IIM Sambalpur Term V: Project Management Session 2 PDF

25-09-2024 Term V: Project Management Session 2: Organization Strategy and Project Selection Prof. Rohit Gupta Operations Management Area Email: [email protected] 1...

25-09-2024 Term V: Project Management Session 2: Organization Strategy and Project Selection Prof. Rohit Gupta Operations Management Area Email: [email protected] 1 Where We Are Now 2 1  25-09-2024 Why Project Managers Need to Understand Strategy  To make appropriate decisions and adjustments How a project manager would respond to a suggestion to modify the design of a product or to delays may vary depending upon strategic concerns.  They can be effective project advocates. They must be able to:  Demonstrate to senior management how their project contributes to the firm’s mission in order to garner the continued support of management.  Explain to stakeholders why certain project objectives and priorities are critical in order to secure buy-in.  Explain why the project is important to motivate and empower the project team. 3 Why Project Managers Need to Understand Strategy Alignment with Organizational Goals  Purpose: Every project is initiated to serve a larger organizational objective. By understanding the strategy, project managers ensure that their projects are aligned with the company’s mission, vision, and long-term goals.  Example: If a company’s strategic goal is to become a leader in sustainability, project managers must prioritize eco-friendly practices in project planning and execution. Prioritization of Projects  Purpose: Organizations often juggle multiple projects. A strategic understanding allows project managers to prioritize their projects based on how much they contribute to the organization’s overall objectives.  Example: A project that directly contributes to increasing market share may be prioritized over a less impactful one. Improved Decision-Making  Purpose: Understanding the bigger picture enables project managers to make better decisions, especially when projects face challenges. It helps them make trade-offs between cost, time, and scope that align with strategic objectives.  Example: A project manager might decide to extend a deadline if the project delivers a strategic competitive advantage even if it incurs higher costs. 4 2  25-09-2024 Cont… Effective Resource Allocation  Purpose: Strategy helps project managers allocate resources like time, budget, and personnel more effectively. Resources should be directed toward projects that have the highest potential for strategic impact.  Example: A company focused on digital transformation would allocate more resources to technology projects that align with its digital strategy. Risk Management  Purpose: Understanding strategy allows project managers to better anticipate and manage risks that could impact the company’s long-term goals. This ensures that risk management strategies are aligned with strategic imperatives.  Example: A project that risks violating data privacy regulations may have greater strategic importance in a company that values customer trust. Adaptability to Change  Purpose: As strategies evolve due to market or internal factors, project managers need to adapt their projects accordingly. By being aware of strategic changes, they can pivot quickly and realign their efforts.  Example: If a company shifts its strategy from growth to cost-saving, project managers may need to adjust project scopes to focus on efficiency rather than expansion. 5 The Need for a Project Priority System A Project Priority System is crucial for organizations that manage multiple projects simultaneously. Here are some key reasons why such a system is necessary: 1. Resource Allocation Resources like time, budget, and manpower, are often limited. A priority system helps allocate these resources to the most critical projects, ensuring that high-impact projects receive the attention and resources they need to succeed. 2. Strategic Alignment Not all projects contribute equally to an organization's strategic goals. A priority system ensures that projects are aligned with the organization's strategic objectives and focusing efforts on initiatives that drive the most value. 