The document contains multiple decision problems involving expected monetary value (EMV) calculations. The first problem involves determining the optimal act from among three acts (A1, A2, A3) based on their payoffs under three possible states of nature (S1, S2, S3) and the given probabilities. The optimal act determined using EMV is A1. Another problem involves determining whether a proposal should be accepted or rejected based on the EMV of each decision. The EMV calculation shows the decision should be to reject the proposal. A third problem involves calculating EMV under different criteria to determine the best investment from among stocks, bonds, and debentures.
The document describes the Modi method for solving transportation problems. It involves finding the unused route with the largest negative improvement index to determine the best way to ship units. The key steps are to construct a transportation table, find the initial basic feasible solution, identify occupied and unoccupied cells, calculate opportunity costs for unoccupied cells, select the cell with the largest negative opportunity cost, and assign units until reaching the optimal solution. The method is demonstrated on two example problems.
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
The document discusses various concepts and approaches related to operation research and decision making under uncertainty and risk. It defines operation research and provides characteristics and scope of OR, including areas such as allocation, production, procurement, marketing, finance, and personnel. The methodology of OR includes problem formulation, model construction, solution, testing, and implementation. Decision making environments like certainty, uncertainty, and risk are explained. Approaches for decision making under uncertainty like maximax, maximin, minimax regret, Hurwicz, and Laplace criteria are illustrated with examples. Decision making under risk assumes state probabilities are known and expected value criterion is used.
Inroduction to Decision Theory and Decision Making Under CertaintyAbhi23396
This document introduces decision theory and decision-making under certainty. It defines decision theory as a descriptive and prescriptive approach to classify levels of knowledge when making decisions. Under certainty, a decision maker has perfect information about outcomes for each alternative, allowing them to choose the best option. An example is provided where a manufacturer must choose between two machines, M1 and M2, to process an order of 1000 units. All costs are known for each machine's setup time, tooling costs, and machining time per unit. Calculations show the total cost is lower to use machine M2, so it is the best choice under the certain conditions given.
This document discusses simulation as a technique used in operations research to analyze the behavior of systems. It provides examples of how simulation works by initializing a system, generating inputs, observing outputs, and collecting statistics. Some key uses of simulation mentioned include testing policy decisions, conducting experiments without disrupting real systems, and obtaining operating characteristics estimates faster than working with actual systems. The document also outlines some advantages and limitations of the simulation approach. It includes two examples demonstrating how to simulate daily demand for a bakery and daily production for a moped manufacturer using random numbers.
The document discusses critical path analysis and provides examples. It begins with definitions of key terms like activity, project, network. It describes the critical path method (CPM) and program evaluation and review technique (PERT) for project planning, scheduling and control. An example project is given with activities, durations and precedence relationships. The critical path is determined by calculating the earliest and latest start/finish times and identifying the activities with no total float.
The document discusses transportation and assignment models in operations research. The transportation model aims to minimize the cost of distributing a product from multiple sources to multiple destinations, while satisfying supply and demand constraints. The assignment model finds optimal one-to-one matching between sources and destinations to minimize costs. Some solution methods for transportation problems include the northwest corner method, row minima method, column minima method, and least cost method. The Hungarian method is commonly used to solve assignment problems by finding the minimum cost matching.
Linear Programming - Meaning, Example and Application in BusinessSundar B N
This document discusses linear programming and its applications. It begins with an introduction and definition of linear programming as a quantitative technique to solve allocation problems. It then provides an example problem formulation to maximize revenue from two products under time and capacity constraints. The document outlines several application areas of linear programming in business, including production management, personnel management, inventory management, marketing management, financial management, and blending problems. It concludes that linear programming is an important mathematical technique for managers to make optimal decisions.
The document describes the Modi method for solving transportation problems. It involves finding the unused route with the largest negative improvement index to determine the best way to ship units. The key steps are to construct a transportation table, find the initial basic feasible solution, identify occupied and unoccupied cells, calculate opportunity costs for unoccupied cells, select the cell with the largest negative opportunity cost, and assign units until reaching the optimal solution. The method is demonstrated on two example problems.
GAME THEORY
Terminology
Example : Game with Saddle point
Dominance Rules: (Theory-Example)
Arithmetic method – Example
Algebraic method - Example
Matrix method - Example
Graphical method - Example
The document discusses various concepts and approaches related to operation research and decision making under uncertainty and risk. It defines operation research and provides characteristics and scope of OR, including areas such as allocation, production, procurement, marketing, finance, and personnel. The methodology of OR includes problem formulation, model construction, solution, testing, and implementation. Decision making environments like certainty, uncertainty, and risk are explained. Approaches for decision making under uncertainty like maximax, maximin, minimax regret, Hurwicz, and Laplace criteria are illustrated with examples. Decision making under risk assumes state probabilities are known and expected value criterion is used.
Inroduction to Decision Theory and Decision Making Under CertaintyAbhi23396
This document introduces decision theory and decision-making under certainty. It defines decision theory as a descriptive and prescriptive approach to classify levels of knowledge when making decisions. Under certainty, a decision maker has perfect information about outcomes for each alternative, allowing them to choose the best option. An example is provided where a manufacturer must choose between two machines, M1 and M2, to process an order of 1000 units. All costs are known for each machine's setup time, tooling costs, and machining time per unit. Calculations show the total cost is lower to use machine M2, so it is the best choice under the certain conditions given.
This document discusses simulation as a technique used in operations research to analyze the behavior of systems. It provides examples of how simulation works by initializing a system, generating inputs, observing outputs, and collecting statistics. Some key uses of simulation mentioned include testing policy decisions, conducting experiments without disrupting real systems, and obtaining operating characteristics estimates faster than working with actual systems. The document also outlines some advantages and limitations of the simulation approach. It includes two examples demonstrating how to simulate daily demand for a bakery and daily production for a moped manufacturer using random numbers.
The document discusses critical path analysis and provides examples. It begins with definitions of key terms like activity, project, network. It describes the critical path method (CPM) and program evaluation and review technique (PERT) for project planning, scheduling and control. An example project is given with activities, durations and precedence relationships. The critical path is determined by calculating the earliest and latest start/finish times and identifying the activities with no total float.
The document discusses transportation and assignment models in operations research. The transportation model aims to minimize the cost of distributing a product from multiple sources to multiple destinations, while satisfying supply and demand constraints. The assignment model finds optimal one-to-one matching between sources and destinations to minimize costs. Some solution methods for transportation problems include the northwest corner method, row minima method, column minima method, and least cost method. The Hungarian method is commonly used to solve assignment problems by finding the minimum cost matching.
Linear Programming - Meaning, Example and Application in BusinessSundar B N
This document discusses linear programming and its applications. It begins with an introduction and definition of linear programming as a quantitative technique to solve allocation problems. It then provides an example problem formulation to maximize revenue from two products under time and capacity constraints. The document outlines several application areas of linear programming in business, including production management, personnel management, inventory management, marketing management, financial management, and blending problems. It concludes that linear programming is an important mathematical technique for managers to make optimal decisions.
The document discusses the assignment problem, which involves assigning people, jobs, machines, etc. to minimize costs or maximize profits. It provides an example of assigning 4 men to 4 jobs to minimize total cost, walking through the Hungarian method steps. It also discusses how to handle imbalance by adding dummy rows or columns, and how to convert a maximization problem to minimization.
Strategic management involves formulation and implementation of major goals and initiatives by top management based on assessments of internal and external environments. [DOCUMENT] outlines the six key steps to effective strategic formulation: 1) define the organization, 2) define the strategic mission, 3) define strategic objectives, 4) define the competitive strategy considering industry, competition, and strengths/weaknesses, 5) implement strategies through tactical actions, and 6) regularly evaluate progress against the strategic plan and make adjustments based on changes in the business environment. Strategic formulation provides a framework for actions to achieve anticipated results but requires flexibility to adapt the strategic plan to changing market conditions.
