Critical Path Method (CPM)

Critical Path Method (CPM)

Critical Path Method(CPM) is a project management technique that identifies the longest path of tasks in a project ,this longest path determines the project duration.Critical Path Method(CPM) was developed in about 1950 for large, complex industrial projects,construction & IT projects. It is deterministic , that means assumes known task times.Where PERT is Probabilistic CPM is deterministic.CPM mainly focuses on time, not cost (cost can be added).

What are Advantage of Critical Path Method(CPM) 

1) Produced clear project timeline.
2) Helps prioritize important tasks.
3) Improves resource allocation.
4) Supports cost-time trade-offs (crashing).
5) Enhances control on projects.
6) Enhance accountability of teams.

Limitations

1)Assumes fixed activity duration.
2)Less effective with uncertain estimates.
3)Network diagrams may become too complex.
4)Requires frequent updating.
5)Doesn’t directly handle resource constraints.

6)Can give misleading results if inputs are wrong.

7)Time-consuming for very large projects.

Terminology 

• Activities = tasks in a project.
• Events = milestones marking task completion.
• Duration = estimated time to finish a task.
• Dependencies = order in which tasks must be done.
• Network diagram = visual representation of activities.
• Nodes = represent tasks/events.
• Arrows = represent dependencies.
• Path = sequence of activities from start to end.
• Critical path = longest path (in time).
• Non-critical paths = shorter paths with slack.

Here is a simple math on CPM

For A missible projects , here is the breatdown 

Activity A : duration 4, start activity

Activity B : duration 3, depends on A

Activity C : duration 2, depends on A

Activity D : duration 5, depends on B

Activity E : duration 6, depends on C

Activity F : duration 2, depends on D and E (finish activity)

Forward pass — compute ES (Earliest Start) and EF (Earliest Finish)

ES of first activity = 0; 
EF = ES + duration; 
for an activity with multiple predecessors, ES = max(EF of predecessors).

Activity A: ES = 0 → EF = 0 + 4 = 4

Activity B: ES = EF(A) = 4 → EF = 4 + 3 = 7

Activity C: ES = EF(A) = 4 → EF = 4 + 2 = 6

Activity D: ES = EF(B) = 7 → EF = 7 + 5 = 12

Activity E: ES = EF(C) = 6 → EF = 6 + 6 = 12

Activity F: ES = max(EF(D), EF(E)) = max(12,12) = 12 → EF = 12 + 2 = 14

Project duration = EF(F) = 14 time units

Backward pass — compute LF (Latest Finish) and LS (Latest Start)

 LF of final activity = project duration; 

 LS = LF − duration; for predecessors, LF = min(LS of successors).

F: LF = 14 → LS = 14 − 2 = 12

Activity D: successor is F (LS_F = 12) → LF_D = 12 → LS_D = 12 − 5 = 7

Activity E: successor is F (LS_F = 12) → LF_E = 12 → LS_E = 12 − 6 = 6

Activity B: successor is D (LS_D = 7) → LF_B = 7 → LS_B = 7 − 3 = 4

Activity C: successor is E (LS_E = 6) → LF_C = 6 → LS_C = 6 − 2 = 4

Activity A: successors B and C have LS 4 and 4 → LF_A = min(4,4) = 4 → LS_A = 4 − 4 = 0

Slack

Activity	Dur	ES	EF	LS	LF	Float
A	4	0	4	0	4	0
B	3	4	7	4	7	0
C	2	4	6	4	6	0
D	5	7	12	7	12	0
E	6	6	12	6	12	0
F	2	12	14	12	14	0

Critical path(s)

Path 1: A → B → D → F (4 + 3 + 5 + 2 = 14)

Path 2: A → C → E → F (4 + 2 + 6 + 2 = 14)

                                                                    By:Ayan Banerjee

PERT Chart : Program Evaluation and Review Technique

PERT Chart : Program Evaluation and Review Technique

Full form of PERT Chart is "Program Evaluation and Review Technique" ,It is a project management tool.PERT chart is used to plan, schedule, and control complex projects.it was developed in the late 1950s byU.S. Navy during Polaris missile project.

PERT Chart is an event-oriented chart ,it focus on Focuses on events,it represents project activities visually.

    1) Each activity is shown as an arrow.
    2) Each event is shown as a node.
    3) Nodes represent the start or completion of activities.

    4) Identifies dependencies between tasks.

    5) Estimates minimum project completion time.

