Chapter 3: Project Scheduling

Introduction

Project scheduling is the time phased processing of operations subject to precedence interactions, time constraints, and resource constraints in order to achieve particular goals.

Project Scheduling Concept

In this section, basic concepts of the project scheduling such as network analysis, components of networks, and the advantages of network analysis are discussed, and different ways of drawing a network are introduced.

Network Analysis

A project’s network of activities provides the basis for scheduling the project. A network is a visual representation of the project’s content and goals. The fundamental network assessment of the project is typically carried out in three stages: stage of network planning, stage of network scheduling, and stage of network control.

Network Planning

Network planning involves identifying the specific project activities. The activities needed and relationships of precedence are defined in this stage. Precedence requirements can be defined by technological, procedural or imposed limitations. Finally, network diagrams are utilized to visually represent the activities. Activity-onarrow (AOA) and activity-on-node (AON) demonstrations are the two common models for network drawing.

Network Scheduling

Network scheduling is carried out using computational methods for forward passes and backward passes to calculate the earliest and latest starting and finishing times of each activity.

Network Control

Network control includes monitoring a project’s progress on a network schedule basis and taking corrective action when necessary. An assessment of overall performance versus expected results will determine the project progress deficiencies.

The Components of the Network

The components of the network are described below:

• Node: Activities are represented as circular nodes in the network.
• Arrow: An arrow is a line that connects two nodes to one end with an arrowhead.
• Activity: An activity is a time-consuming action necessary to accomplish a part of the current project.
• Restriction: A restriction is an arrangement of precedence that determines the pattern of activities.
• Dummy: A dummy is used to show one significant event (e.g. milestone). A dashed circle denotes it and treats it as a zero-time activity.
• Predecessor activity: An activity of the predecessor is the one that instantly follows it.
• Successor activity: A successor activity follows one activity immediately.
• Descendent activity: Any activity limited by the one under consideration is a descendent activity.
• Antecedent activity: An antecedent activity is any activity that must precede one.
• Merge point: Once two or more tasks are predecessors of a single task, a merging point occurs.
• Burst point: A burst point occurs when there is a prevalent predecessor for two or more operations.
• Precedence diagram: A precedence diagram is a visual representation of a project’s activities and the preceding requirements for completing the project.

Drawing Project Network

To describe a project, three kinds of data are required:

• Activity information: Divide the project (at the required point of detail) into its individual operations.
• Precedence relationships: Define the predecessor(s) for each activity.
• Time information: Forecast each activity’s duration.

Activity on Arrow (AOA) and Activity on Node (AON) are two ways to represent the network for a project:

There are two ways in which a network diagram is generally drawn for a project:

• Activity on Arrow (AOA) representation
• Activity on Node (AON) representation

As both methods have the same scheduling results, using any of them does not make any difference. Most software, however, only generates one of them, and it is generally AON. Some programs, like Primavera, enable you to choose your preferred method.

Activity on arrow network (AOA)

The arrows depict activities in this technique, while the nodes denote the start and end of an activity. The arrow distance that connects the nodes is meaningless and arrows may be direct, bent, or curved. If an activity relies on another, the two arrows with a shared node occur on the network diagram.

Activity on node network (AON)

This technique is also called the method of the preceding diagram. The nodes depict activities in this technique and the arrows represent logical interactions between the activities. If the arrow begins at the end of an activity (activity A) and finishes at the beginning of another activity (activity B), then A is a predecessor to B.

Comparison between AOA and AON

It is possible to use both networks to represent a project network. However, there are some differences between them:

• The dummy activities in AON representation are not necessary.
• AON can be drawn and read more readily.
• In AOA, activity can only begin once all of its predecessors have been completed.
• AON enables the depiction of overlag /lag.
• AON enables four kinds of relationships to be represented while AOA enables only finish to start relationship.

Program Evaluation and Review Technique (PERT)

The soul of network based scheduling methods is a visual representation of the plan for accomplishing the program; such a chart shows the precedence interactions i.e. the dependencies of the activities leading to the underlying goal. This chart is called as the network. This concept has evolved from the bar charts through the years. The paper on forecasting and planning with probability based tolerances can be accepted as the pioneer paper for development of the PERT. PERT and CPM can be applied to various types of projects.