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources.A transportation matrix is a way of understanding the maximum possibilities the shipment can be done. It is also known as decision variables because these are the variables of interest that we will change to achieve the objective, that is, minimizing the cost function.
Decision theory as the name would imply is concerned with the process of making decisions. The extension to statistical decision theory includes decision making in the presence of statistical knowledge which provides some information where there is uncertainty. The elements of decision theory are quite logical and even perhaps intuitive. The classical approach to decision theory facilitates the use of sample information in making inferences about the unknown quantities. Other relevant information includes that of the possible consequences which is quantified by loss and the prior information which arises from statistical investigation. The use of Bayesian analysis in statistical decision theory is natural. Their unification provides a foundational framework for building and solving decision problems. The basic ideas of decision theory and of decision theoretic methods lend themselves to a variety of applications and computational and analytic advances.
This document provides an overview of operations research (OR). It defines OR as the scientific approach to problem solving and decision making through mathematical modeling and analysis. The document outlines the history, terminology, problem solving process, and applications of OR. Key points include that OR uses scientific methods to help organizations make better decisions, solve complex problems, and optimize performance across various industries and applications such as production, marketing, finance, and research.
Linear programming - Model formulation, Graphical MethodJoseph Konnully
The document discusses linear programming, including an overview of the topic, model formulation, graphical solutions, and irregular problem types. It provides examples to demonstrate how to set up linear programming models for maximization and minimization problems, interpret feasible and optimal solution regions graphically, and address multiple optimal solutions, infeasible solutions, and unbounded solutions. The examples aid in understanding the key steps and components of linear programming models.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
The process of strategic choice involves focusing on strategic alternatives through gap analysis, analyzing alternatives based on objective and subjective factors, evaluating alternatives against selection criteria, and making a final choice. Subjective factors considered in strategic choice include perceptions of critical success factors, commitment to past actions, decision styles and risk attitudes, and internal politics. Organizations develop contingency strategies in advance to deal with uncertainties and create strategic plans to implement chosen strategies.
Operational research is a systematic approach to decision-making that uses analytical and statistical techniques to arrive at optimal or near-optimal solutions to complex problems. The document provides an overview of operational research, including its history, scope, methodologies, tools and techniques, and applications in various fields such as national planning, defense, and industry. It also discusses some limitations of operational research related to incorporating non-quantifiable factors, computational complexity, and challenges in implementation.
Vogel's Approximation Method (VAM) is a method for solving transportation problems that considers penalties (opportunity costs) associated with not shipping to cells with the lowest costs. It works as follows:
1. Compute penalties for each row and column based on the difference between the lowest and second lowest costs.
2. Ship to the cell in the row or column with the largest penalty, removing that row or column.
3. Recompute penalties and repeat until all shipments are allocated. VAM finds an initial solution close to optimal with few iterations.
Operations research is a scientific approach to problem solving and decision making that is useful for managing organizations. It has its origins in World War II and is now widely used in business and industry. Some key areas where operations research models are applied include forecasting, production scheduling, inventory control, and transportation. Models are an essential part of operations research and can take various forms like physical, mathematical, or conceptual representations of real-world problems. Models are classified in different ways such as by their structure, purpose, solution method, or whether they consider deterministic or probabilistic systems. Operations research techniques help solve complex business problems through mathematical analysis and support improved organizational performance.
This document summarizes a presentation on strategic control. It outlines 5 questions involved in assessing a strategy's success, including whether the organization is moving in the right direction and if objectives are being met. It defines strategic control as focused on achieving future goals rather than past performance, and tracking a strategy as it is implemented. The characteristics, process, and 4 types of strategic control are described: premise control, implementation control, strategic surveillance, and special alert control. Operational control is also briefly discussed.
This document discusses solving assignment problems using the Hungarian method. It provides an 8-step process for solving both balanced and unbalanced assignment problems to minimize or maximize the objective. For balanced problems, the steps include reducing the matrix, finding possible assignments based on zeros, and covering and updating the matrix if no optimal solution is found. For unbalanced problems, dummy rows or columns are added to create a balanced matrix before applying the same steps. Examples demonstrate solving both minimization and maximization problems.
The document provides a summary of a presentation on solving linear programming problems (LPP) using the graphical method. It defines LPP and the graphical method. It then walks through the steps to solve an example LPP problem graphically, including formulating the problem, framing the graph, plotting the constraints, finding the optimal solution point, and determining the maximum value. The summary concludes that the optimal solution for the example problem is 5 male workers and 6 female workers, with a maximum total return of Rs. 1,01,000.
The document discusses the assignment problem and the Hungarian method for solving it. The assignment problem involves finding a maximum weight matching in a weighted bipartite graph. The Hungarian method is an algorithm that solves the assignment problem in polynomial time, originally developed by Harold Kuhn in 1955 based on earlier work by two Hungarian mathematicians. It uses steps like subtracting smallest row and column entries and drawing lines to cover zero entries to find an optimal assignment.
Chapter 1 conceptual framework for strategic management (2)LAXMI VIDYAPEETH
This document provides definitions and explanations of key concepts in strategic management, including:
1. Strategy, policy, tactics, strategic management, programs, procedures, and key stakeholders are defined. The differences between strategy and policy are explained.
2. The strategic management process and its importance for organizational success are overviewed. Strategic intent and how organizational vision, mission, goals, and objectives are formulated is also discussed.
3. Key terms are further explained, including strategic business units (SBUs), environment threat and opportunity profile (ETOP), and examples are provided. The advantages and disadvantages of strategic management and SBUs are summarized.
Transportation Problem in Operational ResearchNeha Sharma
The document discusses the transportation problem and methods for finding its optimal solution. It begins by defining key terminology used in transportation models like feasible solution, basic feasible solution, and optimal solution. It then outlines the basic steps to obtain an initial basic feasible solution and subsequently improve it to reach the optimal solution. Three common methods for obtaining the initial solution are described: the Northwest Corner Method, Least Cost Entry Method, and Vogel's Approximation Method. The document also addresses how to solve unbalanced transportation problems and provides examples applying the methods.
This document discusses decision tree analysis. It provides definitions and examples of decision trees. A decision tree is a graphical representation of decision making that uses nodes to represent decisions, chances, and outcomes. It can be used to identify the strategy most likely to reach a goal. The document includes an example problem where a glass factory is considering three courses of action based on future demand. A decision tree is drawn, expected monetary values are calculated for each alternative, and the alternative with the highest value, constructing a new facility, is identified as the most preferred decision.
Prepared by Students of University of Rajshahi
Pranto Karmoker Ariful Islam Tonmoy Halder Monir Hossain
1711033122 1710733119 1710833120 1711033205
Ashikur Rahman Mahfuzul Haque Jibon Rahman Sohag Miah
1710133113 1710933297 1711033210 1710933202
Siam Hossain Shammira Parvin Farhana Afrose Anjuman Ara
1710333148 1712033136 1712033209 1712433159
Shakil Hossain
1710833138
presented by Group 2
For downloading this contact- bikashkumar.bk100@gmail.com
1 EPOMEECS407 Final Exam Do ALL problems .docxjeremylockett77
1
EPOM/EECS407 Final Exam
Do ALL problems Time allowed: 3 hrs
1. (10 points) A manufacturing plant produces specially crafted engines for high-performance
automobiles. If it takes 3 working days to produce the first engine and the learning curve is such that it
only takes an estimated 70% of the time (required to produce the first engine) to produce the second
engine, determine how long it will take for the plant to be able to produce 2 engines in one working
day.