    6) PERT Chart is useful for projects with uncertainty and helps in decision-making.

    7) PERT Chart emphasizes on time , while CPM emphasizes cost.

    8) PERT Chart is read from left to right.

    9) PERT Chart arrows indicate task order.

    10) PERT Chart events are represented by circles/ellipses.

    11) Suitable for R&D projects.Identifies dependencies between tasks.

Time Estimation in PERT Chart

PERT Chart uses three time estimates Optimistic time (O),Pessimistic time (P) ,Most likely time (M).

Expected time (TE) = (O + 4M + P) ÷ 6.

This formula reduces bias and gives weighted average when accounts for uncertainty (For R&D Projects).This makes estimation more realistic and can work wide ranges projects have higher risk.This identify probable completion time and Standard deviation is used for analysis.

Variance (σ²) = [(P – O) ÷ 6]².

Standard deviation (σ) = (P – O) ÷ 6.

Project variance = sum of variances on critical path.

Probability of completion can be calculated.
Formula: 

Z = (Due Date – TE Project) ÷ σ

Higher Z = higher probability
Lower Z = lower probability

By PERT Chart 

• Risk analysis becomes possible.

• Helps avoid unrealistic scheduling.

• Improves confidence in planning.

• Saves time and cost indirectly.

• Brings accuracy in complex projects.

How To Create  PERT Chart 

• Identify all activities of the project.
• Define dependencies between activities.
• List immediate predecessors.
• Draw network diagram.
• Place events (nodes) in correct order.
• Represent activities with arrows.
• Ensure logical sequence.
• Assign time estimates (O, M, P).
• Calculate expected time (TE).
• Identify critical path.
• Critical path = longest path in the network.
• Calculate earliest start (ES) for each activity.
• ES = earliest time an activity can begin.
• Calculate earliest finish (EF).
• EF = ES + activity time.
• Calculate latest finish (LF).
• LF = latest time an activity can finish without delay.
• Calculate latest start (LS).
• LS = LF – activity time.
• Find total float (slack).
• Float = LS – ES (or LF – EF).
• Zero float = critical activity.
• Positive float = non-critical activity.
• Negative float = project delay risk.
• Mark the critical path.
• Check project duration.
• Analyze variances and risk.
• Recheck logical sequence. 

An Example of PERT Chart 

Here is an example of Work - brakdown and how task is dependent on one another .

Activity	Duration	Predecessor(s)
A	3 days	–
B	6 days	A
C	2 days	A
D	5 days	B, C
E	4 days	C
F	3 days	E
G	6 days	D, F
H	5 days	G

Predecessor  menaing one task is dependent on another task , that means (B, C) , C will starts after B finished

Forward Pass (Earliest Times)

A: ES=0 → EF=3

B: ES=3 (after A) → EF=9

C: ES=3 (after A) → EF=5

D: ES=max(EF(B), EF(C))=max(9,5)=9 → EF=14

E: ES=5 (after C) → EF=9

F: ES=9 (after E) → EF=12

G: ES=max(EF(D), EF(F))=max(14,12)=14 → EF=20

H: ES=20 (after G) → EF=25

Project Duration = 25 days (Project will finish in 25 days minimum)

Backward Pass (Latest Times)

Start from project completion at 25:

H: LF=25 → LS=20

G: LF=20 → LS=14

D: LF=14 → LS=9

F: LF=14 → LS=11

E: LF=11 → LS=7

C: LF=min(9 (D), 7 (E))=7 → LS=5

B: LF=9 → LS=3

A: LF=min(3 (B), 5 (C))=3 → LS=0

Slack Calculation : Slack = LS – ES (or LF – EF)

Activity	ES	EF	LS	LF	Slack
A	0	3	0	3	0
B	3	9	3	9	0
C	3	5	5	7	2
D	9	14	9	14	0
E	5	9	7	11	2
F	9	12	11	14	2
G	14	20	14	20	0
H	20	25	20	25	0

Critical Path :A → B → D → G → H

Project Duration = 25 days

By :Ayan Banerjee 

asdgjasghdjagsdjhas

askjdhaskdh

asdasddERT Chart sadasd

Economic and Non-economic factors impacting Entrepreneurship

Economic and Non-economic factors impacting Entrepreneurship 

        Entrepreneurship is an zeal to do something new , entrepreneurship is an idea and innovation to do a business in a new way or introduce a new product and business idea in the market. Entrepreneurship process the three stage designing, launching, and running a new business.Most of the entrepreneurship start with small one that slowly grows and get a high economic growth that make in huge Employment generation. Various factor that affect the entrepreneurship for developing affective policy and various support systems. The main influence factor are Economical factor and Non-economical factor 

Economical factor related to money, finance, infrastructure, and market condition. 