It is useful to recognize that there are basically two types of project activities: Activities that may have been carried out before, containing a considerable number of elements of chance which are called variable activities, and deterministic type of activity, i.e. one with appropriately known average value and minimal variance in time. Variable activities have comparatively large variance. Development of a new system or research and development projects can be counted as a good example to variable activities. On the other hand, maintenance activities, which have a minimal variance, can be a good example to deterministic activities.

Basic Calculations and Steps of PERT

To calculate the predicted length and variance for each activity, PERT utilizes the three time estimates given above and simple equations. Hence, the calculation and the steps of PERT will be introduced briefly in the following subsections.

Basic Calculations of PERT

Calculations of mean and variance in Beta distribution are utilized to calculate the mean time and variance in PERT. The formula for the mean is a simple weighted average of the three estimates, assuming that the optimistic and pessimistic estimates are equally possible and that the modal is four times more likely than these two estimates. The estimation equation for mean is depended on the acceptance that most of the observations will fall into three standard deviations minus or plus or in other words, distributed in six standard deviations. This also means that standard deviation is one-sixth of the range between optimistic and pessimistic time.

The duration of the project is calculated by summing up the expected modal time of critical activities.

Major Steps of PERT

The major steps in PERT analysis can be summarized as follows:

1. Determine three estimates; optimistic “a “modal “m”, and pessimistic “b” durations for each activity.
2. Calculate the expected value for each activity by using a, m, and b.
3. Compute the variance of each activity by using the formula for.
4. Calculate the expected project duration, Tx. Similar to CPM, the duration of the project is calculated by summing up the expected modal time of critical activities.
5. Similar to expected duration, calculate the variance of the project as the sum of individual variance of activities on the critical path.
6. In addition to expected project duration, the probability of finishing the project within specified time limits can be calculated, which does not exist in CPM.

PERT is pessimistic about the variance in the project duration. Therefore, if there are multiple critical paths in the project network, the critical path with the largest variance must be chosen to determine the project duration and the variance of the project duration.

Probability of Meeting a Scheduled Date

According to the Central Limit Theorem, the probability of meeting a scheduled date, Td, can be calculated by finding the area under the standard normal curve on the left-hand-side of Td, assuming that the project duration Tx is normally distributed.

Estimation of a, m and b

Most important inputs of the PERT are the three estimates: optimistic, pessimistic and the modal duration of each activity in the project network diagram (shown as a, b, and m, respectively). It is possible to use several approaches to determine the duration estimates necessary for PERT. The following are some of the strategies:

• Predictions provided by an experienced person
• Estimates derived from historical data
• Estimates obtained from statistical methods such as regression
• Estimates provided by the results of simulation scenarios
• Approximations obtained from heuristic assumptions
• Customer requirements

Advantages and Limitations of PERT

PERT derives the following advantages:

• Allows managers to analytically plan their projects and evaluate all the factors that affect the progress of the project. The network analysis process involves the project planning to be carried out from start to finish in considerable detail.
• Provides management with a tool to predict the effect of schedule changes and be prepared to resolve such circumstances. The likely trouble areas are placed earlier which gives enough time to apply some preventive or corrective steps.
• Task relationships are represented visually for easier assessment, and individuals can logically deduce their role in the overall task requirements at various steps.
• The PERT time is based on a there estimates, and therefore, it is the most objective prediction under the uncertainties and results in a higher degree of forecast accuracy.
• PERT provides improved communication results. The network diagram provides a mutual interest for different stakeholders such as project managers, customers, contractors, etc., and they all understand the role and contributions of each other.
• The network will illustrate situations that require higher priority attention whereas intention can be applied to key activities without overlooking the lower priority tasks. This provides management a chance to shift focus to any critical activity in order to finish the entire project on time.

There are some constraints or issues that arise in PERT:

• The estimation of duration and resources is uncertain. Keep in mind that these values are just assumptions and outcomes can only be as good as the assumptions
• Final cost may exceed traditional planning and control techniques. Due to the current nature of networking and network analysis, it requires a high level of planning skills and more details that would raise the cost of time and resources for labors,
• It is not appropriate to use PERT for fairly simple and repetitive projects such as fixed-sequence works.

CPM vs. PERT

While both strategies enable you to predict which series of activities (or paths) will take the longest time to finish in a project, there are some differences between PERT and CPM.