Name:……………………………………………………
2
2. (10 points) An investment amount of $10M has to be raised through equity financing and debt
financing. The required debt ratio is 0.40 and the company tax rate is 35%.
a) The current market price of the company’s common stock is $50 and the current dividend is $5
and the dividend is expected to grow at 5% annual rate. The floating cost of issuing a common
stock is 10%. Preferred stocks of $100 par value with 10% fixed annual dividend can also be
issued at 8% floating cost. If the required proportion of funds from retained earnings to common
stocks to preferred stocks are 0.4:0.2:0.4 respectively, what is the cost of equity?
b) Bank loans at 12% annual interest. Also, the company issues 20-year bonds that pay the equivalent
of 9.5% yield to maturity. If the required ratio of funds raised through these two methods of debt
financing is 0.6:0.4 what is the cost of debt?
c) From (a) and (b), what is the cost of capital (WACC)?
3
20000 40000 60000 80000 100000
5
5
10
15
20
25
3. (15 points) EECS Corporation has identified six investment opportunities that will last 1 year. The firm
draws up a list of all potentially acceptable projects, and computes their IRR and PW at 8.5% MARR as
shown below.
Project Initial Investment IRR PW(8.5%) ($)
1 17,000 8% 1300
2 12,000 10% 1120
3 15,000 5% 600
4 20,000 20% 3800
5 10,000 7% 720
6 16,000 15% 1700
a) If the marginal cost of capital for additional funds is 8% for $40,000 and 9% for the next 60,000
and the lending rate (if the company wants to lend their money) is 6% Assume that the company
has an investment budget of (i) $60,000 on hand and (ii) $0 on hand, and that there is no partial
project investment, what is the best investment strategy and MARR in each case? (Note in both
cases, additional borrowing is allowed if it is beneficial to do so.)
Draw an Investment Opportunity Schedule (IOS) and Marginal Cost of Capital (MCC) below.
4
3b) Again with the firm budget of $80,000 (no additional borrowing, allowed) formulate (but DO NOT
solve) an integer programming model to help determine an optimal portfolio of the above projects
based on maximizing the present worth at 8.5%. Also, the following conditions must be observed.
Projects1, 4 and 6 are mutually exclusive, and projec ...
The document discusses the assignment problem, which involves assigning people, jobs, machines, etc. to minimize costs or maximize profits. It provides an example of assigning 4 men to 4 jobs to minimize total cost, walking through the Hungarian method steps. It also discusses how to handle imbalance by adding dummy rows or columns, and how to convert a maximization problem to minimization.
Strategic management involves formulation and implementation of major goals and initiatives by top management based on assessments of internal and external environments. [DOCUMENT] outlines the six key steps to effective strategic formulation: 1) define the organization, 2) define the strategic mission, 3) define strategic objectives, 4) define the competitive strategy considering industry, competition, and strengths/weaknesses, 5) implement strategies through tactical actions, and 6) regularly evaluate progress against the strategic plan and make adjustments based on changes in the business environment. Strategic formulation provides a framework for actions to achieve anticipated results but requires flexibility to adapt the strategic plan to changing market conditions.
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources.A transportation matrix is a way of understanding the maximum possibilities the shipment can be done. It is also known as decision variables because these are the variables of interest that we will change to achieve the objective, that is, minimizing the cost function.
Decision theory as the name would imply is concerned with the process of making decisions. The extension to statistical decision theory includes decision making in the presence of statistical knowledge which provides some information where there is uncertainty. The elements of decision theory are quite logical and even perhaps intuitive. The classical approach to decision theory facilitates the use of sample information in making inferences about the unknown quantities. Other relevant information includes that of the possible consequences which is quantified by loss and the prior information which arises from statistical investigation. The use of Bayesian analysis in statistical decision theory is natural. Their unification provides a foundational framework for building and solving decision problems. The basic ideas of decision theory and of decision theoretic methods lend themselves to a variety of applications and computational and analytic advances.
This document provides an overview of operations research (OR). It defines OR as the scientific approach to problem solving and decision making through mathematical modeling and analysis. The document outlines the history, terminology, problem solving process, and applications of OR. Key points include that OR uses scientific methods to help organizations make better decisions, solve complex problems, and optimize performance across various industries and applications such as production, marketing, finance, and research.
Linear programming - Model formulation, Graphical MethodJoseph Konnully
The document discusses linear programming, including an overview of the topic, model formulation, graphical solutions, and irregular problem types. It provides examples to demonstrate how to set up linear programming models for maximization and minimization problems, interpret feasible and optimal solution regions graphically, and address multiple optimal solutions, infeasible solutions, and unbounded solutions. The examples aid in understanding the key steps and components of linear programming models.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
The process of strategic choice involves focusing on strategic alternatives through gap analysis, analyzing alternatives based on objective and subjective factors, evaluating alternatives against selection criteria, and making a final choice. Subjective factors considered in strategic choice include perceptions of critical success factors, commitment to past actions, decision styles and risk attitudes, and internal politics. Organizations develop contingency strategies in advance to deal with uncertainties and create strategic plans to implement chosen strategies.
Operational research is a systematic approach to decision-making that uses analytical and statistical techniques to arrive at optimal or near-optimal solutions to complex problems. The document provides an overview of operational research, including its history, scope, methodologies, tools and techniques, and applications in various fields such as national planning, defense, and industry. It also discusses some limitations of operational research related to incorporating non-quantifiable factors, computational complexity, and challenges in implementation.
Vogel's Approximation Method (VAM) is a method for solving transportation problems that considers penalties (opportunity costs) associated with not shipping to cells with the lowest costs. It works as follows:
1. Compute penalties for each row and column based on the difference between the lowest and second lowest costs.
2. Ship to the cell in the row or column with the largest penalty, removing that row or column.
3. Recompute penalties and repeat until all shipments are allocated. VAM finds an initial solution close to optimal with few iterations.
Operations research is a scientific approach to problem solving and decision making that is useful for managing organizations. It has its origins in World War II and is now widely used in business and industry. Some key areas where operations research models are applied include forecasting, production scheduling, inventory control, and transportation. Models are an essential part of operations research and can take various forms like physical, mathematical, or conceptual representations of real-world problems. Models are classified in different ways such as by their structure, purpose, solution method, or whether they consider deterministic or probabilistic systems. Operations research techniques help solve complex business problems through mathematical analysis and support improved organizational performance.
This document summarizes a presentation on strategic control. It outlines 5 questions involved in assessing a strategy's success, including whether the organization is moving in the right direction and if objectives are being met. It defines strategic control as focused on achieving future goals rather than past performance, and tracking a strategy as it is implemented. The characteristics, process, and 4 types of strategic control are described: premise control, implementation control, strategic surveillance, and special alert control. Operational control is also briefly discussed.
This document discusses solving assignment problems using the Hungarian method. It provides an 8-step process for solving both balanced and unbalanced assignment problems to minimize or maximize the objective. For balanced problems, the steps include reducing the matrix, finding possible assignments based on zeros, and covering and updating the matrix if no optimal solution is found. For unbalanced problems, dummy rows or columns are added to create a balanced matrix before applying the same steps. Examples demonstrate solving both minimization and maximization problems.
The document provides a summary of a presentation on solving linear programming problems (LPP) using the graphical method. It defines LPP and the graphical method. It then walks through the steps to solve an example LPP problem graphically, including formulating the problem, framing the graph, plotting the constraints, finding the optimal solution point, and determining the maximum value. The summary concludes that the optimal solution for the example problem is 5 male workers and 6 female workers, with a maximum total return of Rs. 1,01,000.
