This document contains 70 multiple choice questions related to decision science concepts. Some key concepts covered in the questions include linear programming models, transportation problems, assignment problems, and queuing systems. The questions test understanding of topics like defining decision variables, characteristics and assumptions of linear programming models, solving transportation and assignment problems using different methods, and identifying properties of queuing systems.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
This document provides an overview of linear programming and the graphical method for solving two-variable linear programming problems. It defines linear programming as involving maximizing or minimizing a linear objective function subject to linear constraints. The graphical method is described as using a graph in the first quadrant to find the feasible region defined by the constraints and then determine the optimal solution by evaluating the objective function at the boundary points. An example problem is presented to demonstrate finding the feasible region and optimal solution graphically. Special cases like alternative optima and infeasible/unbounded problems are also mentioned.
The document provides an overview of operations research, including:
- Operations research developed during World War II to allocate scarce military resources efficiently. It has since been applied to optimize operations in many industries.
- Mathematical modeling involves representing real-world problems mathematically to enable analysis and optimization using tools like linear programming.
- Linear programming formulates problems as mathematical models to find optimal solutions while respecting constraints, and was pioneered in the 1930s-40s. It has become one of the most important developments in 20th century mathematics.
Game theory is the study of strategic decision making between two or more players under conditions of conflict or competition. A game involves players following a set of rules and receiving payoffs depending on the strategies chosen. Strategies include pure strategies that always select a particular action and mixed strategies that randomly select among pure strategies. The optimal strategies are those that maximize the minimum payoff for one player and minimize the maximum payoff for the other player. When the maximin and minimax values are equal, there is a saddle point representing the optimal strategies for both players.
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
The document discusses decision theory and decision trees. It introduces decision making under certainty, risk, and uncertainty. It defines elements related to decisions like goals, courses of action, states of nature, and payoffs. It also discusses concepts like expected monetary value, expected profit with perfect information, expected value of perfect information, and expected opportunity loss. Examples are provided to demonstrate calculating these metrics. Finally, it provides an overview of how to construct a decision tree, including defining the different node types and how to calculate values within the tree.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
This document provides an overview of linear programming and the graphical method for solving two-variable linear programming problems. It defines linear programming as involving maximizing or minimizing a linear objective function subject to linear constraints. The graphical method is described as using a graph in the first quadrant to find the feasible region defined by the constraints and then determine the optimal solution by evaluating the objective function at the boundary points. An example problem is presented to demonstrate finding the feasible region and optimal solution graphically. Special cases like alternative optima and infeasible/unbounded problems are also mentioned.
The document provides an overview of operations research, including:
- Operations research developed during World War II to allocate scarce military resources efficiently. It has since been applied to optimize operations in many industries.
- Mathematical modeling involves representing real-world problems mathematically to enable analysis and optimization using tools like linear programming.
- Linear programming formulates problems as mathematical models to find optimal solutions while respecting constraints, and was pioneered in the 1930s-40s. It has become one of the most important developments in 20th century mathematics.
Game theory is the study of strategic decision making between two or more players under conditions of conflict or competition. A game involves players following a set of rules and receiving payoffs depending on the strategies chosen. Strategies include pure strategies that always select a particular action and mixed strategies that randomly select among pure strategies. The optimal strategies are those that maximize the minimum payoff for one player and minimize the maximum payoff for the other player. When the maximin and minimax values are equal, there is a saddle point representing the optimal strategies for both players.
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
The document discusses decision theory and decision trees. It introduces decision making under certainty, risk, and uncertainty. It defines elements related to decisions like goals, courses of action, states of nature, and payoffs. It also discusses concepts like expected monetary value, expected profit with perfect information, expected value of perfect information, and expected opportunity loss. Examples are provided to demonstrate calculating these metrics. Finally, it provides an overview of how to construct a decision tree, including defining the different node types and how to calculate values within the tree.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
The document summarizes different methods for solving transportation problems in linear programming, which involve distributing goods from multiple sources to multiple destinations at minimum cost. It describes three common methods - the North-West Corner method, Least-Cost method, and Vogel's Approximation Method. Each method involves iteratively allocating quantities to routes based on costs until all supply is distributed and demand is met. Examples are provided to illustrate how each method solves a transportation problem step-by-step.
This document summarizes key concepts in unconstrained optimization of functions with two variables, including:
1) Critical points are found by taking the partial derivatives and setting them equal to zero, generalizing the first derivative test for single-variable functions.
2) The Hessian matrix generalizes the second derivative, with its entries being the partial derivatives evaluated at a critical point.
3) The second derivative test classifies critical points as local maxima, minima or saddle points based on the signs of the Hessian matrix's eigenvalues.
4) Taylor polynomial approximations in two variables involve partial derivatives up to second order, analogous to single-variable Taylor series.
5) An example classifies the critical points
Game theory is the study of how optimal strategies are formulated in conflict situations involving two or more rational opponents with competing interests. It considers how the strategies of one player will impact the outcomes for others. Game theory models classify games based on the number of players, whether the total payoff is zero-sum, and the types of strategies used. The minimax-maximin principle provides a way to determine optimal strategies without knowing the opponent's strategy by having each player maximize their minimum payoff or minimize their maximum loss. A saddle point exists when the maximin and minimax values are equal, indicating optimal strategies for both players.
Linear programming is a mathematical optimization technique used to maximize or minimize an objective function subject to constraints. It involves decision variables, an objective function that is a linear combination of the variables, and linear constraints. The key assumptions of linear programming are certainty, divisibility, additivity, and linearity. It allows improving decision quality through cost-benefit analysis and considers multiple possible solutions. However, it has disadvantages like fractional solutions, complex modeling, and inability to directly address time effects.
Game theory is a mathematical approach that analyzes strategic interactions between parties. It is used to understand situations where decision-makers are impacted by others' choices. A game has players, strategies, payoffs, and information. The Nash equilibrium predicts outcomes as the strategies where no player benefits by changing alone given others' choices. For example, in the Prisoner's Dilemma game about two suspects, confessing dominates remaining silent no matter what the other does, leading both to confess for a worse joint outcome than remaining silent.
Linear Programming Problems : Dr. Purnima PanditPurnima Pandit
Linear programming problems involve optimizing an objective function subject to constraints on variables. They can be modeled and solved using techniques like the simplex method. The simplex method works by moving from one basic feasible solution to an adjacent extreme point through an exchange of variables in and out of the basis. It begins with an initial basic feasible solution and proceeds iteratively until an optimal solution is reached.
Let x1 = Number of units of M1 produced
x2 = Number of units of M2 produced
ii) Write the constraints:
4x1 + 2x2 ≤ 80 (Grinding constraint)
2x1 + 5x2 ≤ 180 (Polishing constraint)
x1, x2 ≥ 0
iii) Write the objective function:
Maximize Z = 3x1 + 4x2
iv) Solve the LP problem graphically or by simplex method to find the optimal solution.
GAME THEORY - Problems on Dominance principleSundar B N
This document discusses the principle of dominance in game theory. The principle states that if one strategy gives a player a better outcome than another strategy in all situations, the inferior strategy can be eliminated. There are two steps to applying the principle of dominance: 1) compare rows and eliminate rows with lower values, and 2) compare columns and eliminate columns with lower values. This process simplifies the game matrix until a solution can be found using saddle point or odds methods. An example problem demonstrates applying the dominance principle to eliminate inferior strategies row-by-row and column-by-column until the game is solved.
This document discusses three main methods for solving operational research (OR) models: analytical methods, iterative methods, and the Monte-Carlo method. Analytical methods use tools like calculus and graphs to find closed-form solutions. Iterative methods are used when analytical methods are too complex; they start with a trial solution and iteratively improve it until optimal. The Monte-Carlo method experiments on a model by inserting random variable values and observing their effects on the criterion over time.
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
This document summarizes integer programming and two methods for solving integer programming problems: Gomory's fractional cut method and branch and bound method.
Gomory's fractional cut method involves first solving the integer programming problem as a linear programming problem by ignoring integer restrictions. If the solution is non-integer, a new constraint called a fractional cut is generated and added to obtain an integer solution. This process repeats until an optimal integer solution is found.
Branch and bound is a search method that involves constructing a tree by branching on integer variables. It prunes branches that cannot produce better solutions than the best known solution to reduce computation.
The document provides an example to illustrate Gomory's fractional cut method and its
The document discusses different classifications and concepts related to game theory, including:
1) Games can be zero-sum, where one player's gains equal another's losses, or non-zero-sum. They can involve 2 players or more.
2) Strategies can be pure, where players always choose the same action, or mixed, where players vary their actions randomly.