3. Risk Management A priority system helps identify and address risks early by highlighting which projects are critical and need closer monitoring. This proactive approach can mitigate potential risks before they become major issues. 4. Improved Decision-Making When faced with multiple projects, decision-makers need a clear framework to evaluate which projects should proceed, be delayed, or canceled. A priority system provides a structured approach for making these decisions based on predefined criteria. 6 3  25-09-2024 Cont… 5. Maximizing ROI Prioritizing projects allows organizations to focus on those with the highest potential return on investment. This strategic focus ensures that resources are spent on initiatives that deliver the most significant benefits. 6. Enhanced Communication and Transparency A well-defined priority system fosters clear communication about why certain projects are prioritized over others. It helps stakeholders understand the rationale behind project selection and resource allocation decisions. 7. Managing Conflicting Demands In environments with multiple stakeholders, conflicting project demands are common. A priority system helps manage these conflicts by providing an objective basis for resolving competing project needs. 8. Adaptability and Flexibility A dynamic priority system allows organizations to adapt to changes in the business environment. By regularly reviewing and adjusting priorities, organizations can remain agile and responsive to new opportunities or challenges. 9. Focus on Deliverables A priority system helps teams concentrate on delivering key projects effectively, reducing the tendency to spread efforts too thin across too many initiatives. This focus increases the likelihood of successful project completion. 10. Improved Project Outcomes Ultimately, a priority system leads to better project outcomes by ensuring that the most important projects are executed effectively, on time, and within budget, enhancing overall organizational performance. 7 Project Classification Project classification involves organizing projects into categories based on specific criteria to better manage, prioritize, and allocate resources. Effective project classification helps organizations make informed decisions about which projects to pursue, how to manage them, and how to align them with strategic objectives. 1. Based on Strategic Alignment  Strategic Projects: Directly support the organization's strategic goals, such as expansion into new markets or launching new products.  Operational Projects: Focus on improving efficiency, reducing costs, or maintaining current operations, like process improvement initiatives.  Compliance Projects: Required to meet regulatory, legal, or safety standards, such as General Data Protection Regulation (GDPR) compliance or environmental regulations. 2. Based on Project Size and Complexity  Large/Complex Projects: High cost, long duration (1-5 years), involve multiple departments (50-500 members), and have significant risks. Examples: Building an airport; Developing a new car model  Medium Projects: Moderate cost and duration (6 months to 1 year), involve a few departments (10-50 members), with manageable risks. Examples: Implementing ERP system; Developing a mobile application  Small/Simple Projects: Low cost, short duration (few weeks to few months), involve a single department or small team (1- 10 members), with minimal risks. Examples: Updating a company website; Organizing a small corporate event 8 4  25-09-2024 Example: Healthcare Industry  Strategic Projects  Telemedicine Implementation: Launching telehealth services to expand patient access and adapt to digital transformation trends.  New Service Lines: Introducing specialized services such as oncology or cardiology units to attract more patients.  Operational Projects  Workflow Automation: Implementing software to automate patient scheduling and billing to improve efficiency.  Equipment Maintenance: Regular maintenance of medical equipment to ensure uninterrupted patient care.  Compliance Projects  Health Insurance Portability and Accountability (HIPA) Compliance Initiatives: Projects focused on securing patient data to meet HIPA requirements.  