The document discusses the assignment problem and the Hungarian method for solving it. The assignment problem involves finding a maximum weight matching in a weighted bipartite graph. The Hungarian method is an algorithm that solves the assignment problem in polynomial time, originally developed by Harold Kuhn in 1955 based on earlier work by two Hungarian mathematicians. It uses steps like subtracting smallest row and column entries and drawing lines to cover zero entries to find an optimal assignment.
Chapter 1 conceptual framework for strategic management (2)LAXMI VIDYAPEETH
This document provides definitions and explanations of key concepts in strategic management, including:
1. Strategy, policy, tactics, strategic management, programs, procedures, and key stakeholders are defined. The differences between strategy and policy are explained.
2. The strategic management process and its importance for organizational success are overviewed. Strategic intent and how organizational vision, mission, goals, and objectives are formulated is also discussed.
3. Key terms are further explained, including strategic business units (SBUs), environment threat and opportunity profile (ETOP), and examples are provided. The advantages and disadvantages of strategic management and SBUs are summarized.
Transportation Problem in Operational ResearchNeha Sharma
The document discusses the transportation problem and methods for finding its optimal solution. It begins by defining key terminology used in transportation models like feasible solution, basic feasible solution, and optimal solution. It then outlines the basic steps to obtain an initial basic feasible solution and subsequently improve it to reach the optimal solution. Three common methods for obtaining the initial solution are described: the Northwest Corner Method, Least Cost Entry Method, and Vogel's Approximation Method. The document also addresses how to solve unbalanced transportation problems and provides examples applying the methods.
This document discusses decision tree analysis. It provides definitions and examples of decision trees. A decision tree is a graphical representation of decision making that uses nodes to represent decisions, chances, and outcomes. It can be used to identify the strategy most likely to reach a goal. The document includes an example problem where a glass factory is considering three courses of action based on future demand. A decision tree is drawn, expected monetary values are calculated for each alternative, and the alternative with the highest value, constructing a new facility, is identified as the most preferred decision.
Prepared by Students of University of Rajshahi
Pranto Karmoker Ariful Islam Tonmoy Halder Monir Hossain
1711033122 1710733119 1710833120 1711033205
Ashikur Rahman Mahfuzul Haque Jibon Rahman Sohag Miah
1710133113 1710933297 1711033210 1710933202
Siam Hossain Shammira Parvin Farhana Afrose Anjuman Ara
1710333148 1712033136 1712033209 1712433159
Shakil Hossain
1710833138
presented by Group 2
For downloading this contact- bikashkumar.bk100@gmail.com
1 EPOMEECS407 Final Exam Do ALL problems .docxjeremylockett77
1
EPOM/EECS407 Final Exam
Do ALL problems Time allowed: 3 hrs
1. (10 points) A manufacturing plant produces specially crafted engines for high-performance
automobiles. If it takes 3 working days to produce the first engine and the learning curve is such that it
only takes an estimated 70% of the time (required to produce the first engine) to produce the second
engine, determine how long it will take for the plant to be able to produce 2 engines in one working
day.
Name:……………………………………………………
2
2. (10 points) An investment amount of $10M has to be raised through equity financing and debt
financing. The required debt ratio is 0.40 and the company tax rate is 35%.
a) The current market price of the company’s common stock is $50 and the current dividend is $5
and the dividend is expected to grow at 5% annual rate. The floating cost of issuing a common
stock is 10%. Preferred stocks of $100 par value with 10% fixed annual dividend can also be
issued at 8% floating cost. If the required proportion of funds from retained earnings to common
stocks to preferred stocks are 0.4:0.2:0.4 respectively, what is the cost of equity?
b) Bank loans at 12% annual interest. Also, the company issues 20-year bonds that pay the equivalent
of 9.5% yield to maturity. If the required ratio of funds raised through these two methods of debt
financing is 0.6:0.4 what is the cost of debt?
c) From (a) and (b), what is the cost of capital (WACC)?
3
20000 40000 60000 80000 100000
5
5
10
15
20
25
3. (15 points) EECS Corporation has identified six investment opportunities that will last 1 year. The firm
draws up a list of all potentially acceptable projects, and computes their IRR and PW at 8.5% MARR as
shown below.
Project Initial Investment IRR PW(8.5%) ($)
1 17,000 8% 1300
2 12,000 10% 1120
3 15,000 5% 600
4 20,000 20% 3800
5 10,000 7% 720
6 16,000 15% 1700
a) If the marginal cost of capital for additional funds is 8% for $40,000 and 9% for the next 60,000
and the lending rate (if the company wants to lend their money) is 6% Assume that the company
has an investment budget of (i) $60,000 on hand and (ii) $0 on hand, and that there is no partial
project investment, what is the best investment strategy and MARR in each case? (Note in both
cases, additional borrowing is allowed if it is beneficial to do so.)
Draw an Investment Opportunity Schedule (IOS) and Marginal Cost of Capital (MCC) below.
4
3b) Again with the firm budget of $80,000 (no additional borrowing, allowed) formulate (but DO NOT
solve) an integer programming model to help determine an optimal portfolio of the above projects
based on maximizing the present worth at 8.5%. Also, the following conditions must be observed.
Projects1, 4 and 6 are mutually exclusive, and projec ...
This document contains practice problems related to risk and return. It discusses different types of risk like sales risk, operating risk, interest rate risk, and how they can vary between firms or bonds. It also covers risk measurement by calculating expected values and standard deviations for probability distributions. Other topics include the capital asset pricing model, portfolio risk and return, diversification, and how correlation between investments affects portfolio risk.
This document provides a mark scheme for an accounting exam assessing corporate and management accounting. It outlines the general marking guidance examiners should follow, including marking positively and according to the mark scheme rather than perceptions of grade boundaries. It also provides sample answers and calculations for questions on the exam, including the preparation of a statement of cash flows, variances analysis, and calculation of asset values in an acquisition. The document aims to ensure consistent and fair marking of the exam according to the schemes and examples provided.
This document provides 14 problems related to risk and return concepts including expected rate of return, standard deviation, portfolio return and risk, and the Capital Asset Pricing Model. The problems cover calculating expected returns and standard deviations for single assets and portfolios. Other problems involve using the CAPM formula to calculate expected returns given risk free rates, market returns and betas. The solutions show the step-by-step workings for each problem.
CA NOTES ON RISK, RETURN AND PORTFOLIO PRACTICALS OF STRATEGIC FINANCIAL MODE...Kanoon Ke Rakhwale India
CA NOTES ON RISK, RETURN AND PORTFOLIO PRACTICALS OF STRATEGIC FINANCIAL MODELING
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Here are the key differences between bad debts and allowance for doubtful debts:
Bad debts refer to specific customer accounts that are known to be uncollectible in the current period. The business has tried to collect on the debt but was unsuccessful. Bad debts are an expense in the current period's income statement.
Allowance for doubtful debts is an estimate of debts that may become uncollectible in a future period, but have not been identified as bad yet. It is calculated as a percentage of total receivables based on past collection experience. The allowance is deducted from trade receivables on the statement of financial position to arrive at the net realizable value.
The main differences are:
- Bad debts are actual un
The document discusses portfolio theory and diversification from a mathematical perspective. It introduces Harry Markowitz's efficient frontier and how diversifying investments reduces portfolio risk. The expected return of a portfolio is a weighted average of the component returns, while the variance is not a linear combination and depends on the covariance between components. Diversification is most effective at reducing risk when the component returns are negatively correlated. The mathematics of diversification for multiple assets uses a variance-covariance matrix to calculate portfolio risk.