3) A payoff matrix outlines the potential payoffs for each combination of strategies between players in a 2-person, zero-sum game. The value of the game is when the maximin and minimax values are equal.
Transportation Problem In Linear ProgrammingMirza Tanzida
This work is an assignment on the course of 'Mathematics for Decision Making'. I think, it will provide some basic concept about transportation problem in linear programming.
This document provides an overview of Markov Decision Processes (MDPs) and related concepts in decision theory and reinforcement learning. It defines MDPs and their components, describes algorithms for solving MDPs like value iteration and policy iteration, and discusses extensions to partially observable MDPs. It also briefly mentions dynamic Bayesian networks, the dopaminergic system, and its role in reinforcement learning and decision making.
Linear programming deals with optimizing a linear objective function subject to linear constraints. It involves determining the values of decision variables to maximize or minimize the objective function. The general linear programming model involves maximizing or minimizing a linear combination of n decision variables subject to m linear constraints, along with non-negativity restrictions on the decision variables. Formulating a linear programming problem involves identifying decision variables, expressing constraints and the objective function linearly in terms of the variables, and adding non-negativity restrictions.
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 introduces nonlinear programming (NLP) and contrasts it with linear programming (LP). NLP involves optimization problems with nonlinear objective functions or constraints, which are more difficult to solve than LP problems. Examples are provided to illustrate how NLP searches can fail to find the global optimum. The document also formulates two NLP examples: one involving profit maximization for chair pricing, and another involving investment portfolio selection to minimize risk.
Decisions Under Risk and Uncertainty - UP.pptxEileenPelo1
This document discusses decision-making under risk and uncertainty. It defines decision-making as selecting an action from alternatives and outlines an eight step process for decision-making. It distinguishes between risk, where probabilities can be assigned to possible outcomes, and uncertainty, where outcomes cannot be probabilistically defined. When managers lack perfect information, they face risk. Decision-making techniques discussed include risk analysis, decision trees, and preference theory. Key aspects of decision problems are identified as the decision-maker, alternatives, possible events or outcomes, and consequences or payoffs. Payoff matrices are presented as a tool to summarize interactions between alternatives and events. Maximizing the best payoff, minimizing the worst payoff, and minimizing maximum regret are presented
This document discusses nonlinear programming (NLP) problems. NLP problems involve objective functions and/or constraints that contain nonlinear terms, making them more difficult to solve than linear programs. While exact solutions cannot always be found, algorithms can typically find approximate solutions within an acceptable error range of the optimum. However, for some NLP problems there is no reliable way to find the global maximum, as algorithms may stop at a local maximum instead. The document describes different types of NLP problems and techniques for solving them, including using Excel Solver with multiple starting values to attempt finding the global rather than just local optima.
This document contains 25 multiple choice questions about quantitative methods in management science. The questions cover topics such as linear programming, transportation problems, critical path method, and PERT networks. Specifically, questions ask about slack variables in linear programming models, the difference between transportation and assignment problems, calculating expected activity times when uncertain, and identifying the critical path as the longest path through a CPM/PERT network.
This document contains 25 multiple choice questions about quantitative methods and management science concepts. The questions cover topics such as management science, linear programming, transportation problems, network models, and critical path analysis. Key concepts addressed include problem identification, quantitative analysis approaches, slack variables, duality theory, network flows, and determining the critical path in a project network diagram.
The document summarizes different methods for solving transportation problems in linear programming, which involve distributing goods from multiple sources to multiple destinations at minimum cost. It describes three common methods - the North-West Corner method, Least-Cost method, and Vogel's Approximation Method. Each method involves iteratively allocating quantities to routes based on costs until all supply is distributed and demand is met. Examples are provided to illustrate how each method solves a transportation problem step-by-step.
This document summarizes key concepts in unconstrained optimization of functions with two variables, including:
1) Critical points are found by taking the partial derivatives and setting them equal to zero, generalizing the first derivative test for single-variable functions.
2) The Hessian matrix generalizes the second derivative, with its entries being the partial derivatives evaluated at a critical point.
3) The second derivative test classifies critical points as local maxima, minima or saddle points based on the signs of the Hessian matrix's eigenvalues.
4) Taylor polynomial approximations in two variables involve partial derivatives up to second order, analogous to single-variable Taylor series.
5) An example classifies the critical points
Game theory is the study of how optimal strategies are formulated in conflict situations involving two or more rational opponents with competing interests. It considers how the strategies of one player will impact the outcomes for others. Game theory models classify games based on the number of players, whether the total payoff is zero-sum, and the types of strategies used. The minimax-maximin principle provides a way to determine optimal strategies without knowing the opponent's strategy by having each player maximize their minimum payoff or minimize their maximum loss. A saddle point exists when the maximin and minimax values are equal, indicating optimal strategies for both players.
Linear programming is a mathematical optimization technique used to maximize or minimize an objective function subject to constraints. It involves decision variables, an objective function that is a linear combination of the variables, and linear constraints. The key assumptions of linear programming are certainty, divisibility, additivity, and linearity. It allows improving decision quality through cost-benefit analysis and considers multiple possible solutions. However, it has disadvantages like fractional solutions, complex modeling, and inability to directly address time effects.
Game theory is a mathematical approach that analyzes strategic interactions between parties. It is used to understand situations where decision-makers are impacted by others' choices. A game has players, strategies, payoffs, and information. The Nash equilibrium predicts outcomes as the strategies where no player benefits by changing alone given others' choices. For example, in the Prisoner's Dilemma game about two suspects, confessing dominates remaining silent no matter what the other does, leading both to confess for a worse joint outcome than remaining silent.
Linear Programming Problems : Dr. Purnima PanditPurnima Pandit
Linear programming problems involve optimizing an objective function subject to constraints on variables. They can be modeled and solved using techniques like the simplex method. The simplex method works by moving from one basic feasible solution to an adjacent extreme point through an exchange of variables in and out of the basis. It begins with an initial basic feasible solution and proceeds iteratively until an optimal solution is reached.
Let x1 = Number of units of M1 produced
x2 = Number of units of M2 produced
ii) Write the constraints:
4x1 + 2x2 ≤ 80 (Grinding constraint)
2x1 + 5x2 ≤ 180 (Polishing constraint)
x1, x2 ≥ 0
iii) Write the objective function:
Maximize Z = 3x1 + 4x2
iv) Solve the LP problem graphically or by simplex method to find the optimal solution.
GAME THEORY - Problems on Dominance principleSundar B N
This document discusses the principle of dominance in game theory. The principle states that if one strategy gives a player a better outcome than another strategy in all situations, the inferior strategy can be eliminated. There are two steps to applying the principle of dominance: 1) compare rows and eliminate rows with lower values, and 2) compare columns and eliminate columns with lower values. This process simplifies the game matrix until a solution can be found using saddle point or odds methods. An example problem demonstrates applying the dominance principle to eliminate inferior strategies row-by-row and column-by-column until the game is solved.
This document discusses three main methods for solving operational research (OR) models: analytical methods, iterative methods, and the Monte-Carlo method. Analytical methods use tools like calculus and graphs to find closed-form solutions. Iterative methods are used when analytical methods are too complex; they start with a trial solution and iteratively improve it until optimal. The Monte-Carlo method experiments on a model by inserting random variable values and observing their effects on the criterion over time.
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
This document summarizes integer programming and two methods for solving integer programming problems: Gomory's fractional cut method and branch and bound method.
Gomory's fractional cut method involves first solving the integer programming problem as a linear programming problem by ignoring integer restrictions. If the solution is non-integer, a new constraint called a fractional cut is generated and added to obtain an integer solution. This process repeats until an optimal integer solution is found.
Branch and bound is a search method that involves constructing a tree by branching on integer variables. It prunes branches that cannot produce better solutions than the best known solution to reduce computation.
The document provides an example to illustrate Gomory's fractional cut method and its
The document discusses different classifications and concepts related to game theory, including:
1) Games can be zero-sum, where one player's gains equal another's losses, or non-zero-sum. They can involve 2 players or more.
2) Strategies can be pure, where players always choose the same action, or mixed, where players vary their actions randomly.
3) A payoff matrix outlines the potential payoffs for each combination of strategies between players in a 2-person, zero-sum game. The value of the game is when the maximin and minimax values are equal.
Transportation Problem In Linear ProgrammingMirza Tanzida
This work is an assignment on the course of 'Mathematics for Decision Making'. I think, it will provide some basic concept about transportation problem in linear programming.
This document provides an overview of Markov Decision Processes (MDPs) and related concepts in decision theory and reinforcement learning. It defines MDPs and their components, describes algorithms for solving MDPs like value iteration and policy iteration, and discusses extensions to partially observable MDPs. It also briefly mentions dynamic Bayesian networks, the dopaminergic system, and its role in reinforcement learning and decision making.
