Sequencing in Network Diagram: Meaning, Steps and Example
Introduction —
Sequencing is an important step in developing a project network. Sequencing in a network diagram means deciding the order in which project activities must be performed and identifying which activities depend on others. It helps us decide which activity should be performed first, which activities can be performed at the same time, and which activities must wait for other activities to finish.
In simple words, sequencing means arranging project activities according to their logical order. A correct sequence is essential because the subsequent calculations of a network, such as activity times, critical path and project duration, depend on the network being correctly constructed.
What is Sequencing in a Network Diagram?
Sequencing in a network diagram means determining the order and precedence relationships among the activities of a project.
Hence, the first step in the project scheduling process (network development) is to identify all of the specific activities that include the project and their interdependence relationships.
For every activity, we need to know what must happen before it can start. Some activities may have to wait for one or more preceding activities, while others may be performed concurrently.
For example, suppose a project has three activities:
- A: Collect raw material
- B: Process the raw material
- C: Prepare tools
Activity B cannot begin until Activity A is completed. However, Activity C may be performed independently of Activity A and B.
Therefore,
A → B
while C may run concurrently with A.
This simple idea forms the basis of sequencing in a project network.
Questions to Consider While Sequencing Activities
Before drawing a network diagram, the following questions should be considered for each activity:
- Which activity or activities must precede it?
- Which activities can be performed concurrently?
- Which activity or activities follow it?
- What controls the start and finish of an activity?
Answering these questions helps us establish the correct precedence relationships between activities. Because all subsequent calculations are based on the network, it is important that the network be carefully drawn. A network can be drawn in many ways.
Why is Correct Sequencing Important?
A network diagram is not simply a drawing of activities. It represents the logical relationships among them.
If an activity is placed incorrectly, the entire network may give incorrect results. Since subsequent network calculations are based on the relationships shown in the network, the network should be constructed carefully.
Correct sequencing helps to:
- represent the actual order of activities;
- identify activities that can run concurrently;
- identify activities that depend on other activities;
- determine the possible paths through the project;
- perform PERT/CPM calculations correctly;
- identify the critical path and project completion time.
Basic Steps in Network Development
The following steps can be used to develop a project network:
Step 1: List all project activities
First, identify all the major activities involved in completing the project.
Step 2: Identify predecessor activities
For each activity, determine which activities must be completed before it can begin.
Step 3: Identify concurrent activities
Determine which activities can be performed independently at the same time.
Step 4: Establish the precedence relationships
Arrange the activities according to their logical dependencies.
Step 5: Draw the network
Represent the established relationships using the appropriate network notation.
Step 6: Check the network
Finally, check whether every activity has been placed correctly and whether all required precedence relationships are represented.
Example of Sequencing in Network Diagram: Paneer Preparation
Let us understand sequencing with a simple example of Paneer (Cottage Cheese) preparation. The basic steps required in drawing a network are illustrated in the following example of Paneer preparation.
Example 1: The following list represents the major activities involved in the preparation of Paneer (Cottage Cheese):
- Receive whole cow/buffalo milk
- To get the level of fat percentage you want, standardize the milk
- Prepare a 1 percent solution of citric acid.
- Heat the citric acid to 70 degrees Celsius.
- Bring the standardized milk to boil on medium heat
- Cool the milk to 70 degrees Celsius and slowly add the citric acid solution until yellowish whey separates.
- Using a clean muslin cloth, strain the mixture.
- Hold it under running water for a minute, then squeeze out any excess water.
- Hang the muslin for 15-20 minutes to drain all of the whey.
- Prepare the mould for making the Paneer block.
- Fill the block with the mass and tie the muslin.
- Place it under a heavy object for up to two hours.
- Paneer should be cut into chunks and used as needed.