This slide set is a work in progress and is embedded in my Principles of Finance course site (under construction) that I teach to computer scientists and engineers
http://awesomefinance.weebly.com/
Equity Financing Capacity and Stock Returns: Evidence from ChinaLalith Samarakoon
This document summarizes research presented at the Global Finance Conference in Chicago in 2012 on the relationship between equity financing capacity and future stock returns in China. The researchers investigated how the ability of Chinese firms to issue equity, as determined by regulations set by the China Securities Regulatory Commission, impacted subsequent stock performance. They found that for firms qualified to issue shares, having the capacity for rights issues or public offerings was strongly negatively correlated with future returns. This relationship held for qualified firms that both applied to issue shares and for those that successfully issued equity. The results support theories that predict investors react negatively to equity issuance due to agency problems, signaling effects, or earnings management.
This document contains solutions to problems related to chapter 13 on dividend policy. Problem P13-1 discusses procedures for declaring a cash dividend, including journal entries to record the declaration and payment. Problem P13-2 discusses ex-dividend dates and whether an investor would be better off buying stock before or after the ex-dividend date. Problem P13-3 discusses residual dividend policy, where a firm pays dividends from funds left over after meeting investment requirements.
Security analysis and portfolio managementHimanshu Jain
Live Project was all about studying the company’s financial health through the movement of their stock price. This live project deals with the basic concepts of investment in securities such as bonds and stocks, and management of such assets. It discusses various aspects of portfolio management, ranging from analysis, selection, and revision to evaluation of portfolio, securities market and risk evaluation that help in understanding the trading system better and making quality investment decisions.
This live project helped to understand how the stock prices vary. It also helped to know and calculate several technical terms. In this project, I was given 5 stocks wherein I need to update opening price, closing price, % change, total shares traded etc. every day. Then it is required to find out the beta, average return etc. of these stocks separately and construct a portfolio with Rs. 50, 00,000 keeping in mind optimum return for the investment. We need to keep in mind beta, standard deviation, risk and return of these stocks and invest to get the optimum returns.
This project helps in knowing the expected return and risk for each stock. Under this project I got to know about portfolio management as well as expected return & risk associate with each company. Through this project my future investment will be better as it helps in knowing the inside depth of companies by analysis the financial details.
decision theory how to make a decision in numbersemailfortestjj
The document discusses decision theory and how to analyze decision problems using decision trees and payoff matrices. It describes key concepts like alternatives, states of nature, and payoff tables. Decision makers select alternatives and receive payoffs depending on the state of nature. Payoff matrices show all possible outcomes. Regret matrices show opportunity losses. The expected monetary value and expected regret are calculated to evaluate alternatives. Non-probabilistic criteria like maximax, maximin, minimax, and minimin are also discussed for analyzing decisions without probabilities.
This document provides a performance analysis of an algorithm (consolidated) over several time periods from 2016-2020. It includes key financial metrics such as sales, operating profit, net income, operating rate, net rate, and debt ratio. It also evaluates the company's stock price against indication prices at different levels and makes recommendations to buy, sell, or hold based on the current stock price gap compared to indication prices. Overall stock price rise probabilities and increase rates are analyzed by sector and time period. The document concludes with a compliance notice regarding the accuracy and responsibility of the information and algorithms provided.
Blockwood Inc. must decide what type of truck to purchase for its operations. Three options are considered: a small import truck, standard pickup, or large flatbed truck. Sales in the first year are expected to fall into one of four categories. A payoff table outlines the expected profits for each truck type across the different sales levels. The document asks to analyze and make a decision using various decision making criteria, including Laplace, Minimax, Maximin, Savage Minimax Regret, and Hurwicz criteria. It also considers incorporating probability assessments and the value of market research.
The document contains 10 economics problems related to concepts like demand and supply, elasticity, costs of production, revenue and game theory. The problems are to be solved by analyzing the data provided in tables or graphs and calculating relevant metrics like price elasticity, average costs, total revenue etc. using formulas. The level of difficulty of the problems ranges from easy to difficult.
This document discusses key concepts related to investment returns and risk. It defines investment returns as measuring the financial results of an investment. Returns can be expressed in dollar or percentage terms. Investment risk refers to the probability of earning a return lower than expected and is greater if the potential downside is larger. The document then provides an example of calculating expected returns and risk for different investment alternatives using probabilities of economic scenarios. It shows how a portfolio with two investments can provide average returns but lower risk through diversification.
This document describes the process of generating a ROC curve to evaluate the performance of a biometric authentication system. It involves:
1) Classifying genuine and imposter scores into ranges from 0-0.1, 0.1-0.2, etc.
2) Counting the classifications in each range to determine true positives, false positives, etc.
3) Plotting the true positive rate against the false positive rate to generate the ROC curve and determine the equal error rate (EER) where the curves intersect.
4) To minimize total cost when false accepts cost 10 euro and false rejects cost 30 euro, the optimal operating point on the ROC curve can be selected.
A Study on the Short Run Relationship b/w Major Economic Indicators of US Eco...aurkoiitk
The objective of this study
was to develop an economic indicator system for the US
economy that will help to forecast the turning points in the
aggregate level of economic activity. Our primary concern
is to study the short run relationship between the major
economic indicators of US economy (eg: GDP, Money
Supply, Unemployment Rate, Inflation rate, Federal Fund
Rate, Exchange Rate, Government Expenditure &
Receipt, Crude Oil Price, Net Import & Export).
Similar to Decision analysis problems online 1 (20)
The document discusses various aspects of issuing debentures, including:
1) Debentures can be issued for cash or other consideration, at par value, at a premium, or at a discount. Accounting entries are provided for each scenario.
2) Interest is paid periodically on debentures and is treated as a charge against company profits. Accounting entries track interest becoming due and payments made.
3) Terms of debenture redemption are specified, which can be at par value, premium, or discount. Provisions are made for premium amounts due at redemption from time of issue.
This document contains the balance sheet and notes to accounts of a company as of March 31, 202x. The balance sheet shows total assets of ₹2,60,700 consisting of non-current assets of ₹94,510 and current assets of ₹1,66,190. The liabilities side shows total equity and liabilities of ₹2,60,700 consisting of shareholders' funds, non-current liabilities, and current liabilities. The notes to accounts provide additional details on items in the balance sheet such as fixed asset details, calculation of depreciation, provisions, reserves and surplus, trade receivables, and payables.
The document discusses the liquidation process for companies. It defines liquidation as the legal procedure for winding up a company's affairs. When a company undergoes liquidation, its assets are realized and proceeds are used to pay off creditors, with any surplus returned to shareholders. A liquidator oversees the process of settling liabilities and distributing assets in an orderly manner. Liquidation can be compulsory, initiated by the court, or voluntary, initiated by creditors or members. The document provides details on the types of liquidation and the order of payments made through the process.
The Indian financial system consists of financial markets, intermediaries, and instruments. It connects savers and suppliers of funds like households to seekers of funds like businesses and the government. The organized Indian financial system includes money markets, capital markets, credit markets, and various financial instruments and regulators. Key financial markets are the money market, which facilitates short-term lending, and the capital market, which enables long-term raising of capital. The main regulators are the Securities and Exchange Board of India (SEBI), which regulates securities markets, and the Reserve Bank of India (RBI), which acts as the central bank.
INTRODUCTION TO OPERATIONS RESEARCH (2).pptxSoumendra Roy
The document discusses operational research (OR), which involves applying scientific principles to complex business and management problems. It notes that modern business decisions involve many interacting variables and competitors, requiring a systematic approach beyond intuition. OR uses quantitative modeling and analysis to help managers evaluate alternatives and make informed decisions. The document outlines the history and applications of OR in various domains like transportation, banking, agriculture, and healthcare.
