5001 Industrial Management and safety Module 3 note

1. Module 3
Project management techniques and
quantitative techniques in
management

2. Network analysis
• Critical path method
• Program Evaluation and Review Technique
(PERT)

3. Critical path method
• The critical path method is a technique that
allows you to identify tasks that are necessary
for project completion.
• The critical path in project management is the
longest sequence of activities that must be
finished on time to complete the entire
project.

4. • A technique where you identify tasks that are
necessary for project completion and determine
scheduling flexibilities.
• Critical path in project management is the longest
sequence of activities that must be finished on time in
order for the entire project to be complete.
• Any delays in critical tasks will delay the whole project.

5. Why use critical path analysis?
• CPA can provide valuable insight on how to
plan projects, allocate resources, pace
towards milestones, and schedule tasks.

6. • Here are some reasons why you should use
the critical path method:
• Improves future planning: CPM can be used
to compare expectations with actual progress.
• The data used from current projects can
inform future project plans.

7. • Facilitates more effective resource
management: CPM helps project managers
prioritize tasks, giving them a better idea of
how to avoid resource constraints.

8. • Helps avoid bottlenecks: Bottlenecks in
projects can result in lost valuable time.
• Plotting out project dependencies using a
network diagram will give you a better idea of
which activities can and can’t run in parallel,
allowing you to schedule work accordingly.

9. How to find a project's critical path
• Finding the critical path involves identifying
the longest path between the start and end of
the project by comparing the duration of
critical and non-critical tasks.

10. 1. List activities
• Use a work breakdown structure to list all the
project activities or tasks required to produce
the deliverables.
• The list of activities in the work breakdown
structure serves as the foundation for the rest
of the CPM.

11. • Use a to list all the project activities or tasks
required to produce the deliverables.
• The list of activities in the work breakdown
structure serves as the foundation for the rest
of the CPM.

13. • For example, let’s say the marketing team is producing a new
interactive blog post.
• Here are some tasks that might be in the work breakdown
structure:

15. • Once you have a high-level idea of everything
that needs to be done, you can start
identifying task dependencies for the whole
project.

16. 2. Identify dependencies
• Based on your work breakdown structure,
determine the tasks that are dependent on
one another.
• This will also help you identify any work that
can be done in parallel with other tasks.

17. • Here are the task dependencies based on the example above:
• Task B is dependent on A
• Task C is dependent on B
• Tasks C and D can run in parallel
• Task E is dependent on D
• Task F is dependent on C, D, and E
• The list of dependent tasks is referred to as an activity sequence, which will
be used to determine the critical path.

18. 3. Create a network diagram
• The next step is to turn the work breakdown structure into a network
diagram, which is a flowchart displaying the chronology of critical path
activities.
• Create a box for each task and use arrows to depict task dependencies.
• You’ll add other time-bound components to the network diagram until you
have the general project schedule figured out.

20. 4. Estimate task duration
• To calculate the critical path, the longest sequence of
tasks, you first need to estimate the duration of each
activity.
• To estimate the duration, try:
– Making educated guesses based on experience and knowledge
– Estimating based on previous project data
– Estimating based on industry standards

21. • Alternatively, try using the forward pass and backward pass technique:
• Forward pass: This is used to calculate earliest start time (ES) and earliest finish
time (EF) by using a previously specified start date.
• ES is the highest EF value from immediate predecessors, whereas EF is ES +
duration.
• The calculation starts with 0 at the ES of the first activity and proceeds through
the schedule.
• Determining ES and EF dates allows for early allocation of resources to the project.

22. 5. Calculate the critical path
• Steps to calculate the critical path
• Step 1: Write down the start and end time next to each
sequence of activities to calculate the sequence's "duration."
– Find the start time of the first activity in the sequence
– Find the end time of the last activity in the sequence
– The duration is the end time of the last activity minus the start
time of the first activity

23. • Step 2: Determine the number of dependencies along each
sequence.
• Step 3: The sequence of activities with the longest duration (end of
sequence date - beginning of sequence date) is the critical path.
• If multiple sequences of activities have the same duration, the
sequence with the greater number of dependencies is the critical
path.

24. 6. Calculate the float
• Float, or slack, refers to the amount of flexibility of a
given task.
• It indicates how much the task can be delayed without
impacting subsequent tasks or the project end date.
• Finding the float is useful in gauging how much flexibility
the project has. Float is a resource that should be used to
cover project risks or unexpected issues that come up.