Linear programming deals with optimizing a linear objective function subject to linear constraints. It involves determining the values of decision variables to maximize or minimize the objective function. The general linear programming model involves maximizing or minimizing a linear combination of n decision variables subject to m linear constraints, along with non-negativity restrictions on the decision variables. Formulating a linear programming problem involves identifying decision variables, expressing constraints and the objective function linearly in terms of the variables, and adding non-negativity restrictions.
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 introduces nonlinear programming (NLP) and contrasts it with linear programming (LP). NLP involves optimization problems with nonlinear objective functions or constraints, which are more difficult to solve than LP problems. Examples are provided to illustrate how NLP searches can fail to find the global optimum. The document also formulates two NLP examples: one involving profit maximization for chair pricing, and another involving investment portfolio selection to minimize risk.
Decisions Under Risk and Uncertainty - UP.pptxEileenPelo1
This document discusses decision-making under risk and uncertainty. It defines decision-making as selecting an action from alternatives and outlines an eight step process for decision-making. It distinguishes between risk, where probabilities can be assigned to possible outcomes, and uncertainty, where outcomes cannot be probabilistically defined. When managers lack perfect information, they face risk. Decision-making techniques discussed include risk analysis, decision trees, and preference theory. Key aspects of decision problems are identified as the decision-maker, alternatives, possible events or outcomes, and consequences or payoffs. Payoff matrices are presented as a tool to summarize interactions between alternatives and events. Maximizing the best payoff, minimizing the worst payoff, and minimizing maximum regret are presented
This document discusses nonlinear programming (NLP) problems. NLP problems involve objective functions and/or constraints that contain nonlinear terms, making them more difficult to solve than linear programs. While exact solutions cannot always be found, algorithms can typically find approximate solutions within an acceptable error range of the optimum. However, for some NLP problems there is no reliable way to find the global maximum, as algorithms may stop at a local maximum instead. The document describes different types of NLP problems and techniques for solving them, including using Excel Solver with multiple starting values to attempt finding the global rather than just local optima.
This document contains 25 multiple choice questions about quantitative methods in management science. The questions cover topics such as linear programming, transportation problems, critical path method, and PERT networks. Specifically, questions ask about slack variables in linear programming models, the difference between transportation and assignment problems, calculating expected activity times when uncertain, and identifying the critical path as the longest path through a CPM/PERT network.
This document contains 25 multiple choice questions about quantitative methods and management science concepts. The questions cover topics such as management science, linear programming, transportation problems, network models, and critical path analysis. Key concepts addressed include problem identification, quantitative analysis approaches, slack variables, duality theory, network flows, and determining the critical path in a project network diagram.
The document provides rules and sample questions for a QT Quiz. It states there will be 6 rounds with 2 questions per round, each question is worth 2 marks. No negative marking. Time limit is 50 seconds per question and questions cannot be passed. There may be a bonus round depending on time. Sample questions provided cover topics like linear programming, transportation problems, constraints, simplex method, etc.
This document contains a question bank with multiple choice questions related to operations research. It covers topics in linear programming problems (LPP) such as the definition of an LPP, feasible solutions, graphical representation, simplex method, objective functions, constraints, unbounded/bounded solutions, degenerate solutions, and slack and surplus variables. There are 27 total multiple choice questions across two units related to modeling problems as LPPs and using the simplex method to solve LPPs.
This document contains questions and answers related to the key concepts in linear programming. It discusses topics like shadow prices, the role of topology in linear programming, goal programming for problems with multiple objectives, and the simplex method for solving linear programming problems. Several examples of linear programming problems are also provided relating to production planning, hospital management, and repellent distribution.
This document contains questions and answers related to the key concepts in linear programming. It discusses topics like shadow prices, the role of topology in linear programming, goal programming for problems with multiple objectives, and the simplex method for solving linear programming problems. Several examples of linear programming problems are also provided relating to production planning, hospital management, and repellent distribution.
Spreadsheet Modeling and Decision Analysis A Practical Introduction to Busine...rikujoxizi
The document discusses key concepts from Chapter 1 of the textbook, including:
- The essence of decision analysis is choosing the best course of action among alternatives.
- Modeling fits into the problem-solving process by helping to generate and evaluate alternatives to analyze the problem.
- The goal of modeling is to help decision makers make good choices, not ensure optimality or determine feasibility.
This document contains a chapter summary for a quantitative analysis textbook. It includes 54 multiple choice questions covering topics related to linear programming models, including graphical and computer solution methods. Key topics assessed include formulating linear programming problems, the requirements and assumptions of linear programs, graphical solutions, special cases like infeasibility and redundancy, and sensitivity analysis.
This document contains a chapter summary for a quantitative analysis textbook. It includes 54 multiple choice questions covering topics related to linear programming models, including graphical and computer solution methods. Key topics assessed include formulating linear programming problems, the requirements and assumptions of linear programs, graphical solutions, special cases like infeasibility and redundancy, and sensitivity analysis.
Pdf smda6e-chapter-04-mathematical-optimization-loss-functionSou Tibon
This document contains 50 multiple choice questions about sensitivity analysis and the simplex method for linear programming models. It covers topics like sensitivity analysis reports in Risk Solver Platform, shadow prices, reduced costs, allowable increases/decreases, and interpreting outputs to determine optimal objective function values or coefficients that will change the optimal solution. The questions provide examples of linear programming outputs and ask the test taker to interpret the results.
This document contains a question bank for a viva on the quantitative techniques course Quantitative Techniques in Management (KMB206). It includes 63 multiple choice questions across two units - Introduction to Operations Research and Linear Programming Problem. The questions cover key concepts in operations research models like linear programming, transportation models, and queuing theory. They also cover linear programming topics such as the objective function, constraints, graphical and algebraic solution methods, and the simplex method.
This document contains questions and answers related to classification, regression, supervised learning, unsupervised learning, and reinforcement learning techniques. It also covers dimensionality reduction methods like principal component analysis and t-distributed stochastic neighbor embedding. Key concepts covered include classification vs regression problems, supervised vs unsupervised vs reinforcement learning, and the goals and techniques involved in dimensionality reduction.
This document contains a quiz for a course on integer linear programming (MAT 540). It consists of 20 multiple choice questions testing concepts related to integer programming models like total, 0-1, and mixed; the branch and bound solution method; and properties of integer programming problems and their linear programming relaxations. Correct answers are provided for each question.
Similar to Decision science/ Operations Research MCQ by Prof. Sujeet Tambe (20)
The document discusses registration thresholds and eligibility criteria under the GST law in India, including:
- Small businesses with annual turnover less than Rs. 20 lakhs are exempt from tax payment. Some northern states have a lower Rs. 10 lakhs threshold.
- Businesses must register if their annual turnover exceeds the threshold amount or they make inter-state supplies, even if turnover is below the limit. Certain other categories like e-commerce operators must also register.
- Small businesses with annual turnover up to Rs. 75 lakhs can opt for the GST composition scheme and pay a lower tax rate. Certain supplier types providing inter-state supplies cannot opt for this scheme.
- Pro
This document discusses indirect taxes in India, including goods and services tax (GST). It provides examples of common indirect taxes like excise duty, VAT, customs duty, and entertainment tax. It notes benefits of indirect taxes like contribution from the poor, convenience, easy collection, and being equitable. The document also outlines the history and implementation of GST in India from 2006 to 2017. When first introduced on July 1, 2017, GST had five tax slabs of 0%, 5%, 12%, 18%, and 28% for various goods and services. The tax rates were later revised lower for some items on January 25, 2018.
The document discusses the results of a study on the impact of COVID-19 lockdowns on air pollution. Researchers found that lockdowns led to significant short-term reductions in nitrogen dioxide and fine particulate matter pollution globally as human activity declined. However, the impacts on air quality were temporary and pollution levels rebounded once lockdowns were lifted and human activity resumed.
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Making meditation a part of a daily routine, even if just 10-15 minutes per day, can have mental and physical health benefits over time by helping people feel more relaxed and better able to handle life's stresses.
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Studies have shown that meditating for just 10-20 minutes per day can have significant positive impacts on both mental and physical health over time.
Business research methods are systematic activities undertaken to increase knowledge. Research is needed to make informed business decisions and solve problems. Good research is guided by a clear question or problem, has a specific plan, interprets data to resolve the issue, and is cyclical in nature. Decision support systems and business intelligence systems help managers make decisions by providing access to large data volumes and using analytical models to identify patterns and trends. These systems support a variety of decision processes without making the final decision.
1. Measurement is the foundation of scientific investigation and involves assigning numbers or symbols to characteristics of objects.