Accreditation Preparation: Ensuring all standards are met for healthcare facility accreditation and ongoing compliance with regulatory bodies. 9 Project Selection Project selection based on both non-financial and financial criteria involves evaluating potential projects using a mix of qualitative and quantitative measures. This comprehensive approach ensures that projects not only offer financial benefits but also align with strategic goals, mitigate risks, and enhance overall value to the organization. Non-Financial Criteria Selection Criteria Description Strategic Alignment Assesses how well the project aligns with the organization's strategic goals and vision. Risk Level Evaluates the potential risks associated with the project including technical, operational, and market risks. Regulatory Compliance Determines if the project is necessary to meet regulatory or legal requirements. Customer Impact Measures the potential impact on customer satisfaction, experience, or retention. Environmental and Social Considers the project's effects on the environment and society, including sustainability and community Impact benefits. Brand and Reputation Assesses how the project could affect the organization's brand image or reputation. Evaluates the project's potential to improve internal processes, productivity, or reduce operational Operational Efficiency challenges. Innovation and Technology Considers how the project contributes to innovation, technology adoption, or competitive differentiation. Advancement Checks if the necessary resources (personnel, skills, equipment) are available to successfully execute the Resource Availability project. Time to Market Measures how quickly the project can be completed and deliver its intended benefits. 10 5  25-09-2024 Financial Criteria Selection Criteria Description Net Present Value Calculates the present value of future cash flows generated by the project and discounted back to (NPV) today's dollars. Internal Rate of Determines the discount rate at which the project’s NPV equals zero which indicates its potential Return (IRR) profitability. Measures how long it will take for the project to repay its initial investment from its net cash Payback Period inflows. Cost-Benefit Analysis Compares the total expected costs to the total expected benefits to determine the project's value. Return on Calculates the percentage return expected from the project relative to its cost. Investment (ROI) Profitability Index Assesses the ratio of the present value of future cash flows to the initial investment, indicating (PI) value creation per unit of investment. Capital Evaluates the amount of capital required for the project, including initial investment and ongoing Requirements expenses. Cash Flow Forecasts the project's cash inflows and outflows over time to assess financial feasibility and Projections liquidity. Budget Constraints Considers the project’s cost relative to the available budget and other financial limitations. Economic Value Measures the project's ability to generate profits above its cost of capital. Added (EVA) 11 Cash Flows Cash flows refer to the movement of money into and out of a business, project, or financial investment over a specific period.  Project selection methods using financial criteria are based on estimating the future cash flows related to the project.  The future cash flows for a project are estimated using certain principles and calculation procedures.  Project cash flows may be classified as investment for fixed assets, margins for working capital, surplus generated from project operations and economic recovery from the project’s assets at the end of project life. 12 6  25-09-2024 Project Selection Methods based on Financial Criteria Raw Cash Flows (Without Discounting) Discounted Cash Flows  Return on Investment (ROI)  Net Present Value (NPV)  Payback Period (PBP)  Internal rate of Return (IRR) 13 Calculation of ROI and PBP ROI measures the return or profit generated relative to the investment cost. Measures Description Implication Return on 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 The higher the percentage, the Investment (ROI) 𝑅𝑂𝐼 % = × 100 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 more attractive the investment. Method The Payback Period (PBP) method is a simple capital budgeting technique used to determine how long it will take for an investment or project to recover its initial cost from the cash inflows it generates. 