Table of Contents

List of Figures ................................................................................................................................. 2

Introduction to engineering project scheduling .............................................................................. 3

Nature and definition of the engineering project scheduling ...................................................... 3

Existing classifications of this project scheduling problem. ....................................................... 4

Scope of this study ...................................................................................................................... 4

Methodology to be used in this study ......................................................................................... 5

Survey of project scheduling methods and techniques ................................................................... 6

Classification of existing procedures, techniques, methods for engineering project scheduling 6

Scheduling procedures and methods ........................................................................................... 9

The Critical Path Method ........................................................................................................ 9

Program Evaluation and Review Technique......................................................................... 11

Gantt Chart ............................................................................................................................ 12

Quantitative techniques ............................................................................................................. 13

Qualitative (heuristic) techniques ............................................................................................. 14

Summary ....................................................................................................................................... 17

Conclusion ................................................................................................................................ 17

List of Figures

Figure 1: Job-on-arc format

Figure 2: Job-on-node format

Figure 3: Job-on-node format example

Figure 4: Job-on-arc format example

Figure 5: Representing nodes as rectangles

Figure 6: The Critical Path Method

Figure 7: Program Evaluation and Review Technique

Figure 8: Gantt Chart

Figure 9: Gantt Chart with interdependencies

Introduction to engineering project scheduling

Nature and definition of the engineering project scheduling

A schedule can be described as a list of a project's tasks and deliverables, with indicated start and

finish dates. These are estimated in terms of resource allocation, budget and duration. The

various components are linked by dependencies where execution of a particular activity relies on

the completion of another precedent activity.

Engineering project scheduling is one of the major determinants of project success. However,

most engineers have no understanding of the basics of project scheduling. Following recent

economic downturns, businesses today face major challenges in their operation. This has led to

low market demand and investors now emphasize on reducing overhead costs through enhanced

efficiencies using existing and new infrastructure. The scope and complexity of engineering

projects present additional challenges to engineering firm investors. The pressure for quick

delivery of engineering project continue to increase in an effort to speed time-to-market while at

the same time, overall project costs need to be reduced.

These challenge can be addressed by adopting engineering scheduling techniques. Engineering

scheduling offers a planned approach to accomplishing projects tasks and efficient allocation of

resources throughout project lifecycle thus leading to much reduced timelines and efficient use

of resources.

Existing classifications of this project scheduling problem.

Engineering project scheduling relies on both heuristic and mathematical methods in allocatation

of limited resources to tasks at hand. There are three ways of classifying project scheduling

namely;

a) Critical path Method,

b) Project Evaluation and Review Technique and

c) Gantt Charts

All of these methods are based on information driven at the initial phase of a project. The

information may include estimation of resources required and a breakdown of all major tasks. In

both methods, it is possible to identify a critical path and estimate total duration of each task.

Interdependencies can also be established in both methods by identifying boundary times for the

various tasks.

Scope of this study

An engineering project schedule usually concerns a single project that consists of a number of

separate tasks which are related to one another through precedence constraints. In this study, we

will only consider a single project with multiple tasks that have precedence constraints. This

implies that a task can only start when all its predecessors have been completed.

Engineering project scheduling provides the necessary tools to save time and costs on a project.

In this study, we provide techniques for avoiding common problems that result from long-term

nature of engineering projects and unrealistic scheduling.

Methodology to be used in this study

We will assume that individual task durations are not entirely fixed initially. The scheduler has

some control on the processing duration of the different tasks through the allocation of additional

resources at their disposal. Important to note is that some engineering projects have deadlines

and delays may involve expensive penalties. Management has to therefore analyze the

consequences of late completion. For the purpose of clarity of expression, we will assume a

project scheduling problem without resources constraints.

Survey of project scheduling methods and techniques

Classification of existing procedures, techniques, methods for engineering project scheduling

Before creating a project schedule, the project manager should prepare a work breakdown

structure (WBS), an estimate duration for each task, and a resources list. If this information for

some of the tasks is not available, they can be created with an estimated. This is because a

schedule is itself is an estimate. The personnel involved in the project have to agree on the

estimated dates for the estimates to be accurate.

An effective engineering project schedule must meet the following standards:

The schedule must be regularly updated.

The remaining workload must be appropriately distributed among resources (taking into

account vacations and public holidays).

The Estimation at Completion value must be equal to the baseline value.

The dependency between the tasks is the basic constraint of the engineering project scheduling

problems. The precedence constraints may be represented in two formats, that is, job-on-arc

format or job-on-node format. In the job-on-arc format, the arcs in represent the tasks while the

nodes represent the milestones as shown in Figure 1. In the job-on-node format, the nodes

represent the tasks and the connecting arcs the dependency relationships between the tasks as

outlined in Figure 2. In practice, the job-on-arc format is more widely used than the job-on-node

format.