STEP 1: First make the list of Activities
| Activity | Description |
|---|---|
| A | Receive whole cow/buffalo milk |
| B | Standardize the milk to the required fat percentage |
| C | Prepare a 1% citric acid solution |
| D | Heat the citric acid solution to about 70°C |
| E | Bring the standardized milk to a boil |
| F | Cool the milk to about 70°C and add the citric acid solution until whey separates |
| G | Strain the mixture using a clean muslin cloth |
| H | Hold it under running water and squeeze out excess water |
| I | Hang the muslin cloth to drain the remaining whey |
| J | Prepare the mould for the Paneer block |
| K | Fill the mould with the Paneer mass and tie the muslin |
| L | Place it under a heavy object for pressing |
| M | Cut the Paneer into pieces |
STEP 2: The next step is to determine the immediate predecessor of each activity.
A precedence table can be formed based on the above list of different activities, as shown in Table:
Precedence Table for Paneer Preparation:
| Activity | Description | Immediate Predecessor |
|---|---|---|
| A | Receive milk | — |
| B | Standardize milk | A |
| C | Prepare citric acid solution | — |
| D | Heat citric acid solution | C |
| E | Boil standardized milk | B |
| F | Cool milk and add citric acid | D, E |
| G | Strain the mixture | F |
| H | Wash and squeeze the mixture | G |
| I | Drain the remaining whey | H |
| J | Prepare the mould | H* |
| K | Fill the mould and tie the muslin | J |
| L | Press the Paneer mass | K |
| M | Cut the Paneer | L |
Note: The exact precedence assigned to an activity depends on the assumptions of the problem. In a real Paneer-making process, mould preparation may be possible while whey is draining. Therefore, when solving an examination problem, always follow the precedence relationships specified in the question.
Understanding the Precedence Relationships
The table becomes much easier to understand if we examine the activities step by step.
◾Activities A and C can start independently
Activity A is: Receive milk
Activity C is: Prepare citric acid solution
Neither A nor C has a predecessor. Therefore, both activities can start independently.
They may proceed concurrently.
◾Activity B follows Activity A
The milk must first be received before it can be standardized. Therefore:
A → B
◾Activity D follows Activity C
The citric acid solution must first be prepared before it can be heated. Therefore:
C → D
◾Activity E follows Activity B
The standardized milk is then brought to a boil. Therefore:
B → E
◾Activity F requires both D and E
This is an important precedence relationship in the example.
Before Activity F can begin:
- the citric acid solution must have been heated — D;
- the standardized milk must have been boiled — E.
Therefore, both activities are predecessors of F:
D + E → F
Activity F can begin only after both D and E have been completed.
◾Activity G follows Activity F
After the milk has been treated with the citric acid solution and whey has separated, the mixture is strained.
Therefore:
F → G
◾Activity H follows Activity G
After straining, the material is held under running water and excess water is squeezed out. Therefore:
G → H
◾Activities I and J
After H, the whey can be allowed to drain from the muslin cloth, represented by Activity I.
The mould preparation is represented by Activity J according to the precedence assumption used in this example.
These relationships should always be checked against the assumptions given in the particular network problem.
◾Activities K, L and M
Once the mould is ready, the Paneer mass is filled into it and the muslin is tied. Therefore:
J → K
The filled mould is then placed under a heavy object for pressing:
K → L
Finally, the pressed Paneer is cut into pieces:
L → M
Thus, the final sequence is:
J → K → L → M
Simplified Flow of the Example
The main relationships can be understood as:
A → B → E
and
C → D
Then both branches meet:
D + E → F → G → H
After that, the remaining activities continue according to their specified precedence relationships.
This illustrates an important feature of network sequencing: different activities may start independently, several activities may proceed concurrently, and their paths may later merge when a succeeding activity requires all relevant predecessors to be completed.
The precedings of an activity have been given due consideration in the above table. Other factors will be considered while drawing the network.
Draw the Network Diagram for this example
In above tables and explanation, we see that, there is no preceding activity for activity A, which is represented by an arrow line (see figure).
Similarly, activity C has no preceding activity, and both activities A and C can be completed concurrently, so they are displayed as concurrent activities. Activities A and C come before activities B and D, respectively.