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑃𝐵𝑃(𝑌𝑟𝑠) = Payback Period 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝑟𝑒𝑡𝑢𝑟𝑛𝑠 The shorter the period, the (PBP) 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝐶𝑜𝑠𝑡 more attractive the investment. Method 𝑃𝐵𝑃(𝑌𝑟𝑠) = 𝐴𝑛𝑛𝑢𝑎𝑙 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 14 7  25-09-2024 Discounting Cash Flows  Future cash flows are discounted to equate them with their present values using a pre- selected annual discounting factor.  The most common factor is 14 % to 16 % per annum.  The advanced financial investment theory recommends use of weighted average cost of capital to be used as discounting factor. if 𝑟 % = 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟, 𝑝𝑣 = 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑛𝑑 𝑝𝑓 = 𝑟𝑎𝑤 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑡ℎ𝑒 𝑛𝑡ℎ 𝑦𝑒𝑎𝑟 𝑝𝑣 = 𝑝𝑓 / ( 1 + 𝑟) 𝑛 𝑎𝑛𝑑 𝑝𝑓 = 𝑝𝑣 ∗ ( 1 + 𝑟) 𝑛 15 Calculation of NPV and IRR  Calculation of NPV  If CF1, CF2, … CFn are the estimated cash inflows in the first, second and nth year of the operation and I is the initial project investment (i.e. cash outflow) in the first year, r is the required rate of return. NPV = CF1 /(1+r) + CF2 /(1+r)2 + … +CFn /(1+r)n - I  Implication : The higher the positive value of NPV, more attractive the project investment.  Calculation of IRR  In the above equation of NPV, that value of r , which makes NPV equal to zero is the internal rate of return for the project.  Implication : The higher the internal rate of return, the more attractive the project investment is. 16 8  25-09-2024 Problem 1 Part-1: Project Selection based on payback period and ROI Project A has initial investment of $700000 and projected cash inflows of $225000 for 5 years. Project B has initial investment of $400000 and projected cash inflows of $110000 for 5 years. Acceptance Criteria is as follows:  Desired return on investment should be more than or equal to 15% ; Payback period should be less than 5 years Determine the payback period and ROI of Project A & B. Comment on the acceptance of the projects for each criteria. Project A Project B Investment $700000 $400000 Annual Savings $225000 $110000 Payback Period (in years) 3.111 3.6363 ROI(%) 32.142 27.5 Acceptance Criteria (PBP) Accepted Accepted Acceptance Criteria (ROI) Accepted Accepted 17 Problem 1 Part-2: Project Selection based on NPV Acceptance Criteria is as follows: NPV should be positive. Project A Project B Cash Outflows -$700000 -$400000 Cash Inflow-Year 1 $225000 $110000 Cash Inflow-Year 2 $225000 $110000 Cash Inflow-Year 3 $225000 $110000 Cash Inflow-Year 4 $225000 $110000 Cash Inflow-Year 5 $225000 $110000 Discount Rate 0.15 0.15 NPV $54234.897 -$31262.939 Acceptance Criteria (NPV) Accepted Not Accepted 18 9  25-09-2024 Problem 2 Two new software projects are proposed to a young, start-up company. The Alpha project will cost $150,000 to develop and is expected to have annual net cash flow of $40,000. The Beta project will cost $200,000 to develop and is expected to have annual net cash flow of $50,000. The company is very concerned about their cash flow. Using the payback period, which project is better from a cash flow standpoint? Why? Solution 𝐼𝑛𝑣𝑒𝑟𝑠𝑡𝑚𝑒𝑛𝑡 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 = 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 $150,000 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 = = 3.75 𝑦𝑒𝑎𝑟𝑠 $40,000 $200,000 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 = = 4.00 𝑦𝑒𝑎𝑟𝑠 $50,000 A lower payback is better. Project Alpha has the lower payback and so has the better payback. 