The document discusses various concepts and theories of profit. It defines accounting profit as revenue minus explicit costs, while economic profit subtracts both explicit and implicit opportunity costs. Several theories of profit are outlined, including Walker's view of profit as a reward for exceptional abilities, Clark's theory that profit arises in dynamic economies with technological change, and Schumpeter's theory that profit stems from innovation. The document also discusses monopoly profit and conditions for profit maximization, stating firms aim to produce where marginal revenue equals marginal cost.
Country evaluation and selection of international businessSoumendra Roy
This document outlines the steps involved in evaluating and selecting countries for international business opportunities. It discusses scanning for alternative locations, choosing and weighing variables like market size, costs and risks. Data is collected and analyzed using tools like matrices to compare countries. The key factors of market size, costs, risks, and competition are evaluated. A final country is then selected based on detailed estimates and consideration of undertaking the venture alone or with a partner. The overall process allows companies to systematically evaluate international opportunities and allocate resources efficiently.
There are several options for entering a foreign market. These options vary in cost, risk, and the level of control they provide. One important strategic decision is the mode of market entry. The document then discusses various market entry strategies such as exporting, licensing, franchising, joint ventures, contract manufacturing, mergers and acquisitions, fully owned subsidiaries, countertrade, turnkey contracts, and third country locations. For each strategy, it provides details on how the strategy works, examples, advantages and disadvantages.
The document discusses several limitations and challenges of fiscal policy as a tool for economic stabilization. It identifies 13 issues that can hamper the effectiveness of fiscal policy: policy lags due to recognition, administrative, and operational delays; difficulties with forecasting economic conditions; challenges determining the appropriate size and timing of fiscal measures; the selective nature of fiscal policy; potential inadequacy or self-offsetting effects of fiscal actions; unintended impacts on income redistribution; issues related to maintaining employment incentives; problems of growing public debt over time; potential adverse psychological reactions; additional difficulties implementing fiscal policy in underdeveloped economies; and administrative challenges in democratic systems with longer legislative and approval processes.
The document provides an overview of insurance law and regulations in India. It begins with definitions of life insurance and general insurance under the Insurance Act of 1938. It then discusses the importance of insurance, principles of insurance, types of insurance plans, and regulations set by the Insurance Regulatory and Development Authority (IRDA). Key acts governing insurance in India include the Insurance Act of 1938, the Insurance Regulatory and Development Authority Act of 1999, and the Actuaries Act of 2006. Guidelines for insurance companies include registration requirements, maintaining separate accounts for different lines of business, and circumstances for winding up a company.
This document discusses key legal principles related to insurance contracts. It covers the distribution of insurance contracts, characteristics of insurance contracts as legally binding agreements, and fundamental principles including indemnity, insurable interest, utmost good faith, and subrogation. The principles of indemnity and insurable interest help ensure the insured does not receive more compensation than their actual loss.
The document discusses various theories of capital structure, including the Net Income Approach, Net Operating Income Approach, Traditional Approach, and Modigliani-Miller Model. The Modigliani-Miller Model proposes that in a perfect market without taxes, the value of a firm and its cost of capital are independent of its capital structure. It consists of two propositions: 1) a firm's value depends only on its operating income and risk level, and 2) the cost of equity rises with leverage to offset the benefit of low-cost debt. Later models incorporate taxes, showing firm value increases with debt due to tax deductibility of interest payments.
Responsibility accounting is a management control system that delegates authority and responsibility to managers of responsibility centers. It collects planned and actual accounting data on inputs (costs) and outputs (revenues) of responsibility centers. The goals of responsibility accounting are to measure divisional performance, evaluate manager performance, and motivate managers to achieve organizational goals. It enables easy identification of responsible managers and provides relevant and timely information for planning, control, and decision-making. Responsibility centers can be cost centers, which measure only inputs, profit centers, which measure both inputs and outputs, and investment centers. Responsibility accounting reports provide budgeted and actual data in a timely manner to assist managers in identifying variances.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
Decision analysis problems online 1
1. DECISION ANALYSIS
1. The payoffs (in ₹) of three acts A1, A2 and A3 and the possible states of nature S1, S2 and
S3 are given in the adjoining table.
States of nature Acts
A1 A2 A3
S1 -20 -50 200
S2 200 -100 -50
S3 400 600 300
The probabilities of the states of nature are 0.3, 0.4 and 0.3 respectively.
Determine the optimal act using the expectation principle.
2. Marketing staff of a certain industrial organization has submitted the following payoff table,
giving profits in million rupees, concerning a certain proposal depending upon the rate of
technological advance in the next three years:
Technological
Advance
Decision
Accept Reject
Much 2 3
Little 5 2
None -1 4
The probabilities are 0.2, 0.5 and 0.3 for Much, Little and None technological advance
respectively. What decision should be taken?
3. A physician purchases a particular vaccine on Monday of each week. The vaccine must be
used within the week following, otherwise it becomes worthless. The vaccine costs ₹ 2 per
dose and the physician charges ₹ 4 per dose. In the past weeks the physician has administered
the vaccine in the following quantities:
Dose per week 20 25 40 60
Number of weeks 5 15 25 5
On the basis of EMV, find how many doses the physician must purchase each week to
maximize his profits.
4. A producer of boats has estimated the following distribution of demand for a particular kind
of boat:
No. demanded 0 1 2 3 4 5 6
Probability 0.14 0.27 0.27 0.18 0.09 0.04 0.01
Each boat cost him ₹ 7,000 and he sells them for ₹ 10,000 each. Any boats that are left
unsold at the end of the season must be disposed of for ₹ 6,000 each. How many boats should
be in stock so as to maximize his expected profit?
5. A person wants to invest in one of the three alternative investment plans: Stock, Bonds,
Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The
payoff matrix based on three potential economic conditions is given in the adjoining table:
Alternative
Investment
Economic Conditions
High Growth (₹) Normal Growth (₹) Slow Growth (₹)
Stock 10,000 7,000 3,000
2. Bonds 8,000 6,000 1,000
Debentures 6,000 6,000 6,000
Determine the best investment plan using each of the following criteria:
(i) Laplace, (ii) Maximin, (iii) Maximax
6. Given is the following payoff matrix
States of Nature Probability Courses of Action
Do not expand Expand 200
units
Expand 400
units
High Demand 0.4 2,500 3,500 5,000
Medium Demand 0.4 2,500 3,500 2,500
Low Demand 0.2 2,500 1,500 1,000
What should be the decision if we use: (i) EMV criterion, (ii) The Maximin criterion, (iii)
The maximax criterion, (iv) Minimax regret criterion?
7. The research director of XYZ Pharmaceutical Laboratory has to decide about one of three
influenza vaccines (P1, P2, P3) which should be funded for mass production. Payoffs depend
upon the type of influenza outbreak (S1, S2, S3, S4) that is most persuasive in the next year.
The payoff matrix, with profits (in millions of rupees), is given below:
States of Nature Courses of Action
P1 P2 P3
S1 10 8 -15
S2 4 12 12
S3 0 -5 8
S4 -2 -10 8
Prior to acquiring any additional information about the occurrence of states of nature, the
director’s probability judgements are: P(S1) = 0.2 and P(S2) = 0.2, P(S3) = 0.5 and P(S4) =
0.1.
(i) If the director could consult an authority who could tell him which state will occur,
what is the expected value of this information using above payoff matrix.
(ii) Verify your answer by calculating EVPI from the loss matrix.
8. An executive has to make a decision. He has four alternatives D1, D2, D3 and D4. When the
decision has been made events may lead such that any of the four results may occur. The
results are R1, R2, R3 and R4. Probabilities of occurrence of these results are as follows:
R1 = 0.5, R2 = 0.2, R3 = 0.2 and R4 = 0.1
The matrix of payoff between the decision and the results is indicated in the adjoining table:
R1 R2 R3 R4
D1 14 9 10 5
D2 11 10 8 7
D3 9 10 10 11
D4 8 10 11 13
Show this decision situation in the form of a decision tree and indicate the most preferred
decision and corresponding expected value.