2. There are four levels of measurement: nominal, ordinal, interval, and ratio. Nominal involves classification while ordinal captures ordering. Interval captures equal distances between intervals and ratio includes having a true zero point.
3. Reliability and validity are important for ensuring measurements accurately capture the construct being measured. Reliability looks at consistency over time, across items, and between raters. Validity compares measurements to conceptual definitions and whether scores relate to other expected outcomes.
This document provides an overview of exploratory research design. It discusses several techniques used in exploratory research, including experience surveys, focus groups, and projective techniques. Experience surveys involve speaking to knowledgeable individuals through unstructured interviews to explore and understand issues. Focus groups bring together a small group of similar individuals to discuss a topic of interest moderated by a facilitator. Projective techniques use indirect methods to uncover underlying motives and intentions by having participants project their own attitudes onto the research subject. Exploratory research is used to gain initial insights and better define problems when issues are not yet clearly understood.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
Marketing Management MCQ by Prof. Sujeet TambeSUJEET TAMBE
The document contains 45 multiple choice questions about marketing management and the product life cycle prepared by Assistant Professor Sujeet Tambe. The questions cover topics such as the 4 P's of marketing, pricing strategies, the stages of the product life cycle including introduction, growth, maturity and decline, new product development processes, and the functions of packaging and labeling. The MCQ questions are intended to test marketing students' understanding of fundamental marketing concepts.
Leading Change_ Unveiling the Power of Transformational Leadership Style.pdfEnterprise Wired
In this comprehensive guide, we delve into the essence of transformational leadership style, its core principles, key characteristics, and its transformative impact on organizational culture and outcomes.
A comprehensive-study-of-biparjoy-cyclone-disaster-management-in-gujarat-a-ca...Samirsinh Parmar
Disaster management;
Cyclone Disaster Management;;
Biparjoy Cyclone Case Study;
Meteorological Observations;
Best practices in Disaster Management;
Synchronization of Agencies;
GSDMA in Cyclone disaster Management;
History of Cyclone in Arabian ocean;
Intensity of Cyclone in Gujarat;
Cyclone preparedness;
Miscellaneous observations - Biparjoy cyclone;
Role of social Media in Disaster Management;
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solutions that help the organization achieve sustainable growth. Therefore, the purpose of this
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Originally presented at XP2024 Bolzano
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The Ready-Made Garments (RMG) industry in Bangladesh is a cornerstone of the economy, but increasing costs and stagnant productivity pose significant challenges to profitability. This study explores the implementation of Lean Management in the Sampling Section of RMG factories to enhance productivity. Drawing from a comprehensive literature review, theoretical framework, and action research methodology, the study identifies key areas for improvement and proposes solutions.
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Decision science/ Operations Research MCQ by Prof. Sujeet Tambe
1. Decision Sciences MCQ by Prof. Sujeet Tambe
Decision Science MCQ by Prof. Sujeet Tambe Page 1
MULTIPLE CHOICE QUESTIONS
DECISION SCIENCE
1. Decision Science approach is
a. Multi-disciplinary
b. Scientific
c. Intuitive
d. All of the above
2. For analyzing a problem, decision-makers should study
a. Its qualitative aspects
b. Its quantitative aspects
c. Both a & b
d. Neither a nor b
3. Decision variables are
a. Controllable
b. Uncontrollable
c. Parameters
d. None of the above
4. A model is
a. An essence of reality
b. An approximation
c. An idealization
d. All of the above
5. Managerial decisions are based on
a. An evaluation of quantitative data
b. The use of qualitative factors
c. Results generated by formal models
d. All of the above
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6. The use of decision models
a. Is possible when the variables value is known
b. Reduces the scope of judgement & intuition known with certainty in decision-
making
c. Require the use of computer software
d. None of the above
7. Every mathematical model
a. Must be deterministic
b. Requires computer aid for its solution
c. Represents data in numerical form
d. All of the above
8. A physical model is example of
a. An iconic model
b. An analogue model
c. A verbal model
d. A mathematical model
9. An optimization model
a. Provides the best decision
b. Provides decision within its limited context
c. Helps in evaluating various alternatives
d. All of the above
10. The quantitative approach to decision analysis is a
a. Logical approach
b. Rational approach
c. Scientific approach
d. All of the above
11. The qualitative approach to decision analysis relies on
a. Experience
b. Judgement
c. Intuition
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d. All of the above
12. The mathematical model of an LP problem is important because
a. It helps in converting the verbal description & numerical data into
mathematical expression
b. Decision-makers prefer to work with formal models
c. It captures the relevant relationship among decision factors
d. It enables the use of algebraic technique
13. Linear programming is a
a. Constrained optimization technique
b. Technique for economic allocation of limited resources
c. Mathematical technique
d. All of the above
14. A constraint in an LP model restricts
a. Value of objective function
b. Value of a decision variable
c. Use of the available resources
d. All of the above
15. The distinguishing feature of an LP model is
a. Relationship among all variables is linear
b. It has single objective function & constraints
c. Value of decision variables is non-negative
d. All of the above
16. Constraints in an LP model represents
a. Limitations
b. Requirements
c. Balancing limitations & requirements
d. All of the above
17. Non-negativity condition is an important component of LP model because
a. Variables value should remain under the control of the decision-maker
b. Value of variables make sense & correspond to real-world problems
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c. Variables are interrelated in terms of limited resources
d. None of the above
18. Before formulating a formal LP model, it is better to
a. Express each constrain in words
b. Express the objective function in words
c. Verbally identify decision variables
d. All of the above
19. Maximization of objective function in an LP model means
a. Value occurs at allowable set of decisions
b. Highest value is chosen among allowable decisions
c. Neither of above
d. Both a & b
20. Which of the following is not a characteristic of the LP model
a. Alternative courses of action
b. An objective function of maximization type
c. Limited amount of resources
d. Non-negativity condition on the value of decision variables.
21. The best use of linear programming technique is to find an optimal use of
a. Money
b. Manpower
c. Machine
d. All of the above
22. Which of the following is not a characteristic of the LP
a. Resources must be limited
b. Only one objective function
c. Parameters value remains constant during the planning period
d. The problem must be of minimization type
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23. Non-negativity condition in an LP model implies
a. A positive coefficient of variables in objective function
b. A positive coefficient of variables in any constraint
c. Non-negative value of resources
d. None of the above
24. Which of the following is an assumption of an LP model
a. Divisibility
b. Proportionality
c. Additivity
d. All of the above
25. Which of the following is a limitation associated with an LP model
a. The relationship among decision variables in linear
b. No guarantee to get integer valued solutions
c. No consideration of effect of time & uncertainty on LP model
d. All of the above
26. The graphical method of LP problem uses
a. Objective function equation
b. Constraint equations
c. Linear equations
d. All of the above
27. A feasible solution to an LP problem
a. Must satisfy all of the problem’s constraints simultaneously
b. Need not satisfy all of the constraints, only some of them
c. Must be a corner point of the feasible region
d. Must optimize the value of the objective function
28. Which of the following statements is true with respect to the optimal
solution of an LP problem
a. Every LP problem has an optimal solution
b. Optimal solution of an LP problem always occurs at an extreme point
c. At optimal solution all resources are completely used
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d. If an optimal solution exists, there will always be at least one at a corner
29. An iso-profit line represents
a. An infinite number of solutions all of which yield the same profit
b. An infinite number of solution all of which yield the same cost
c. An infinite number of optimal solutions
d. A boundary of the feasible region
30. If an iso-profit line yielding the optimal solution coincides with a constaint
line, then
a. The solution is unbounded
b. The solution is infeasible
c. The constraint which coincides is redundant
d. None of the above
31. While plotting constraints on a graph paper, terminal points on both the
axes are connected by a straight line because
a. The resources are limited in supply
b. The objective function as a linear function
c. The constraints are linear equations or inequalities
d. All of the above
32. A constraint in an LP model becomes redundant because
a. Two iso-profit line may be parallel to each other
b. The solution is unbounded
c. This constraint is not satisfied by the solution values
d. None of the above
33. If two constraints do not intersect in the positive quadrant of the graph,
then
a. The problem is infeasible
b. The solution is unbounded
c. One of the constraints is redundant
d. None of the above
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34. Constraints in LP problem are called active if they
a. Represent optimal solution
b. At optimality do not consume all the available resources
c. Both a & b
d. None of the above
35. The solution space (region) of an LP problem is unbounded due to
a. An incorrect formulation of the LP model
b. Objective function is unbounded
c. Neither a nor b
d. Both a & b
36. While solving a LP model graphically, the area bounded by the constraints
is called
a. Feasible region
b. Infeasible region
c. Unbounded solution
d. None of the above
37. Alternative solutions exist of an LP model when
a. One of the constraints is redundant
b. Objective function equation is parallel to one of the constraints
c. Two constraints are parallel
d. All of the above
38. While solving a LP problem, infeasibility may be removed by
a. Adding another constraint
b. Adding another variable
c. Removing a constraint
d. Removing a variable
39. If a non-redundant constraint is removed from an LP problem then
a. Feasible region will become larger
b. Feasible region will become smaller
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c. Solution will become infeasible
d. None of the above
40. If one of the constraint of an equation in an LP problem has an
unbounded solution, then
a. Solution to such LP problem must be degenerate
b. Feasible region should have a line segment
c. Alternative solutions exist
d. None of the above
41. The initial solution of a transportation problem can be obtained by
applying any known method. However, the only condition is that
a. The solution be optimal
b. The rim conditions are satisfied
c. The solution not be degenerate
d. All of the above
42. The dummy source or destination in a transportation problem is added to
a. Satisfy rim conditions
b. Prevent solution from becoming degenerate
c. Ensure that total cost does not exceed a limit
d. None of the above
43. The occurrence of degeneracy while solving a transportation problem
means that
a. Total supply equals total demand
b. The solution so obtained is not feasible
c. The few allocations become negative
d. None of the above
44. An alternative optimal solution to a minimization transportation problem
exists whenever opportunity cost corresponding to unused route of
transportation is:
a. Positive & greater than zero
b. Positive with at least one equal to zero
c. Negative with at least one equal to zero
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d. None of the above
45. One disadvantage of using North-West Corner rule to find initial solution
to the transportation problem is that
a. It is complicated to use
b. It does not take into account cost of transportation
c. It leads to a degenerate initial solution
d. All of the above
46. The solution to a transportation problem with ‘m’ rows (supplies) & ‘n’
columns (destination) is feasible if number of positive allocations are
a. m+n
b. m*n
c. m+n-1
d. m+n+1
47. If an opportunity cost value is used for an unused cell to test optimality, it
should be
a. Equal to zero
b. Most negative number
c. Most positive number
d. Any value
48. During an iteration while moving from one solution to the next,
degeneracy may occur when
a. The closed path indicates a diagonal move
b. Two or more occupied cells are on the closed path but neither of them represents
a corner of the path.