19 Problem 3 There are two projects that a company is reviewing. Management must decide whether to move forward with one, none or both of the projects. The cash flow patterns for each project are as follows: Project A Initial investment = $5,000, Year one cash inflow = $1,700, Year two cash inflow = $1,900, Year three cash inflow = $1,600, Year four cash inflow = $1,500, Year five cash inflow = $700 Project B Initial investment = $2,000, Year one cash inflow = $400, Year two cash inflow = $700, Year three cash inflow = $500, Year four cash inflow = $400, Year five cash inflow = $300  What are the IRR of Project A and B? If the company's cost of capital is 10%, What management should do? 20 10  25-09-2024 Problem 3: Solution  IRR Project A: $0 = (-$5,000) + $1,700 / (1 + IRR) ^ 1 + $1,900 / (1 + IRR) ^ 2 + $1,600 / (1 + IRR) ^ 3 + $1,500 / (1 + IRR) ^ 4 + $700 / (1 + IRR) ^ 5  IRR Project B: $0 = (-$2,000) + $400 / (1 + IRR) ^ 1 + $700 / (1 + IRR) ^ 2 + $500 / (1 + IRR) ^ 3 + $400 / (1 + IRR) ^ 4 + $300 / (1 + IRR) ^ 5  IRR Project A = 16.61%  IRR Project B = 5.23%  If the company's cost of capital is 10%, management should proceed with Project A and reject Project B. 21 Project Selection Methods based on Non-Financial Criteria  The Non-Financial Criteria method for project selection is essential because it evaluates projects based on factors beyond just financial returns.  Financial metrics like Net Present Value (NPV), Internal Rate of Return (IRR), and Return on Investment (ROI) are crucial, but they do not capture the full picture of a project’s impact.  Many strategic, operational, environmental, and social factors can significantly influence the long-term success and sustainability of a project.  Different organizations have preferences for different project evaluation methods. However, two important points should always be borne in mind:  Whatever analytical method is used, the integrity and accuracy of data used plays a very important role.  The analysis can provide some objective basis for decision making, but in the final analysis, it is the knowledge, experience, judgment, and entrepreneurial risk taking capability of the decision maker that lies behind successful investment decisions. 22 11  25-09-2024 Multi-Criteria Selection Models Checklist Models This method uses a list of questions to review potential projects and to determine their acceptance and rejection. Key Features of Checklist Models:  Predefined Criteria: A list of important factors is created to evaluate the project. These criteria often include elements such as alignment with strategy, feasibility, budget, risk, and resource availability.  Yes/No Assessment: Each project is typically reviewed with a simple "yes" or "no" for each criterion to determine if it meets the necessary conditions.  Non-Quantitative: Unlike other project selection methods (such as scoring models), checklist models don’t assign numerical values to criteria. Instead, they provide a quick qualitative assessment.  Flexibility: The model can be tailored to the specific needs of an organization by adjusting the criteria based on priorities like financial return, strategic alignment, or risk. 23 Example: Checklist Model for IT Project Selection Criteria Yes/No Does the project align with the organization’s IT strategy? Will the project improve existing systems or processes? Is the technology required for the project available? Is the project scalable and adaptable to future needs? Are the necessary IT resources (software, hardware, expertise) in place? Are the security risks of the project minimal? Does the project offer a positive return on investment (ROI)? Can the project be integrated with existing systems?  Checklist models are an efficient, straightforward way to evaluate and compare potential projects. Though they may lack the complexity of more advanced selection tools, they provide a practical method for ensuring that projects meet basic organizational standards before proceeding to more detailed evaluation stages.  The Checklist Model for project selection is best used when simplicity, speed, and qualitative factors are important. It works well during the early stages of project evaluation, for routine or low-risk projects, or when ensuring that all stakeholders consider the same basic criteria. 