3. 9. A Finance Manager is considering drilling a well. In the past, only 70% of wells drilled were
successful at 20 metres depth in that area. Moreover on finding no water at 20 metres, some
persons in that area drilled it further up to 25 metres but only 20 % struck
10. Expected return (in million rupees) from the sale of three machines A, B and C under
expected market condition as poor (S1), Fair (S2) and Good (S3) are given in the following
table below:
Sales Courses of Action
Poor (S1) Fair (S2) Good (S3)
S1 0.5 1.0 1.5
S2 0 1.5 2.5
S3 -1.5 0.5 3.5
Chance of market at states S1, S2 and S3 are 30%, 50% and 20% respectively. But the
market research finds the actual chances of states of market as follows:
Actual State M1 (Poor) M2 (Fair) M3 (Good)
S1 0.7 0.2 0.1
S2 0.2 0.7 0.1
S3 0 0.2 0.8
Find (i) Conditional expected loss table
(ii) Expected Value of Perfect Information (EVPI).
(iii) Expected loss table on the basis of the results of market research.
(iv) Economic cost of market research
Illustration
Suppose a electrical good has a resource base to buy for resale purposes in a market, electric
irons in the range of 0 to 4. His resource base permits him to buy nothing or 1 or 2 or 3 or 4
units. These are his alternative courses of action or strategies. The demand for electric irons in
any month is something beyond his control and hence is a state of nature. Let us presume that the
4. dealer does not know how many units will be bought from him by the customers. The demand
could be anything from 0 to 4. The dealer can buy each unit of electric iron @ ₹ 40 and sell it at
₹ 45 each, his margin being ₹ 5 per unit. Assume the stock on hand is valueless. Portray in a
payoff table the EMV.
COMPUTATION OF EXPECTED MONETRAY VALUE (EMV)
States
of
nature
Probability Conditional Payoff (₹)
Courses of action
Expected Payoff (₹)
Courses of action
A1(0) A2(1) A3(2) A4(3) A5(4) A1(0) A2(1) A3(2) A4(3) A5(4)
(1) (2) (3) (4) (5) (6) (1) x
(2)
(1) x
(3)
(1) x
(4)
(1) x
(5)
(1) x
(6)
S1(0) 0.04 0 -40 -80 -120 -160 0 -1.6 -3.2 -4.8 -6.4
S2(1) 0.06 0 5 -35 -75 -115 0 0.30 -2.1 -4.5 -6.9
S3(2) 0.20 0 5 10 -30 -70 0 1.0 2.0 -6.0 -14.0
S4(3) 0.30 0 5 10 15 -25 0 1.5 3.0 4.5 -7.5
S5(4) 0.40 0 5 10 15 20 0 2.0 4.0 6.0 8.0
EMV 0 3.2 3.7 -4.8 -26.8
Conditional payoff value = (Marginal profit (Units sold) – (Marginal Loss) (Units not sold)
= (₹ 45 - ₹ 40) (Units sold) – (₹ 40)(Units not sold)
PAYOFF AND REGRET TABLE
States of
nature
(Probable
Demand)
Conditional Payoff (₹)
Courses of action (Strategies
Possible Supply)
Conditional Opportunity Loss (₹)
Courses of action (Strategies Possible Supply)
0 1 2 3 4 0 1 2 3 4
0 0 -40 -80 -120 -160 0 0 – (-40) = 40 0 – (-80) = 80 0 – (-120) = 120 0 – (-160) = 160
1 0 5 -35 -75 -115 5 – 0 = 5 5 – 5 = 0 5 – (-35) = 40 5 – (-75) = 80 5 – (-115) = 120
2 0 5 10 -30 -70 10 – 0 = 10 10 – 5 = 5 10 – 10 = 0 10 – (-30) = 40 10 – (-70) = 80
3 0 5 10 15 -25 15 – 0 = 15 15 – 5 = 10 15 – 10 = 5 15 – 15 = 0 15 – (-25) = 40
4 0 5 10 15 20 20 – 0 = 20 20 – 5 = 15 20 – 10 = 10 20 – 15 = 5 20 – 20 = 0
States of
nature
Probability Conditional Opportunity Loss (₹) Expected Opportunity Loss (₹)
Courses of action
0 1 2 3 4 0 1 2 3 4
0 0.04 0 40 80 120 160 0 1.6 3.2 4.8 6.4
1 0.06 5 0 40 80 120 0.3 0 2.4 4.8 7.2
2 0.20 10 5 0 40 80 2 1 0 8 16
3 0.30 15 10 5 0 40 4.5 3 1.5 0 12
4 0.40 20 15 10 5 0 8 6 4 2 0
Expected Opportunity Loss (EOL) 14.8 11.6 11.1 19.6 41.6
Decision Making under Uncertainty
Maximin
States of Nature
(Possible Demand)
Courses of Action (Possible Supply)
A1: 0 A2: 1 A3: 2 A4: 3 A5: 4
S1: 0
S2: 1
S3: 2
S4: 3
S5: 4
Minimum in
5. columns
Solutions
1. COMPUTATION OF EXPECTED MONETRAY VALUE (EMV)
States
of
Nature
(Sj)
Probability
P(S)
Conditional Payoff(₹)
Acts
Expected Payoff (₹)
Acts
A1 A2 A3 A1 A2 A3
S1 0.3 -20 -50 200 -6 -15 60
S2 0.4 200 -100 -50 80 -40 -20
S3 0.3 400 600 300 120 180 90
Expected Monetary Value (EMV) 194 125 130
The maximum value of EMV is corresponding to act A1. Hence, according to the EMV
criterion, the optimal act is A1.
2. COMPUTATION OF EMV FOR VARIOUS ACTS
Technological
Advance
Probability Conditional Payoff Expected Payoff
Accepting Rejecting Accepting Rejecting
Much 0.2 2 3 0.4 0.6
Little 0.5 5 2 2.5 1.0
None 0.3 -1 4 -0.3 2.8
Expected Monetary Value (EMV) 2.6 2.8
Since EMV of rejecting the proposal is 2.8 which is more than EMV of accepting the
proposal, the decision should be ‘reject the proposal’.
5. Let HG: High Growth, NG: Normal Growth, SG: Slow Growth
PAYOFF TABLE (in Rupees)
Act
(Investment
States of nature Row
Minimum
Row
Maximum
Row
Total
S1:
HG
S2: NG S3: SG
(1) (2) (3) (4) (5) (6) (7)
A1: Stocks 10,000 7,000 3,000 3,000 10,000 20,000
A2: Bonds 8,000 6,000 1,000 1,000 8,000 15,000
A3: Debentures 6,000 6,000 6,000 6,000 6,000 18,000
Probability 1/3 1/3 1/3 Column (5)
Max. = 6,000
Column (6)
Max. = 10,000
(i) Laplace Criterion
EMV (A1: Stocks) = ₹ 1/3(10,000 + 7,000 + 3,000) = ₹ 20,000/3 = ₹ 6,666.67
EMV (A2: Bonds) = ₹ 1/3(8,000 + 6,000 + 1,000) = ₹ 15,000/3 = ₹ 5,000
EMV (A3: Debentures) = ₹ 1/3(6,000 + 6,000 + 6,000) = ₹ 18,000/3 = ₹ 6,000
6. Max. (EMV) = ₹ 6,666.67 which corresponds to acts A1. Hence, under Laplace criterion act
A1: Stock, can be taken as the optimal act.
(ii) Maximin Criterion
From column (5) of the above Table, we get
Maximum (Minimum Payoffs) = ₹ 6,000, which corresponds to act A3.