27. • A project has 9 activities. The expected time of
each activity is as shown below.

28. – Draw the project network
– Identify the critical path
– Find project duration
•

30. • Project duration is 33 weeks
• Critical path is 1-3-4-6-7

33. Project Evaluation Review Technique (PERT)
• Project Evaluation Review Technique, or PERT, is used to
identify the time it takes to finish a particular task or
activity.
• It is a system that helps in the proper scheduling and
coordination of all tasks throughout a project.
• It also helps in keeping track of the progress, or lack
thereof, of the overall project.

34. • In the 1950s, the Project Evaluation Review
Technique was developed by the US Navy to
manage the Polaris submarine missile
program of their Special Projects Office.

36. Creating a PERT Chart
• A flowchart is used to depict the Project Evaluation
Review Technique.
• Nodes represent the events, indicating the start or end
of activities or tasks.
• The directorial lines indicate the tasks that need to be
completed, and the arrows show the sequence of the
activities.

37. Definitions of time used to estimate project
time requirements
• Optimistic time – The least amount of time it can take to complete a
task
• Pessimistic time – The maximum amount of time it should take to
complete a task
• Most likely time – Assuming there are no problems, the best or most
reasonable estimate of how long it should take to complete a task.
• Expected time – Assuming there are problems, the best estimate of
how much time will be required to complete a task.

38. Here are several terms used in a PERT chart:
• Float/Slack – Refers to the amount of time a task can be
delayed without resulting in an overall delay in completion
of other tasks or the project
• Critical Path – Indicates the longest possible continuous
path from the start to the end of a task or event
• Critical Path Activity – Refers to an activity without any slack

39. • Lead Time – Refers to the amount of time needed to finish a
task without affecting subsequent tasks
• Lag Time – The earliest time by which a successor event/task
can follow a prior event/task
• Fast Tracking – Refers to handling tasks or activities in parallel
• Crashing Critical Path – Shortening the amount of time to do
a critical task

40. To implement a PERT chart:
• Identify the different tasks needed to complete a
project. Make sure to add these in the right order
and indicate the duration of each task.
• Create a network diagram. Use arrows to represent
the activities and use nodes as milestones.
• Determine the critical path and possible slack.

41. Advantages of PERT
• It helps maximize the use of resources.
• It makes project planning more manageable.
• It’s useful even if there is little or no previous
schedule data.
• It enables project managers to better estimate or
determine a more definite completion date.

42. Disadvantages of PERT
• In complex projects, many find PERT hard to interpret, so they may
also use a Gantt chart, another popular method for project
management.
• It can be tedious to update, modify, and maintain the PERT
diagram.
• It entails a subjective time analysis of activities and, for those who
are less experienced or are biased, this may affect the project’s
schedule.

43. How to Make a PERT Chart
– 1. Break Down Your Project Scope
• Begin by identifying the project milestones and then
identify the individual tasks required to achieve them.
• Then, figure out the sequence of your project tasks and
their dependencies.

44. • 2. Create Your PERT Chart
– Now that you have the information that you need,
you can now make the PERT diagram.

45. • 3. Estimate Your Project Duration
– Now that you have drafted a PERT diagram and
added task details, it’s time to add the estimated
durations of all tasks to create a project schedule.
– If you’re drawing your PERT diagram, you’ll use
the PERT chart formula to do so.

46. • 4. Find the Critical Path & Slack
– While CPM and PERT are two different methods,
once you have a PERT chart that has your project
tasks, their durations and due dates, you can
calculate the critical path and identify any possible
slack.

47. PERT Chart Example

49. • Now, let’s draw the network diagram.
• We can see that activities A, B, and C don’t have any
immediate predecessors.
• This means that we can draw individual arcs to each of them.
• Let’s draw the nodes for the first activity, activity A.
• We can see that activity A acts as the immediate predecessor
for the activity D.

51. • activities B and C don’t have any immediate
predecessors

52. • look at activity D. This activity is the
immediate predecessor for activity A. This
means that we can directly draw an arc from
node 2.

53. • looking at activity E, it acts as the immediate
predecessor to activity H along with activity F.