24 12  25-09-2024 Weighted Scoring Models: Project Screening Matrix Weighted Scoring Models are a structured, quantitative method for project selection that involves evaluating and prioritizing projects based on multiple criteria and each of which is assigned a weight according to its importance. Projects are scored on each criterion, and the total score is calculated by multiplying the score for each criterion by its respective weight. The project with the highest total weighted score is usually prioritized for selection. Steps to Create a Weighted Scoring Model 1. Identify the criteria important to the decision process 2. Assign a weight to each criterion based on its relative importance in the decision 3. Assign numerical scores to each criterion for all of the options being considered 4. Calculate the weighted scores by multiplying the weight for each criterion by its score and adding the resulting values. 25 Problem 4 An organization is evaluating six projects on seven different criteria. The weights of the criteria and scores of different project in various criteria is given below. Determine the rank of the projects. C1 C2 C3 C4 C5 C6 C7 Weight 2 3 2 2.5 1 1 3 Proj 1 1 8 2 6 0 6 5 Proj 2 3 3 2 0 0 5 1 Proj 3 9 5 2 0 2 2 5 Proj 4 3 0 10 0 0 6 0 Proj 5 1 10 5 10 0 8 9 Proj 6 6 5 0 2 0 2 7 26 13  25-09-2024 Solution C1 C2 C3 C4 C5 C6 C7 Score Rank Weight 2 3 2 2.5 1 1 3 Proj 1 1 8 2 6 0 6 5 66 2 Proj 2 3 3 2 0 0 5 1 27 6 Proj 3 9 5 2 0 2 2 5 56 3 Proj 4 3 0 10 0 0 6 0 32 5 Proj 5 1 10 5 10 0 8 9 102 1 Proj 6 6 5 0 2 0 2 7 55 4 27 Problem 5 Selecting an Automotive Project Company Background: An automotive company is looking to invest in one of three potential projects: 1.Project X: Develop a new electric vehicle (EV) model. 2.Project Y: Launch a new marketing campaign for an existing luxury SUV. 3.Project Z: Upgrade the manufacturing plant with automation technology. The company wants to ensure that the selected project aligns with its strategic goals while considering financial and non-financial factors. Each project is scored on a scale of 1 to 5, where 1 is poor and 5 is excellent. Strategic Risk Level Time to Environmental ROI Alignment (lower is better) Market Impact Weight 0.35 0.25 0.15 0.15 0.10 Proj X 5 4 3 2 5 Proj Y 3 5 4 4 3 Proj Z 4 3 5 3 4 28 14  25-09-2024 Selection of Project through Multi-criteria decision-making methods C NPV Investments Payback (Lakh IRR(%) Risk Growth (in lakhs Rs.) (in Years) P Rs. P1 10 40 10 Low V. Good 6 P2 6 30 12 Low Good 4 P3 15 50 15 High Excellent 3 P4 20 60 20 Medium Poor 5 P5 12 20 12 V. High Good 6 29 C NPV Investments Payback (Lakh IRR(%) Risk Growth (in lakhs Rs.) (in Years) P Rs. Weight 0.1 0.3 0.2 0.1 0.1 0.2 P1 10 40 10 1 4 6 P2 6 30 12 1 3 4 P3 15 50 15 4 5 3 P4 20 60 20 3 1 5 P5 12 20 12 5 2 6 30 15  25-09-2024 TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) 1980: development by Kwangsun Yoon and Hwang Ching-Lai Yoon, K., “System Selection by Multiple Attribute Decision Making,” Ph. D. Dissertation, Kansas State University, Manhattan, Kansas, 1980. Yoon, K. and C. L. Hwang, “TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)- A Multiple Attribute Decision Making,” a paper to be published, 1980. The TOPSIS method requires only a minimal number of inputs from the user and its output is easy to understand. 31 Basic Concept The chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS). PIS represents the ideal optimal solution NIS represents the ideal inferior solution Criterion 𝑋 (increasing preference) PIS Benefit criteria: Criteria/attributes that have a positive impact to achieve goal. A Cost criteria: Criteria/attributes that have a negative impact to achieve goal. B NIS Criterion 𝑋 (increasing preference) 32 16  25-09-2024 Assumptions Each attribute/criterion in the decision matrix takes either monotonically increasing or monotonically decreasing utility. A set of weights for the attributes/criteria is required. Any outcome which is expressed in a non-numerical way should be quantified through the appropriate scaling technique. 33 Computation Steps Step 1: Construct the Decision Matrix (Problem formulation) Let us assume 𝑘 number of experts (𝐸 , 𝐸 , 𝐸 , … , 𝐸 ) comprised of 𝑚 number C C C 1 2 3... C n of alternatives (𝐴 , 𝐴 , 𝐴 , … , 𝐴 ) with 𝑛 A  x x x 1 11 12 13... x  1n number of criteria (𝐶 , 𝐶 , 𝐶 , … , 𝐶 ). A x x x 2 21 22 23... x  2n A  x x x 3 31 32 33... x  3n The decision matrix 𝐷 is constructed as: D1 . .... . ....    