The following figure depicts the complete network:
Concurrent Activities in a Network
Two or more activities are called concurrent activities when they can be performed independently during the same period.
In the above example:
- A: Receive milk
- C: Prepare citric acid solution
Both have no predecessor in the example. Therefore, they can be started independently.
Concurrency is important in project scheduling because performing independent activities at the same time can reduce the overall project duration.
However, activities should be shown as concurrent only when the precedence relationships allow them to be performed independently.
Predecessor and Successor Activities
These two terms are important for examinations.
➡️ Predecessor Activity
A predecessor activity is an activity that must be completed before another activity can begin. For example:
A → B
Here, A is the predecessor of B.
➡️ Successor Activity
A successor activity is an activity that follows another activity in the logical sequence. For example:
A → B
B is the successor of A.
Easy way to remember
Predecessor = comes before
Successor = comes after
Network Representation
Once the precedence relationships have been identified, the activities can be represented in a project network.
Different network conventions exist. In an Activity-on-Arrow (AOA) representation, activities are shown by arrows and events are represented by nodes. In an Activity-on-Node (AON) representation, activities are generally shown in nodes.
Therefore, the notation used should be identified before interpreting or drawing a network diagram.
The most important point is that the network must correctly represent the logical precedence relationships among the project activities.
Common Mistakes in Sequencing a Network
Students often make the following mistakes while constructing a network:
1. Ignoring predecessor relationships
An activity should not be shown as starting before all of its required predecessors have been completed.
2. Treating every activity as sequential
Not every project activity has to be performed one after another. Independent activities may run concurrently.
3. Missing a predecessor
If an activity requires two previous activities but only one is shown, the network may give incorrect results.
For example:
D + E → F
must not be incorrectly represented as only:
E → F
4. Creating an unnecessary dependency
An activity should not be made dependent on another activity unless the problem requires that relationship.
5. Drawing the network before preparing the precedence relationships
It is generally easier and safer to identify the predecessor relationships first and then draw the network.
Key Points to Remember
- Sequencing determines the logical order of project activities.
- A predecessor activity must be completed before its dependent activity can begin.
- Activities with no required predecessor may start independently.
- Independent activities may run concurrently.
- An activity with multiple predecessors can begin only after all required predecessors have been completed.
- A precedence table is useful before drawing the network.
- The network should accurately represent all logical relationships.
- Correct sequencing is essential for subsequent PERT/CPM calculations.
Frequently Asked Questions
Q. What is sequencing in a network diagram?
Sequencing is the process of determining the logical order and precedence relationships among project activities before constructing the network diagram.
Q. What is a predecessor activity?
A predecessor activity is an activity that must be completed before another activity can start.
Q. What are concurrent activities?
Concurrent activities are activities that can be performed independently during the same period because neither activity has to wait for the other.
Q. Why is sequencing important in network analysis?
Sequencing is important because the network represents the logical relationships among activities. Incorrect relationships can lead to incorrect project scheduling and network calculations.
Q. What is a precedence table?
A precedence table lists the project activities and identifies the activity or activities that must be completed before each activity can begin.
Q. Can two activities be performed at the same time?
Yes. If two activities are independent and neither depends on the completion of the other, they may be performed concurrently.
Conclusion
Sequencing is one of the basic steps in developing a project network. The main purpose is to establish which activities come before, which activities follow, and which activities can proceed concurrently.
A simple way to approach any sequencing problem is:
List activities → Identify predecessors → Identify concurrent activities → Establish precedence relationships → Draw the network → Check the network
Once these relationships are correctly established, the network can be used for further project scheduling analysis such as PERT and CPM.
References
- Hamdy A. Taha, Operations Research: An Introduction, 10th Edition, Pearson.
- Frederick S. Hillier and Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill Education.
- J. K. Sharma, Operations Research: Theory and Applications, Macmillan India.
- Kanti Swarup, P. K. Gupta and Man Mohan, Operations Research, Sultan Chand & Sons.
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