Hence, under the Maximin criterion, act A3: Debenture is the optimal choice
(iii) Maximax Criterion
From column (6) of the above Table, we get
Maximum (Maximum Payoffs) = ₹ 10,000, which corresponds to act A1.
Hence, under the Maximax criterion, act A1: Stock is the optimal choice
6. Payoff Table
Act
(Investment
Probability Conditional Payoff (₹)
Courses of action
Expected Payoff (₹)
Courses of action
A1: Do
not
expand
A2:
Expand
200 units
A3:
Expand
400 units
A1: Do
not
expand
A2:
Expand
200 units
A3:
Expand
400 units
(1) (2) (3) (4) (1) x (2) (1) x (3) (1) x (4)
S1: High
Demand
0.4 2,500 3,500 5,000 1,000 1,400 2,000
S2: Medium
Demand
0.4 2,500 3,500 2,500 1,000 1,400 1,000
S3: Low
Demand
0.2 2,500 1,500 1,000 500 300 200
EMV 2,500 3,100 3,200
Minimum Payoff (₹) 2,500 1,500 1,000
Maximum Payoff (₹) 2,500 3,500 5,000
(i) EMV criterion thus suggests that we should decide to expand 400 units since EMV
3,200 is highest.
(ii) In the maximin criterion the strategy for which minimum payoff is maximum is
chosen. The minimum payoff values corresponding to the strategies: Do not expand,
Expand 200 units, and Expand 400 units, are 2,500; 1,500 and 1,000 respectively. Of
these payoffs 2,500 is maximum which corresponds to the strategy ‘Do not expand’.
Therefore, a decision maker using Maximin criterion would decide ‘Not to expand’.
Overall maximum payoff values (due to high demand) are ₹ 5,000 that corresponds to
the act – Expand 400 units. By using maximax criterion the decision maker would
decide ‘Expanding 400 units’.
Minimax Regret:
In this criterion profits are transformed into opportunity losses (or regret). A regret
matrix is obtained from the payoff matrix by subtracting each of the values in a row
from the largest payoff value in the row. Under this approach the decision – maker
identifies the maximum regret for each act and selects the act due to which maximum
7. regret value is minimum. This may be achieved by selecting the act which maximum
regret (i.e. column maximum of the regret matrix) is minimum.
Regret matrix of the previous payoff matrix is as follows:
States of Nature Probability Courses of Action (Possible Supply)
A1: Do not
Expand
A2: Expand
200 units
A3: Expand 400
units
S1: High Demand 0.4 5,000 – 2,500 =
2,500
5,000 – 3,500 =
1,500
5,000 – 5,000 = 0
S2: Medium
Demand
0.4 3,500 – 2,500 =
1,000
3,500 – 3,500 =
0
3,500 – 2,500 =
1,000
S3: Low Demand 0.2 2,500 – 2,500 = 0 2,500 – 1,500 =
1,000
2,500 – 1,000 =
1,500
Maximum Regret 2,500 1,500 1,500
The decision – maker must choose ‘Expand 200 units’ or ‘Expand 400 units’ for it
minimizes the maximum possible return.
7. COMPUTATION OF EXPECTED PAYOFF
Act
(Investment
Probability Conditional Payoff (₹)
Courses of action
Expected Payoff (₹)
Courses of action
P1 P2 P3 P1 P2 P3
(1) (2) (3) (4) (1) x (2) (1) x (3) (1) x (4)
S1 0.2 10 8 -15 2.0 1.6 -3.0
S2 0.2 4 12 12 0.8 2.4 2.4
S3 0.5 0 -5 8 0 -2.5 4.0
S4 0.1 -2 -10 8 -0.2 -1.0 0.8
EMV 2.6 0.5 4.2
From the table, we find that the highest prior expected value is 4.2 (million rupees). Prior
expected value of selecting the optimal act after learning which state will occur
= 10 x 0.2 + 12 x 0.2 + 8 x 0.5 + 8 x 0.1 = 9.2
Expected value of perfect information = 9.2 – 4.2 = ₹ 5 million
8. Decision Tree Diagram
D1
D2
D3
D4
R1
R2
R3
R4
8. Monetary Value Prob. Expected Value EMV
D1
14 0.5 7.0
11.3
9 0.2 1.8
10 0.2 2.0
5 0.1 0.5
D2
11 0.5 5.5
9.8
10 0.2 2.0
8 0.2 1.6
7 0.1 0.7
D3
9 0.5 4.5
9.6
10 0.2 2.0
10 0.2 2.0
11 0.1 1.1
D4
8 0.5 4.0
9.5
10 0.2 2.0
11 0.2 2.2
13 0.1 1.3
The most preferred decision at the decision node 1 is found by calculating expected value of each decision branch
and selecting the path (course of action) with high value.
Since node D1 has the highest EMV, the decision at node A will be choose the course of action D1.
States of Nature Probability Courses of Action (Possible Supply)
A1: Do not
Expand
A2: Expand
200 units
A3: Expand 400
units
S1: High Demand 0.4 5,000 – 2,500 =
2,500
5,000 – 3,500 =
1,500
5,000 – 5,000 = 0
S2: Medium
Demand
0.4 3,500 – 2,500 =
1,000
3,500 – 3,500 =
0
3,500 – 2,500 =
1,000
S3: Low Demand 0.2 2,500 – 2,500 = 0 2,500 – 1,500 =
1,000
2,500 – 1,000 =
1,500
Maximum Regret 2,500 1,500 1,500
9. (i) (a) The conditional profit table is given below:
States of
Nature
Prior
Probability
Courses of Action (Buying Decision)
A B C
S1: Poor 0.30 0.5 0 -1.5
S2: Fair 0.50 1.0 1.5 0.5
S3: Good 0.20 1.5 2.5 3.5
9. (b) Subtracting the payoffs against each event from the largest payoffs (market*) gives the conditional
opportunity losses (COL) as shown in the table below:
Act
(Investment
Probability Conditional Loss (₹)
Courses of action
Expected Opportunity Loss (₹)
Courses of action
A B C A B C
S1 0.30 0 0.5 2.0 0 0.15 0.60
S2 0.50 0.5 0 1.0 0.25 0 0.50
S3 0.20 2.0 1.0 0 0.40 0.20 0
EMV 0.65 0.35 1.10
(ii) EOL for machine B is least (0.35). Under perfect information, the opportunity loss would be zero, so
the expected value under EVPI is 0.35.
(iii) The margin and joint prob. Is computed as under:
Act
(Investment
Probability Conditional Prob.
Courses of action
Joint Prob.
Courses of action
S1 0.30 0.7 0.2 0.1 0.21 0.06 0.03
S2 0.50 0.2 0.7 0.1 0.10 0.35 0.05
S3 0.20 0 0.2 0.8 0 0.04 0.16
Total P(M1)
= 0.31
P(M2) =
0.45
P(M3) =
0.24
Revising the prior prob with the help of Bayes’ Theorem, the reqd. posterior prob. Are computed as
below:
Outcome Prob. States of nature Posterior prob.
M1 0.31 S1 0.21/0.31 = 0.677
S2 0.10/0.31 = 0.323
S3 0/0.31 = 0
M2 0.45 S1 0.06/0.45 = 0.133
S2 0.35/0.45 = 0.778
S3 0.04/0.45 = 0.089
M3 0.24 S1 0.03/0.24 = 0.125
S2 0.05/0.24 = 0.208
S3 0.16/0.24 = 0.667
Act
(Investment
I II
Prob COL EOL A B C
S1 0 0.5 2.0 0 0.15 0.60
S2 0.5 0 1.0 0.25 0 0.50
S3 2.0 1.0 0 0.40 0.20 0