c. Two or more occupied cells on the closed path with minus sign are tied for
lowest circled value
d. Either of the above
49. The large negative opportunity cost value in an unused cell in a
transportation table is chosen to improve the current solution because
a. It represents per unit cost reduction
b. It represents per unit cost improvement
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c. It ensure no rim requirement violation
d. None of the above
50. The smallest quantity is chosen at the corners of the closed path with
negative sign to be assigned at unused cell because
a. It improve the total cost
b. It does not disturb rim conditions
c. It ensure feasible solution
d. All of the above
51. When total supply is equal to total demand in a transportation problem,
the problem is said to be
a. Balanced
b. Unbalanced
c. Degenerate
d. None of the above
52. Which of the following methods is used to verify the optimality of the
current solution of the transportation problem
a. Least cost method
b. Vogel’s approximation method
c. Modified distribution method
d. All of the above
53. The degeneracy in the transportation problem indicates that
a. Dummy allocation(s) needs to be added
b. The problem has no feasible solution
c. The multiple optimal solution exist
d. a & b but not c
54. An assignment problem is considered as a particular case of a
transportation problem because
a. The number of rows equals columns b. All xij = 0 or 1
c. All rim conditions are 1 d. All of the above
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55. An optimal assignment requires that the maximum number of lines that
can be drawn through squares with zero opportunity cost be equal to the
number of
a. Rows or columns b. Rows & columns
c. Rows + columns – 1 d. None of the above
56. While solving an assignment problem, an activity is assigned to a resource
through a square with zero opportunity cost because the objective is to
a. Minimize total cost of assignment
b. Reduce the cost of assignment to zero
c. Reduce the cost of that particular assignment to zero
d. All of the above
57. The method used for solving an assignment problem is called
a. Reduced matrix method b. MODI method
c. Hungarian method d. None of the above
58. The purpose of a dummy row or column in an assignment problem is to
a. Obtain balance between total activities & total resources
b. Prevent a solution from becoming degenerate
c. Provide a means of representing a dummy problem
d. None of the above
59. Maximization assignment problem is transformed into a minimization
problem by
a. Adding each entry in a column from the maximization value in that column
b. Subtracting each entry in a column from the maximum value in that column
c. Subtracting each entry in the table from the maximum value in that table
d. Any one of the above
60. If there were n workers & n jobs there would be
a. n! solutions b. (n-1)! solutions
c. (n!)n solutions d. n solutions
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61. An assignment problem can be solved by
a. Simplex method
b. Transportation method
c. Both a & b
d. None of the above
62. For a salesman who has to visit n cities which of the following are the ways
of his tour plan
a. n!
b. (n+1)!
c. (n-1)!
d. n
63. The assignment problem
a. Requires that only one activity be assigned to each resource
b. Is a special case of transportation problem
c. Can be used to maximize resources
d. All of the above
64. An assignment problem is a special case of transportation problem, where
a. Number of rows equals number of columns
b. All rim conditions are 1
c. Values of each decision variable is either 0 or 1
d. All of the above
65. Every basic feasible solution of a general assignment problem, having a
square pay-off matrix of order, n should have assignments equal to
a. 2n+1
b. 2n-1
c. m+n-1
d. m+n
66. To proceed with the MODI algorithm for solving an assignment problem,
the number of dummy allocations need to be added are
a. n b. 2n
c. n-1 d. 2n-1
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67. The Hungarian method for solving an assignment problem can also be
used to solve
a. A transportation problem
b. A travelling salesman problem
c. A LP problem
d. Both a & b
68. An optimal solution of an assignment problem can be obtained only if
a. Each row & column has only one zero element
b. Each row & column has at least one zero element
c. The data is arrangement in a square matrix
d. None of the above
69. Customer behavior in which the customer moves from one queue to
another in a multiple channel situation is
a. Balking
b. Reneging
c. Jockeying
d. Altering
70. Which of the following characteristics apply to queuing system
a. Customer population
b. Arrival process
c. Both a & b
d. Neither a nor b
71. Which of the following is not a key operating characteristics apply to
queuing system
a. Utilization factor
b. Percent idle time
c. Average time spent waiting in the system & queue
d. None of the above
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72. Priority queue discipline may be classified as
a. Finite or infinite
b. Limited & unlimited
c. Pre-emptive or non-pre-emptive
d. All of the above
73. The calling population is assumed to be infinite when
a. Arrivals are independent of each other
b. Capacity of the system is infinite
c. Service rate is faster than arrival rate
d. All of the above
74. Which of the cost estimates & performance measures are not used for
economic analysis of a queuing system
a. Cost per server per unit of time
b. Cost per unit of time for a customer waiting in the system
c. Average number of customers in the system
d. Average waiting time of customers in the system
75. A calling population is considered to be infinite when
a. All customers arrive at once
b. Arrivals are independent of each other
c. Arrivals are dependent upon each other
d. All of the above
76. The cost of providing service in a queuing system decreases with
a. Decreased average waiting time in the queue
b. Decreased arrival rate
c. Increased arrival rate
d. None of the above
77. Service mechanism in a queuing system is characterized by
a. Server’s behavior b. Customer’s behavior
c. Customers in the system d. All of the above
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78. Probabilities of occurrence of any state are
a. Collectively exhaustive
b. Mutually exclusive
c. Representing one of the finite numbers of states of nature in the system
d. All of the above
79. In a matrix of transition probability, the probability values should add up
to one in each
a. Row
b. Column
c. Diagonal
d. All of the above
80. In a matrix of transition probability, the element aij where i=j is a
a. Gain
b. Loss
c. Retention
d. None of the above
81. In Markov analysis, state probabilities must
a. Sum to one
b. Be less than one
c. Be greater than one
d. None of the above
82. State transition probabilities in the Markov chain should
a. Sum to 1 b. Be less than 1
c. Be greater than 1 d. None of the above
83. If a matrix of transition probability is of the order n*n, then the number of
equilibrium equations would be
a. n
b. n-1
c. n+1
d. None of the above
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84. In the long run, the state probabilities become 0 & 1
a. In no case
b. In same cases
c. In all cases
d. Cannot say
85. While calculating equilibrium probabilities for a Markov process, it is
assumed that
a. There is a single absorbing state
b. Transition probabilities do not change
c. There is a single non-absorbing state
d. None of the above
86. The first-order Markov chain is generally used when
a. Transition probabilities are fairly stable
b. Change in transition probabilities is random
c. No sufficient data are available
d. All of the above
87. A problem is classified as Markov chain provided
a. There are finite number of possible states
b. States are collectively exhaustive & mutually exclusive
c. Long-run probabilities of being in a particular state will be constant over time