Non-Economical factors are  social and environmental education , social status, economical factor refer to the major microeconomics condition that affect the feasibility and profitability of the starting business. This include capital availability for starting business infrastructure , market ,condition and physical policy , labor availability for entrepreneurship. 

Economical factor 

Finance is essential for entrepreneurship or set up a new business , sustainable  finance condition is required to become an entrepreneur, this may come from various source like personal savings , bank loan, venture capital, investors sometime Government support also help for set up a new business infrastructure.

Infrastructure is the next important for new small business , this includes transportation network , communication system , power supply ,waters and sanitation, market accessibility, import export farm.High is this factor , more favorable for a new business 

Market condition ,demand and supply of the goods must balance competition level of the product , consumer behavior and consumer awareness ,awareness program of the particular product. Size of the market an very important factor for entrepreneurship, because a big market can help a new entrepreneur to introduce a new product, entry level  should be low and customer must be aware of the product with various kind of advertisement, online ,offline, electronic media.

Fiscal policy is an another important point for entrepreneurship , subsidies and investment incentives ,import export duties are the factor for entrepreneurship growth.

Availability of skill labor is another important factor of entrepreneurship.Human capital play a vital role for any industry , the availability of educated and skill labor effect the industry health and overall labor policy and productivity of a industry. Educated and skill labor reduce skills shortage problem and the problem of high labor cost and operational efficiency.

Economic stability is another important for set up a new business , inflammation  currency stability , interest rate and political stability of is also play crucial role for entrepreneurship. If currency is not stable and country political stability is affected small business.

Cost of inputs & resources is another factor , this includes  raw materials, energy, land, and labour.high input costs reduce margins and increase pricing risk, that leads  frequent price spikes, supply bottlenecks, seasonal shortages, relocation of production to cheaper regions.

Non-Economical factors 

Technology Advancement is also a part of entrepreneurship factor, Technology cal advancement create new industries and improve productivity, create new opportunity and reduce human effort . RND infrastructure Availability of skill labor is another important part of entrepreneurship. 

Education is an tool to build knowledge ,education build  skill and behavior of the community , it create critical thinking ,financial literacy ,exposure to entrepreneurship and Tec-savy man forece.

Social and Cultural norms are also a part of the factor , risk-taking is the main mindset for Entrepreneurship , accepting of failure , face controversies,  adverse society an accept the growth of large factor for entrepreneurship. Family and community support is also a factor .Family may support to set up a new business ,  emotional encouragement , community network and strong social support system also encourage entrepreneurship.

Legal Framework is also a factor for entrepreneurship , easy of legalization of business ,contract enforcement ,corruption free society ,supportive regulated authority is the key factor for growth of entrepreneurship.

Media plays a transformative role in shaping the mindset of society, especially among the youth. 

       1)Documentaries and Films :Media can create documentaries and highlight the struggles, failures of entrepreneurs.They provide authentic path into the entrepreneurial journey, making it relatable for viewers.

      2)Biographical books and media features on successful entrepreneurs give detailed accounts of how ordinary individuals achieved extraordinary results.

      3)Television, radio, podcasts, and YouTube interviews with entrepreneurs provide a knowledge about a motivational entrepreneurs.It also provides practical tips on finance, market entry, product development, and scaling.

       4)Creating Awareness Among the Youth ,Media campaigns can target young audiences to showcase entrepreneurship not just as a profession, but as a way to contribute to national development.

Cultural Attitudes Toward Failure & Risk is an important factor for developing entrepreneurship . In a society where failure is criticized may discourage entrepreneurship . Risk taking attitute  differs by  society to society and their norms while  starting small and waiting for safe stability.

Gender & Social Equity is a great factor for developing entrepreneurship , both man and woman must have equal right and dignity , barriers to women entrepreneurs face access to financing, social norms, childcare responsibilities.

Behavior of competitors & market structure also effecttive facor developing entreprneurship .Degree of competition, dominance by large firms, informal/unfair competition, collusion is highly effective mater, monopoy business  or high pricing can raise entry barriers , informal competitors able to avoid taxes can undercut formal firms , that creates  price wars, dominant platform fees, many small vendors operating informally.

 

By :Ayan Banerjee