A major disadvantage of the job-on-arc format is the need to introduce dummy tasks to enforce

precedence constraints, tasks that otherwise would not have been enforceable. Below is a

demonstration of using dummy tasks;

Figure 1: Job-on-arc format

Figure 2: Job-on-node format

Example 1 (Setting up a manufacturing plant).

The tasks involved in the project are outlines as below:

Job Description Duration

1 Engineering design 2 Weeks

2 Prepare engineering drawings 1 Week

3 Prepare manufacturing plant 7 Weeks

4 Source machinery 5 Weeks

5 Source Materials 8 Weeks

6 Procure parts 3 Weeks

7 Installation of machinery 5Weeks

8 Testing and Handover 1 Week

The precedence constraints for the above project are as detailed below:

Task Immediate Predecessor Immediate successor

1 -- 4

2 -- 5

3 -- 6, 7

4 1 6, 7

5 2 6

6 3, 4, 5 8

7 3, 4 8

8 6, 7 --

Task s Task t

Task s Task t

1 4 7

3 8

2 5 6

Figure 3: Job-on-node format example

2 5

6

1 4 7 8

3

Figure 4: Job-on-arc format example

From figure 4, it can be denoted that there is a need for a dummy task in the job-on-arc format.

In a large engineering project, the number of dummy tasks maybe up to 10% of the total tasks

required.

The job-on-node format can also be shown using rectangles. The horizontal sides indicate the

time-axis corresponding to the processing duration of the task. If the task is allowed to start after

half the precedent task is completed, then the dependency is shown by an arc starting from the

midpoint of the horizontal side as seen in Figure 5 below.

Figure 5: Representing nodes as rectangles

Scheduling procedures and methods

The Critical Path Method

Consider (x) number of tasks which are subject to precedence constraints. The processing

duration of task t is fixed and equal to pt. Assuming that resources are unlimited, the Critical

Path Method main objective will be to minimize the duration it takes to complete a task. The

algorithm that yielding the minimum duration can be described in as follows;

Start all tasks without processors right at the beginning of the project.

Every time a task concludes its processing, start on those tasks of which all the

predecessors have been completed.

In order to outline the algorithm more elaborately, we will use some notations. Let C(t) denote

the earliest possible completion time of task t and S(t) the earliest possible starting time. We will

note clearly that, C(t) = S(t)+pt. Let’s also set (all s → t) as tasks that are predecessors of task t.

This implies that if task s is a predecessor of task t, task s has to be completed before task t can

be started. This algorithm is referred to as the forward procedure. This is because a task can start

its processing only after all its predecessors have been completed. The earliest starting time of a

task is thus equivalent to the maximum of the earliest completion times of all its predecessors.

Task t

Task s

There is another algorithm called the backward procedure. This technique determines the latest

possible starting time and completion times of all tasks. The backward procedure allows for the

possibility of delaying the start of some of the tasks without increasing the project duration.

Forward procedure and backward procedure vary in that the forward procedure determines the

earliest possible starting times and completion times while the backward procedure determines

the latest starting times and latest completion times. The minimum duration still can be achieved

in the backward procedure. A task of which the earliest starting time is earlier than the latest

starting time is referred to as a slack task. The difference between a task’s latest possible starting

time and earliest possible starting time is the amount of slack. A task with the earliest starting

time being equal to the latest starting time is called a critical task. Acritical path comprises of a

set of critical tasks. A critical path can also be described as a chain of non-slack tasks, beginning

with a task that starts at time zero and ending with a task that completes its processing at the

planned end of the project.

In any given engineering project, there exists one longest chain of tasks which form the critical

path. These tasks have an impact on the project duration and it is critical to consider them when

allocating resources for the project.

Figure 6: The Critical Path Method

Program Evaluation and Review Technique

In contrast to the Critical Path Method, the processing duration of the x tasks are random. The

mean µx and the variance σ2 x of each of these random variables may either be accurate or

estimated. The technique minimizing the expected duration is just like in the Critical Path

Method. To compute the processing duration, the following three variable are required.

pa t = the optimistic processing duration of task t,

pm t = the most likely processing duration of task t,

pb t = the pessimistic processing duration of task t.

The three variables can be used to estimate the expected processing duration as follows:

µt =(pa t + pm t + pb t)/6

Based on the estimates of the expected processing duration the engineering project lifetime can

be obtained by applying the Critical Path Method with fixed processing times that are equal to

the estimates. Only tasks on the critical path are used to estimates the duration of the entire

project.

This method is better for managing complex dependencies but does not provide the best snapshot

of the overall project progress like Gantt charts. Tasks are shown as a series of nodes and

arrows:

Figure 7 shows an example of a Program Evaluation Review Technique. Dependencies are can

be seen in that Task 1 needs to be complete before commencement of task 2. From this example,

we can see that the Program Evaluation Review Technique is suitable for managing complex

networks.

Figure 7: Program Evaluation and Review Technique

Gantt Chart

Gantt charts are useful in showing the time required for various tasks. They are best at giving an

instantaneous snapshot of the overall progress of the project in relation to all the varied tasks. A

gantt chart is represented as a bar chart with all the tasks listed. Tasks can be grouped together

and listed with all subtasks involved.