d. All of the above
88. The transition matrix elements remain positive from one point to the next.
This property is known as:
a. Steady-state property
b. Equilibrium property
c. Regular property
d. All of the above
89. Markov analysis is useful for:
a. Predicting the state of the system at some future time
b. Calculating transition probabilities at some future time
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c. All of the above
d. None of the above
90. Which of the following is not one of the assumptions of Markov analysis:
a. There are a limited number of possible states
b. A future state can be predicted from the preceding one
c. There are limited number of future periods
d. All of the above
91. An advantage of simulation as opposed to optimization is that
a. Several options of measure of performance can be examined
b. Complex real-life problems can be studied
c. It is applicable in cases where there is an element of randomness in a system
d. All of the above
92. The purpose of using simulation technique is to
a. Imitate a real-world situation
b. Understand properties & operating characteristics of complex real-life problems
c. Reduce the cost of experiment on a model of real situation
d. All of the above
93. Which of the following is not the special purpose simulation language
a. BASIC
b. GPSS
c. GASP
d. SIMSCRIPT
94. As simulation is not an analytical model, therefore the result of simulation
must be viewed as
a. Unrealistic
b. Exact
c. Approximation
d. Simplified
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95. While assigning random numbers in Monte Carlo simulation, it is
a. Not necessary to assign the exact range of random number interval as the
probability
b. Necessary to develop a cumulative probability distribution
c. Necessary to assign the particular appropriate random numbers
d. All of the above
96. Analytical results are taken into consideration before a simulation study so
as to
a. Identify suitable values of the system parameters
b. Determine the optimal decision
c. Identify suitable values of decision variables for the specific choices of
system parameters
d. All of the above
97. Biased random sampling is made from among alternatives which have
a. Equal probability
b. Unequal probability
c. Probability which do not sum to 1
d. None of the above
98. Large complicated simulation models are appreciated because
a. Their average costs are not well-defined
b. It is difficult to create the appropriate events
c. They may be expensive to write and use as an experimental device
d. All of the above
99. Simulation should not be applied in all cases because it
a. Requires considerable talent for model building & extensive computer
programming efforts
b. Consumes much computer time
c. Provides at best approximate solution to problem
d. All of the above
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100. Simulation is defined as
a. A technique that uses computers
b. An approach for reproducing the processes by which events by chance &
changes are created in a computer
c. A procedure for testing & experimenting on models to answer what if ___, then
so & so ___ types of questions
d. All of the above
101. The general purpose system simulation language
a. Requires programme writing
b. Does not require programme writing
c. Requires predefined coding forms
d. Needs a set of equations to describe a system
102. Special simulation languages are useful because they
a. Reduce programme preparation time & cost
b. Have the capability to generate random variables
c. Require no prior programming knowledge
d. All of the above
103. Few causes of simulation analysis failure are
a. Inadequate level of user participation
b. Inappropriate levels of detail
c. Incomplete mix of essential skills
d. All of the above
104. To make simulation more popular, we need to avoid
a. Large cost over runs
b. Prolonged delays
c. User dissatisfaction with simulation results
d. All of the above
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105. The important step required for simulation approach in solving a
problem is to
a. Test & validate the model
b. Design the experiment
c. Conduct the experiment
d. All of the above
106. The field of management science
1. Concentrates on the on the use of quantitative methods to assists in decision
making
2. Approaches decision making with techniques based on the scientific method
3. is another name for decision science and for operation research
4. each of the above is true
107. Identification and definition of a problem
1. Can not be done until alternatives are proposed
2. Is the first step of decision making
3. Is the final step of problem solving
4. Requires consideration of multiple criteria
108. Decision alternatives
1. Should be identified before decision criteria are established
2. Are limited to quantitative solutions
3. Are evaluated as a part of the problem definition stage
4. Are best generated by brain storming
109. Decision Criteria
1. are the choices faced by the decision maker
2. are the problems faced by the decision maker
3. are the ways to evaluate the choices faced by the decision maker
4. must be unique for the problem
110. In a multi criteria decision problem
1. it is impossible to select a single decision alternative
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2. the decision maker must evaluate each alternative with respect to each
criterion
3. successive decisions must be made over time
4. each of the above is true
111. The quantitative analysis approach requires
1. the managers prior experience with similar problem
2. a relatively uncomplicated problem
3. mathematical expressions for the relationship
4. each of the above is true
112. maximization or minimization of the quantity is the
1. a goal of management science
2. decision for decision analysis
3. constraint of operation research
4. objective of linear programming
113. Decision variables
1. tells how much or how many of something to produce, invest, purchase ,hire
2. represent the values of the constraints
3. measure the objective function
4. must exist for each constraint
114. Which of the following is the valid objective function of LPP?
1. Maximize 5xy
2. Minimize 4x+3y+3z
3. Maximize 3xy+5xy
4. Minimize(x1+x2)/x3
115. Which of the following statement is not true?
1. feasible solution satisfies all the constraints
2. an optimal solution satisfies all the constraints
3. an infeasible solution violates all constraints
4. a feasible solution point does not have to lie on the boundary of the feasible region
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116. A solution that satisfies all the constraints of the LPP except the non
negativity constraints is called
1. optimal
2. feasible
3. infeasible
4. semi-feasible
117. Slack
1. is the difference between the left and right sides of the constraints
2. is the amount by which the left side of the constraint is smaller than the right
side
3. is the amount by which the left side of the constraint is larger than the right side
4. exists for each variable in a linear programming problem
118. To find the optimal solution to the LPP using the graphical method
1. find the feasible point that is the farthest away from the region
2. find the feasible point that is at the highest location
3. find the feasible point that is closest to the origin
4. None of the alternative is correct
119. Which of the following cases does not require reformulation of the
problem in order to obtain a solution?
1. Alternate optimality
2. Infeasibility
3. Unboundness
4. Each case requires a reformulation
120. Whenever all constraints in the LPP are expressed as equalities, the
linear program is said to be written in
1. Standard form
2. Bounded form
3. Feasible form
4. Alternate form
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121. Problem solving encompasses
1. Identification of problem
2. Identification of problem and the action to resolve it
3. Identification of problem and finding of objective function
4. All of above
122. Long form of LPP is
1. Linear programming problem
2. Linear Problem parameters
3. Linear programming parameters
4. None of above
123. Assignment model can be applied in
1. Decision making
2. Problem solving
3. Manufacturing Industry
4. Only in service sector
124. A dummy job is an
1. Imaginary
2. Real
3. Rigid
4. Can’t say
125. In transportation problem following are always transported
1. Consignments
2. Goods
3. Demand
4. Supply
126. Initial basic solution from VAM IS
1. Least
2. Maximum
3. Can’t say
4. None of above
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127. Demand variation occurs because of change in
1. Customer preference
2. Competitors entry
3. Market condition
4. None of above
128. Following represents the aim or goal of the system
1. Decision variable
2. Objective function
3. Constraints
4. None of above
129. In real life supply & demand requirement will be rarely
1. Equal
2. Unequal
3. Stable
4. None of above
130. LPP is widely used ………………modelling technique
1. Mathematical
2. Statistical
3. Graphical
4. None of above
131. LP Consists of linear objectives &……………….
1. Linear variables
2. Linear constraints
3. Linear functions
4. None of above
132. .………………… represents the aim of the system.
1. Constraints
2. Decision variable
3. Objective functions
4. Cann’t say
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133. …………………method solve the LPP in iteration to enhance the value of
the objective function
1. Complex
2. Simplex
3. Corner point
4. Iso profit
134. …………….is special type of linear programming
1. Transportation problem
2. Assignment
3. Cann’t say
4. Queuing
135. …………… model helps to manager to take decision
1. Transportation
2. Assignment
3. LPP
4. All above
136. ……………is used to collect a set of experimental data and figure out to
graph
1. LPP
2. Mathematical model
3. Corner point model
4. Operation research model
137. Initial basic solution can be obtained by modified distribution method
1. True
2. False
3. Cannot say
4. Data is not sufficient
138. Least cost method is a best method to find basic solution
1. True
2. False
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Decision Science MCQ by Prof. Sujeet Tambe Page 26
3. Cannot say
4. Data is not sufficient
139. …………. Method is more accurate
1. North west corner
2. Least cost
3. VAM
4. None of above
140. In a balanced transportation model where supply equals demand,
1. all constraints are equalities
2. none of the constraints are equalities
3. all constraints are inequalities
4. none of the constraints are inequalities
141. In a transportation problem, items are allocated from sources to
destinations
1. at a maximum cost
2. at a minimum cost
3. at a minimum profit
4. at a minimum revenue
142. The assignment model is a special case of the ________ model.
1. maximum-flow
2. transportation
3. shortest-route
4. none of the above
143. An assignment problem is a special form of transportation problem
where all supply and demand values equal
1. 0
2. 1
3. 2
4. 3
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144. The transportation model relies on certain assumptions. They include all
of the following except
1. the items must be homogeneous
2. there is only one route being used between each origin and destination
3. the shipping cost per unit is the same
4. the items must be large scale
5. none of the above
145.Which of the following are supply points that a transportation model can
analyze?