where, 𝑥 is the rating/score of. ....  alternative 𝐴 with respect to criteria 𝐶 Am  xm1 x m2 x m3... xmn 34 17  25-09-2024 Steps 2: Construct the normalized decision matrix To transform the various attribute/criteria dimensions into non-dimensional attributes, which allows comparison across the attributes/criteria. The decision matrix 𝐷 is normalized using the following normalization method:  r11 r... r... r  x 12 1j 1n   ij ....  r ij  m . ...   x 2 ....  ij R   r i1 r r r in  i 1  i2 ij ....  ....    This process will result a new Matrix R which is ....  represented as:   r m1 r r r mn m2... mj... 35 Step 3: Construct the weighted normalized decision matrix  v11 v 12... v 1j... 1n v   w1 r11 wr 2 12... wr j ij... wr  n 1n     ....  ....  ....  ....      ....  ....  V   vi1 v v vin    w1ri1 wr wr wn rin   i2 ij 2 i2 j ij ....  ....  ....  ....      ....  ....  ... vmn w1 rm1... wn rmn vm1 v v wr wr...... m2 mj   2 m2 j mj  36 18  25-09-2024 Steps 4: Determine positive ideal and negative ideal solutions  ' A  {(max v ij j  J ), (min v ij j  J ) i  1,2,...m } i i      {v 1 , v 2 ,..., v j ,..., v n }  ' A  {(min v ij j  J ), (max v ij j  J ) i  1,2,...m } i i      {v 1 , v 2 ,..., v j ,..., v n } where J   j  1,2,..., n j associated with benefit criteria    '  criteria  J   j  1,2,..., n j associated with cos t  37 Steps 5: Calculate the separation measure Positive ideal separation   n 2 vij v j  s i  j 1 i  1,2,..., m Negative ideal separation  vij vj  n 2  s i  j 1 i  1,2,..., m 38 19  25-09-2024 Step 6: Calculate the relative closeness coefficient 𝑆 𝐶∗ = , 0 < 𝐶∗ < 1 , 𝑖 = 1,2, … , 𝑚 𝑆 +𝑆 𝐶 ∗ = 1 𝑖𝑓 𝐴 = 𝐴 𝐶 ∗ = 0 𝑖𝑓 𝐴 = 𝐴 Step 7: Ranking of Alternatives A set of alternatives can now be preference ranked according to the descending order of closeness coefficient. The highest value of closeness coefficient represents the top rank of alternative. 39 Numerical Example: 1 Decision Matrix (D) 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐴 2.0 1500 20000 5.5 5 9 𝐴 2.5 2700 18000 6.5 3 5 𝐴 1.8 2000 21000 4.5 7 7 𝐴 2.2 1800 20000 5.0 5 5 Benefit Criteria: 𝐶 , 𝐶 , 𝐶 , 𝐶 , 𝐶 Cost Criteria: 𝐶 40 20  25-09-2024 Numerical Example 1 Normalized decision matrix x ij r ij  m x 2 ij i 1 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐴 0.4671 0.3662 0.5056 0.5069 0.4811 0.6708 𝐴 0.5839 0.6591 0.4550 0.5990 0.2887 0.3727 𝐴 0.4204 0.4882 0.5308 0.4147 0.6736 0.5217 𝐴 0.5139 0.4392 0.5056 0.4608 0.4811 0.3727 41 Numerical Example 1 Weights=(0.2, 0.1, 0.1, 0.1, 0.2, 0.3) 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐴 0.4671 0.3662 0.5056 0.5069 0.4811 0.6708 Normalized decision matrix 𝐴 0.5839 0.6591 0.4550 0.5990 0.2887 0.3727 𝐴 0.4204 0.4882 0.5308 0.4147 0.6736 0.5217 𝐴 0.5139 0.4392 0.5056 0.4608 0.4811 0.3727 𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 𝐴 0.0934 0.0366 0.0506 0.0507 0.0962 0.2012 Weighted decision matrix 𝐴 0.1168 0.0659 0.0455 0.0599 0.0577 0.1118 𝐴 0.0841 0.0488 0.0531 0.0415 0.1347 0.1565 𝐴 0.1028 0.0439 0.0506 0.0461 0.0962 0.1118 42 21  25-09-2024 Numerical Example 1 Computation of PIS and NIS 𝐴 = 0.1168, 0.0659, 0.0531, 0.0415, 0.1347, 0.2012 𝐴 = 0.0841, 0.0366, 0.0455, 0.0599, 0.0577, 0.1118 43 Numerical Example 1 Separation measures 6 2  (v ij v j )  s i  j 1 i  1, 2, 3, 4   s 1  0.0545 ; s 2  0.1197   s 3  0.0580 ; s 4  0.1009 6 2  (v ij v j )  s i  j 1 i  1, 2,3, 4   s 1  0.0983 ; s 2  0.0439   s 3  0.0920 ; s 4  0.0458 44 22  25-09-2024 Numerical Example 1 The relative closeness to the ideal solution 𝑆 𝐶∗ = = 0.643 𝑆 +𝑆 𝐶 ∗ = 0.268 𝐶 ∗ = 0.613 𝐶 ∗ = 0.312 Rank the preference order 𝑨𝟏 > 𝑨 𝟑 > 𝑨 𝟒 > 𝑨 𝟐 45 Numerical Example 2: Selection of Project C NPV Investments Payback (Lakh IRR(%) Risk Growth (in lakhs Rs.) (in Years) P Rs. P1 10 40 10 Low V. Good 6 P2 6 30 12 Low Good 4 P3 15 50 15 High Excellent 3 P4 20 60 20 Medium Poor 5 P5 12 20 12 V. High Good 6 Weights 0.1 0.3 0.2 0.1 0.1 0.2 46 23  25-09-2024 C NPV Investments Payback (Lakh IRR(%) Risk Growth (in lakhs Rs.) (in Years) P Rs. Weight 0.1 0.3 0.2 0.1 0.1 0.2 P1 10 40 10 1 4 6 P2 6 30 12 1 3 4 P3 15 50 15 4 5 3 P4 20 60 20 3 1 5 P5 12 20 12 5 2 6 47 24