarrow D \rightarrow Finish$

Since the second path has the longest duration, this is the critical path.

Figure 3. Example with ES and EF calculated

Latest start- and finish time

Another question, the project manager could ask, is how much the individual activities can be delayed, before the whole project is delayed. To answer this question, the next step is to calculate the latest start time (LS) and the latest finish time (LF) for every activity, where LS is equal to LF minus the estimated duration of the given activity. The times are still based on time periods, for example weeks.

How to find LF

When those parameters are estimated the procedure is to start backwards in the network. The method assumes that an activity's successors cannot start before the given activity is done.

For the finish node, LF will always be equal to ES, so that the project is still completed within the estimated time frame. LS is then equal LF minus the duration time, which is 0 for the finish node. The explanation of how to find LS and LF will again use the small example from before. This means that the next step is to find LS and LF for activity D, LF_D=22 and LS_D=22-7=15. This continues for the rest of the nodes until Start. Node A has two successors and therefor LF is equal the lowest value of the B and C's LS, which is 10 instead of 13. All the blue values therefor indicates that last possible chance for an activity to finish before the whole project will be delayed. The values are visualized together with the critical path in figure 4.

Figure 4. Example with LF and LS calculated and the critical path illustrated

Slack in the schedule

It is noticeable that node B is the only node with a different LS and LF value than ES and EF. To understand what this means for the project, is slack investigated in the schedule. The slack is calculated using LF and EF for every activity:

$Slack = LF - EF$

Calculating that slack for all 4 nodes, the only node with a slack different from 0 is B.

$Slack_B = LF_B - EF_B = 15-12 = 3$

This means that activity B can be delayed with up to 3 weeks and the project will still be completed within the estimated time frame of 22 weeks. This also means that the nodes A, C and D with a slack value of 0 cannot be delayed without delaying the whole project. Those nodes are therefor also forming the critical path, which is illustrated with a yellow line in figure 4. This is how the PERT/CPM method identifies the critical path.

Limitations

The PERT/CPM method has answered the questions that was presented in this article, but there are some limitations to be aware of. The method is great to visualise the small examples, but it will be difficult to use it with large complex projects where the time estimations and predecessors are harder to identify. It can rapidly become a time consuming task to draw up the diagram and make the scheduling calculations for every activity. To solve this on larger problems, you may have to use linear programming, but that can as well be complex and time consuming to set up.

The method is based on estimations, which may have to be revisited once the activities are scheduled and the critical path is identified. If the critical path is estimated to have a completion date later than what is required, the estimations may need to be adjusted . This is resulting in an increasing uncertainty of the estimations. In case this should happen the estimation process would change to a top-down estimate. This type of estimation is often connected to more uncertainty since the activities no longer are being assessed individually. Generally bottom-up estimates tend to be more accurate than top-down estimates, but are more time consuming.

The method is simple to use, but not focused on any resources involved in the project. This is causing a lot of inflexibility for the process and may not work on the long term projects. Other than that the method is not taking adaptation into account, regarding the threes steps (separating, integrating and adapting), which is big part of project management. Separating and integrating the project is a balance, because the more you separate the more you need to integrate. Choosing the right level of separation and integration is central to managing the complexity of a project. This article is narrowed down to only looking at the time aspect of project network planning, but there is more of the tool to investigate. The method may be expanded to uncertainty and costs which are also important aspects of project planning. The method is using accurate estimations of activity duration, which is associated with some uncertainty. Therefor it is relevant for the project manager to know what the probability is to meet the deadline. The uncertainty is then expanded to include time-costs trade offs. So whether it possible to decrease uncertainty with increased cost. This part of the method will not be further investigated in this article.

Taken the limitations of the tool into account, the PERT/CPM is still one of the most widely used OR techniques used by project managers. Even though the tool does not answer all the questions that a project manager may have, the answers that it does give, are very usefull. Also a lot of software package is already installed on many workstations in order to use this tool. This tool is applicable for many projects even though other great project planning tools are available too. Which tool to choose is highly dependent on preferences and the complexity of the projects. It is important to notice that all the project planning tools is intended to reduce complexity of a project and it is therefor important to choose the correct tool so that it doesn't have the opposite effect. This tool could as well be applied for program or portfolio management.

Alternative planning tools

Multiple planning tools are widely used in project, program and portfolio management. Given the scope of the project, some tools are more relevant than others. Other examples of project planning tools are Gantt Charts and Milestone Planning. Just like the CPM/PERT method, the Gantt Charts is graphical description of a projects timeline and is used in the same way as the PERT alone. Where the CPM/PERT displayed the activities as a network, the Gantt Charts display it as bar chart. The CPM can as well be identified using the Gantt Charts, making the two methods very similar. Some project managers think that the Gantt Charts is easier to include resources in, which the CPM/PERT does not include. Using the Gantt Charts is possible to follow how the resources are utilised, making it a great alternative to CPM/PERT.

Another possible planning tool is Milestone Planning, where it is also possible to implement the CPM. The Milestone Planning method is a great reactive tool to evaluate on the progress of the project. At the same time, this tool is more simple than the CPM/PERT and could therefor be easier to use on big projects.

Annotated Bibliography

If you find this topic interesting, some articles are presented in order to dig deeper into the subject:

Retrieved from F. S. Hillier & G. J. Lieberman. (2015). Introduction to operation research. This article is narrowed down only looking at the time aspect of project network planning, but there is more of the tool to investigate. The method may be expanded to uncertainty and costs which are also very important aspects of project planning.

It is also possible to factor risk into the PERT. Focusing on this technique only, it calculates the weighted average using an optimistic and pessimistic approach.

D. Simchi-Levi, X. Chen, J. Bramel (2014). Logic of logistic, pp. 379-402. 3. edition. https://www-scopus-com.proxy.findit.cvt.dk/record/display.uri?eid=2-s2.0-85098061835&origin=inward&txGid=e4025bf0be0a6349538f43c3a2fc9c59 The chapter focuses on the issues regarding network planning within supply chain design and planning.

https://www.yourarticlelibrary.com/project-management/project-scheduling-and-network-planning-with-diagram/95024 This article presented the method Activity-on-arc which is also relevant to understand in depth if you want to know more about project network planning.