1. factories
2. warehouses
3. departments
4. all of the above
5. none of the above
146. The basis for the transportation model is
1. a way to provide a map for people to see results
2. a method to arrive at the lowest total shipping cost
3. so delivery drivers know where to go
4. a form of accounting
5. to provide data for use in other areas
147. The following transportation model is a programming model:
1. analytical
2. non-linear
3. linear
4. rotating
5. variable
148. Before the analyst of the transportation model can begin, what data
would they need to collect?
1. A list of destinations
2. Unit cost to ship
3. A list of origins
4. All of the above
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5. None of the above
149. What does the transportation problem involve finding:
1. highest cost-plan
2. lowest cost-plan
3. closest destinations
4. farthest destinations
5. none if the above
150. Transportation problems be solved
1. manually
2. with a table
3. with excel
4. with software packages
5. all of the above
151. The objective function of the transportation model is to
1. reduce shipping costs
2. decrease shipping distance
3. maximize costs
4. minimize costs
5. none of the above
152. Goods are not sent from
1. warehouses
2. factories
3. grocery stores
4. department stores
5. goods are sent from all of these locations
153. Goods are received at all of the following except
1. docks
2. departments
3. factories
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Decision Science MCQ by Prof. Sujeet Tambe Page 29
4. warehouses
5. all of the above
154. The method for finding the lowest-cost plan for distributing stocks of
goods or supplies from multiple origins to multiple destinations that demand
the goods is
1. cost-volume analysis
2. transportation model analysis
3. factor rating analysis
4. linear regression analysis
5. MODI analysis
155. Except to be used to minimized the costs associated with distributing
good, transportation model can also be used in
1. production planning
2. capacity planning
3. transshipment problem
4. comparison of location alternative
5. all of the above
156. Which one of the following is a linear programming model ?
1. Cost-volume analysis
2. Transportation model analysis
3. Factor rating analysis
4. Linear regression analysis
5. MODI analysis
157. Destination points are
1. points that receive goods from factories, warehouses, and departments
2. points where goods are sent from factories, warehouses, and departments
3. supply points
4. selling points
5. none of the above
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Decision Science MCQ by Prof. Sujeet Tambe Page 30
158. Transportation problems can be solved manually in a straightforward
manner except for
1. medium problems
2. very small, but time consuming problems
3. large problems
4. all of the above
5. none of the above
159.The field of management science
a. Concentrates on the on the use of quantitative methods to assists in decision
making
b. Approaches decision making with techniques based on the scientific method
c. is another name for decision science and for operation research
d. each of the above is true
160.Identification and definition of a problem
a. Cannot be done until alternatives are proposed
b. Is the first step of decision making
c. Is the final step of problem solving
d. Requires consideration of multiple criteria
161.Decision alternatives
a. Should be identified before decision criteria are established
b. Are limited to quantitative solutions
c. Are evaluated as a part of the problem definition stage
d. Are best generated by brain storming
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162. Decision Criteria
a. are the choices faced by the decision maker
b. are the problems faced by the decision maker
c. are the ways to evaluate the choices faced by the decision maker
d. must be unique for the problem
163. In a multi criteria decision problem
a. it is impossible to select a single decision alternative
b. the decision maker must evaluate each alternative with respect to each
criterion
c. successive decisions must be made over time
d. each of the above is true
164. The quantitative analysis approach requires
a. the managers prior experience with similar problem
b. a relatively uncomplicated problem
c. mathematical expressions for the relationship
d. each of the above is true
165. Maximization or minimization of the quantity is the
a. a goal of management science
b. decision for decision analysis
c. constraint of operation research
d. objective of linear programming
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166. Decision variables
a. tells how much or how many of something to produce, invest, purchase ,hire
b. represent the values of the constraints
c. measure the objective function
d. must exist for each constraint
167. Which of the following is the valid objective function of LPP?
a. Maximize 5xy
b. Minimize 4x+3y+3z
c. Maximize 3xy+5xy
d. Minimize(x1+x2)/x3
168. Which of the following statement is not true?
a. feasible solution satisfies all the constraints
b. an optimal solution satisfies all the constraints
c. an infeasible solution violates all constraints
d. a feasible solution point does not have to lie on the boundary of the feasible
region
169. A solution that satisfies all the constraints of the LPP except the non-
negativity constraints is called
a. optimal
b. feasible
c. infeasible
d. semi-feasible
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Decision Science MCQ by Prof. Sujeet Tambe Page 33
170. Slack
a. is the difference between the left and right sides of the constraints
b. is the amount by which the left side of the constraint is smaller than the
right side
c. is the amount by which the left side of the constraint is larger than the right side
d. exists for each variable in a linear programming problem
171. To find the optimal solution to the LPP using the graphical method
a. find the feasible point that is the farthest away from the region
b. find the feasible point that is at the highest location
c. find the feasible point that is closest to the origin
d. None of the alternative is correct
172. Which of the following cases does not require reformulation of the problem
in order to obtain a solution?
a. Alternate optimality
b. Infeasibility
c. Unsoundness
d. Each case requires a reformulation
173. Whenever all constraints in the LPP are expressed as equalities, the linear
program is said to be written in
a. Standard form
b. Bounded form
c. Feasible form
d. Alternate form
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Decision Science MCQ by Prof. Sujeet Tambe Page 34
174. Problem solving encompasses
a. Identification of problem
b. Identification of problem and the action to resolve it
c. Identification of problem and finding of objective function
d. All of above
175. Long form of LPP is
a. Linear programming problem
b. Linear Problem parameters
c. Linear programming parameters
d. None of above
176. Assignment model can be applied in
a. Decision making
b. Problem solving
c. Manufacturing Industry
d. Only in service sector
177. In transportation problem following are always transported
a. Consignments
b. Goods
c. Demand
d. Supply
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Decision Science MCQ by Prof. Sujeet Tambe Page 35
178. Initial basic solution from VAM IS
a. Least
b. Maximum
c. Can’t say
d. None of above
179. Demand variation occurs because of change in
a. Customer preference
b. Competitors entry
c. Market condition
d. None of above
180. Following represents the aim or goal of the system
a. Decision variable
b. Objective function
c. Constraints
d. None of above
181. In real life supply & demand requirement will be rarely
a. Equal
b. Unequal
c. Stable
d. None of above
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Decision Science MCQ by Prof. Sujeet Tambe Page 36
182. LPP is widely used ………………modeling technique
a. Mathematical
b. Statistical
c. Graphical
d. None of above
183. LPP Consists of linear objectives &……………….
a. Linear variables
b. Linear constraints
c. Linear functions
d. None of above
184.………………… represents the aim of the system.
a. Constraints
b. Decision variable
c. Objective functions
d. Can’t say
185.…………………method solve the LPP in iteration to enhance the value of
the objective function
a. Complex
b. Simplex
c. Corner point
d. none of above
186…………….is special type of linear programming
a. Transportation problem
b. Assignment
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Decision Science MCQ by Prof. Sujeet Tambe Page 37
c. Can’t say
d. Queuing
187…………… model helps to manager to take decision
a. Transportation
b. Assignment
c. LPP
d. All above
188……………is used to collect a set of experimental data and figure out to
graph
a. LPP
b. Mathematical model
c. Corner point model
d. Operation research model
189. Initial basic solution can be obtained by modified distribution method
a. True
b. False
c. Cannot say
d. Data is not sufficient
190. Least cost method is a best method to find basic solution
a. True
b. False
c. Cannot say
d. Data is not sufficient
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Decision Science MCQ by Prof. Sujeet Tambe Page 38
191. In a balanced transportation model where supply equals demand,
a. all constraints are equalities
b. none of the constraints are equalities
c. all constraints are inequalities
d. none of the constraints are inequalities
192. In a transportation problem, items are allocated from sources to
destinations
a. at a maximum cost
b. at a minimum cost
c. at a minimum profit
d. at minimum revenue
193. The assignment model is a special case of the ________ model.
a. maximum-flow
b. transportation
c. shortest-routed.
d. none of the above
194. The linear programming model for a transportation problem has
constraints for supply at each ______ and _______ at each destination.
a. destination / source
b. source / destination
c. demand / source
d. source / demand
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Decision Science MCQ by Prof. Sujeet Tambe Page 39
195. An assignment problem is a special form of transportation problem
where all supply and demand values equal
a. 0
b. 1
c. 2
d. 3
196. Initial basic solution can be obtained by modified distribution method
a. True
b. False
c. Cannot say
d. Data is not sufficient
197. Least cost method is a best method to find basic solution
a. True
b. False
c. Cannot say
d. Data is not sufficient
198. The field of management science
a. concentrates on the use of quantitative methods to assist in decision making.
b. approaches decision making rationally, with techniques based on the scientific
method.
c. is another name for decision science and for operations research.
d. each of the above is true.