54. • for activity F. If we have a look at the table, we
can see that a combination of the activities E
and F act as immediate predecessors for
activity H.

55. • Let’s have a look at activity G. It is immediately
preceded by activity C, and acts as an
immediate predecessor for activity J, along
with activity H.

56. • For activity H, we can see that it and G act as
immediate predecessors for activity J.

57. • finally, we activities I and J. These activities
don’t act as immediate predecessors for any
other activity.

58. Linear programming (LP)
• Linear programming (LP) is a mathematical
technique used in management to optimize
resource allocation and decision-making
processes.

59. Definition
• Linear Programming is a method for achieving the
best outcome (such as maximum profit or minimum
cost) in a mathematical model whose requirements
are represented by linear relationships.
• The goal is to determine the optimal way to allocate
limited resources.

60. Key Components
• Objective Function: This is the function that needs to be
optimized. For instance, maximizing profit or minimizing costs.
• Decision Variables: These are the variables that decision-
makers will decide the values of, such as the quantity of
products to produce or the number of workers to hire.

61. • Constraints: These are the restrictions or limitations on resources,
such as budget limits, resource availability, or time constraints.
Constraints are usually linear equations or inequalities.
• Non-negativity Constraints: These ensure that the decision
variables cannot take negative values, reflecting practical
constraints like not being able to produce a negative number of
products.

62. Applications
• Resource Allocation: Linear programming helps in determining the most efficient
way to allocate resources among various projects or departments to achieve
maximum profitability or efficiency.
• Production Planning: It assists in deciding the optimal quantity of each product
to manufacture to maximize profit while considering constraints like labor,
materials, and machine time.
• Scheduling: LP can be used to develop schedules that optimize the use of
resources, such as workforce scheduling, production schedules, or delivery
schedules.

63. • Financial Management: It helps in optimizing investment portfolios or
managing budgets by finding the best mix of assets or expenditures to
achieve financial goals.
• Supply Chain Management: LP is used to optimize logistics, such as
minimizing transportation costs, managing inventory levels, or balancing
supply and demand.
• Marketing and Sales: It can help in setting sales targets, determining the
optimal distribution of marketing resources, or deciding on pricing strategies.

64. • LP problems can be solved using various methods, such as:
• Graphical Method: Useful for problems with two decision variables. The
feasible region is graphed, and the optimal solution is found at the
vertices of the feasible region.
• Simplex Method: A widely used algorithm for solving LP problems,
especially for problems with more than two variables.
• Interior Point Methods: Another approach used for larger problems,
providing an efficient way to find the optimal solution.

65. Transportation problem
• The transportation problem is a type of linear
programming problem used to determine the most
cost-effective way to transport goods from multiple
suppliers to multiple consumers.
• The objective is to minimize the total transportation
cost while satisfying supply and demand constraints.

66. Definition
• Transportation Problem: It involves finding the
optimal distribution plan that minimizes the
total transportation cost of shipping goods
from a set of suppliers (or sources) to a set of
consumers (or destinations), given the supply
and demand constraints.

67. Key Components
• Suppliers: Entities that provide goods. Each
supplier has a certain supply capacity.
• Consumers: Entities that receive goods. Each
consumer has a certain demand that needs to
be fulfilled.
• Cost Matrix: A matrix representing the cost of
transporting one unit of goods from each
supplier to each consumer.

68. • Supply Constraints: Each supplier's total
shipment must not exceed its supply capacity.
• Demand Constraints: Each consumer’s total
receipt must meet its demand exactly.

69. Special Cases
• Balanced Transportation Problem: If the total
supply equals the total demand, the problem
is balanced.
• In this case, every unit of supply is exactly
used to meet demand.

70. • Unbalanced Transportation Problem: If the
total supply does not equal total demand,
dummy suppliers or consumers are introduced
to balance the problem.
• Dummy suppliers have zero costs and supply,
while dummy consumers have zero demand.

71. Benefits
• Cost Efficiency: Helps in minimizing transportation
costs, leading to significant savings.
• Optimal Allocation: Ensures that supply meets
demand in the most economical way.
• Scalability: Can be adapted to various sizes and
complexities of transportation networks.

72. Limitations
• Linear Assumptions: Assumes linear costs and
constraints, which may not capture all real-
world scenarios.
• Complexity in Large Problems: Solving large-
scale transportation problems can be
computationally intensive.