Figure 8: Gantt Chart

Gantt charts can also contain dependencies, such as:

Finish to Start: Task t starts after completion of Task s.

Start to Start: Task t starts as soon as Task s commences.

Start to Finish: Task t must complete before Task s starts.

Finish to Finish: Task t must complete before Task s ends.

Percent Complete: Task t can only proceed through a% complete before Task s

is b% complete

Figure 9: Gantt Chart with interdependencies

Quantitative techniques

Quantitative techniques are used in solving engineering scheduling problems that can be

formulated as mathematical algorithms. To understand this technique, knowledge of notations

used in elementary operations research is required.

The most used mathematical technique is the Linear Program. A linear program is an

mathematical solution in which the task and the constraints are linear in the variables to be

determined. This can be expressed as follows:

minimize c1x1+c2x2+···+cnxn

subject to:

a11x1 + a12x2 +···+ a1nxn ≤ b1

a21x1 + a22x2 +···+ a2nxn ≤ b2

.

.

.

am1x1 + am2x2 +···+ amnxn ≤ bm

xt ≥ 0 for t =1,...,n.

The objective of this mathematical method is to minimize costs. c1,...,cn referrs to as the cost

vector. Variables x1,...,xn have to be determined so that the cost function is minimized. The

column vector a1t,...,amt is referred to as activity vector t. The value of the variable xt refers to the

time at which this activity t is performed. The b1,...,bm is referred to as the resource vector. In

linear programming n refers to the number of activities while m refers to the number of

resources.

Qualitative (heuristic) techniques

Some engineering scheduling problems can be formulated as linear programs and are thus

inherently easy. They can be solved readily using existing algorithms. There are however other

engineering scheduling problems that are very difficult. It may not be possible to formulate such

problems as linear programs since there are no simple algorithms that can yield optimal solutions

in a timely manner. Heuristic methods are useful in engineering scheduling such scenarios.

Although heuristic methods do not guarantee optimal solutions, they provide a reasonably good

solution in a relatively short time. Discussed below is a set of simple and basic dispatching rules

that can be applied to different engineering scheduling problems with only minor modifications.

Basic Dispatching Rules

A dispatching rule is a rule that prioritizes all the tasks that are awaiting execution by a set of

resources. Prioritization takes into account the task’s attributes, resources capabilities and

availability. As soon as resource has been freed, the rule selects a task with the highest priority

rating. Dispatching rules can be based on either static or dynamic rules. Static rules are not time

dependent while dynamic rules are time dependent.

Other dispatching rules include:

Service in Random Order.

According to this priority rule, whenever a resource is freed, the next task is selected at random

from those waiting for execution.

Earliest Release Date first.

Just like the First-Come-First-Served rule, the waiting times of the tasks at hand are minimized.

Earliest Due Date first.

Whenever a resource is freed, the task with the earliest due date is selected to be executed next.

This rule minimizes lateness among the tasks waiting for execution.

Minimum Slack first.

This is similar to the Earliest Due Date first rule. If a resource is freed at time t the remaining

slack of each task at that time is computed. The task with the minimum slack is scheduled next.

Longest Processing Time first.

This rule orders tasks in decreasing order of processing duration. This rule evenly distributes the

tasks to the available resources. The reasoning behind this is that it is advantageous in that, the

tasks with shorter processing times are processed last and are easily distributed to balancing the

workload.

Shortest Setup Time first.

Whenever a resource is freed, this rule selects for processing the task with the shortest setup

time.

Least Flexible Job first.

This rule is used when there are resources with varying attributes in parallel and the tasks are

subject to resource capability constraints.

Critical Path.

The Critical Path rule is used with tasks subject to precedence constraints. It chooses the next

task as the one at the start of the longest chain of processing times.

Summary

Planning and scheduling problems in engineering projects have many different aspects. For

instance, scheduling problems are never static in practice since the input data is continually

varying. Some tasks are time dependent and it may turn out that a job that is not important today

suddenly becomes important and very critical the following day. Scheduling objectives vary

depending on the stage of the project execution. It is therefore crucial that these objectives are

balanced carefully so as not to undermine the overall project goal.

Given the varied nature of employee personalities, project planners may have differing opinions

regarding the order of tasks. It is therefore imperative that personnel and scheduling problems

are handled well at the initial stages of the projects or as promptly as they arise. Therefore,

scheduling in engineering projects may have to deal with reactive issues as well as both long

term issues and medium term engineering scheduling issues.

Conclusion

In this study, each staff is assumed to have the same capabilities of doing a tasks assigned to

them. A practical scenario would be that every staff has a subset of skills and two or more

personnel may have overlapping skill sets. In such instances, engineering project scheduling is

complex when there are human resources’ constraints. This is made worse when a random

processing approach is adopted. More studies need to be carried out on human resources’

constrained engineering projects to find out the best way arrive at optimized schedule.