199. Identification and definition of a problem
a. cannot be done until alternatives are proposed.
b. is the first step of decision making.
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c. is the final step of problem solving.
d. requires consideration of multiple criteria.
200. The quantitative analysis approach requires
a. the manager’s prior experience with a similar problem.
b. a relatively uncomplicated problem.
c. mathematical expressions for the relationships.
d. each of the above is true.
201. A physical model that does not have the same physical appearance as the
object being modeled is
a. an analog model.
b. an iconic model.
c. a mathematical model.
d. a qualitative model.
202. Management science and operations research both involve
a. qualitative managerial skills.
b. quantitative approaches to decision making.
c. operational management skills.
d. scientific research as opposed to applications.
203. George Dantzig is important in the history of management science
because he developed
a. the scientific management revolution.
b. World War II operations research teams.
c. the simplex method for linear programming.
d. powerful digital computers.
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Decision Science MCQ by Prof. Sujeet Tambe Page 41
204.A model that uses a system of symbols to represent a problem is called
a. mathematical.
b. iconic.
c. analog.
d. constrained.
205. Slack
a. is the difference between the left and right sides of a constraint.
b. is the amount by which the left side of a < constraint is smaller than the
right side.
c. is the amount by which the left side of a > constraint is larger than the right side.
d. exists for each variable in a linear programming problem.
206.Which of the following special cases does not require reformulation of the
problem in order to obtain a solution?
a. alternate optimality
b. infeasibility
c. unboundedness
d. each case requires a reformulation.
207.The range of feasibility measures
a. the right-hand-side values for which the objective function value will not
change.
b. the right-hand-side values for which the values of the decision variables will not
change.
c. the right-hand-side values for which the dual prices will not change.
d. each of the above is true.
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Decision Science MCQ by Prof. Sujeet Tambe Page 42
208. The amount that the objective function coefficient of a decision variable
would have to improve before that variable would have a positive value in the
solution is the
a. dual price.
b. surplus variable.
c. reduced cost.
d. upper limit.
209. The values in the cj - zj , or net evaluation, row indicate
a. the value of the objective function.
b. the decrease in value of the objective function that will result if one unit of the
variable corresponding to the jth column of the A matrix is brought into the basis.
c. the net change in the value of the objective function that will result if one
unit of the variable corresponding to the jth column of the A matrix is brought into
the basis.
d. the values of the decision variables.
210. In the simplex method, a tableau is optimal only if all the cj – zj values are
a. zero or negative.
b. zero.
c. negative and nonzero.
d. positive and nonzero.
211. For the basic feasible solution to remain optimal
a. all cj - zj values must remain £ 0.
b. no objective function coefficients are allowed to change.
c. the value of the objective function must not change.
d. each of the above is true.
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Decision Science MCQ by Prof. Sujeet Tambe Page 43
212.The dual variable represents
a. the marginal value of the constraint
b. the right-hand-side value of the constraint
c. the artificial variable
d. the technical coefficient of the constraint
213. The parts of a network that represent the origins are
a. the axes
b. the flow
c. the nodes
d. the arrows
214. The number of units shipped from origin i to destination j is represented
by
a. xij.
b. xji.
c. cij.
d. cji.
215. The difference between the transportation and assignment problems is
that
a. total supply must equal total demand in the transportation problem
b. the number of origins must equal the number of destinations in the
transportation problem
c. each supply and demand value is 1 in the assignment problem
d. there are many differences between the transportation and assignment problems
216. In an assignment problem,
a. one agent can do parts of several tasks.
b. one task can be done by several agents.
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c. each agent is assigned to its own best task.
d. None of the alternatives is correct.
217. Arcs in a transshipment problem
a. must connect every node to a transshipment node.
b. represent the cost of shipments.
c. indicate the direction of the flow.
d. All of the alternatives are correct.
218. To use the Hungarian method, a profit-maximization assignment
problem requires
a. converting all profits to opportunity losses.
b. a dummy agent or task.
c. matrix expansion.
d. finding the maximum number of lines to cover all the zeros in the reduced
matrix.
219. The critical path
a. is any path that goes from the starting node to the completion node.
b. is a combination of all paths.
c. is the shortest path.
d. is the longest path.
220. When activity times are uncertain,
a. assume they are normally distributed.
b. calculate the expected time, using (a + 4m + b)/6.
c. use the most likely time.
d. calculate the expected time, using (a + m + b)/3.
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Decision Science MCQ by Prof. Sujeet Tambe Page 45
221. The critical path is the __________ path through the network.
a. longest
b. shortest
c. straightest
d. none of the above
222. In a CPM/PERT network the critical path is the
a. lowest path through the network
b. highest path through the network
c. shortest path through the network
d. longest path through the network
223. The transportation model relies on certain assumptions. They include all
of the following except
a. the items must be homogeneous
b. there is only one route being used between each origin and destination
c. the shipping cost per unit is the same
d. the items must be large scale
224. Which of the following are supply points that a transportation model can
analyze?
a. Factories
b. warehouses
c. departments
d. all of the above
e. none of the above
225. The basis for the transportation model is
a. a way to provide a map for people to see results
b. a method to arrive at the lowest total shipping cost
c. so delivery drivers know where to go
d. a form of accounting
e. to provide data for use in other areas
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Decision Science MCQ by Prof. Sujeet Tambe Page 46
226. The following transportation model is a programming model:
a. analytical
b. non-linear
c. linear
d. rotating
e. variable
227. Before the analyst of the transportation model can begin, what data
would they need to collect?
a. A list of destinations
b. Unit cost to ship
c. A list of origins
d. All of the above
e. None of the above
228. What does the transportation problem involve finding:
a. highest cost-plan
b. lowest cost-plan
c. closest destinations
d. farthest destinations
e. none if the above
229. Transportation problems be solved
a. manually
b. with a table
c. with excel
d. with software packages
e. all of the above
230. The objective function of the transportation model is to
a. reduce shipping costs
b. decrease shipping distance
c. maximize costs
d. minimize costs
e. none of the above
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Decision Science MCQ by Prof. Sujeet Tambe Page 47
231. Goods are not sent from
a. warehouses
b. factories
c. grocery stores
d. department stores
e. goods are sent from all of these locations
232. Goods are received at all of the following except
a. docks
b. departments
c. factories
d. warehouses
e. all of the above
233. The method for finding the lowest-cost plan for distributing stocks of
goods or supplies from multiple origins to multiple destinations that demand
the goods is
a. cost-volume analysis
b. transportation model analysis
c. factor rating analysis
d. linear regression analysis
e. MODI analysis
234. Except to be used to minimized the costs associated with distributing
good, transportation model can also be used in
a. production planning
b. capacity planning
c. transshipment problem
d. comparison of location alternative
e. all of the above
235. Which one of the following is a linear programming model ?
a. Cost-volume analysis
b. Transportation model analysis
c. Factor rating analysis
d. linear regression analysis
e. MODI analysis
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Decision Science MCQ by Prof. Sujeet Tambe Page 48
236. Destination points are
a. points that receive goods from factories, warehouses, and departments
b. points where goods are sent from factories, warehouses, and departments
c. supply points
d. selling points
e. none of the above
237. Transportation problems can be solved manually in a straightforward
manner except for
a. medium problems
b. very small, but time consuming problems
c. large problems
d. all of the above
e. none of the above
238. The transportation model is a
a. linear model
b. quadratic model
c. model with two variables
d. both a and c
e. none of the above
239. The transportation model is used to determine
a. what type of transportation to use (boat, truck, train or plane) to transport goods,
while minimizing costs
b. what day of the week goods should be transportation on to minimize costs
c. how to distribute goods from multiple origins to multiple destinations to
minimize total shipping costs
d. how to best package goods so that they wouldn't break while transporting them
e. none of the above
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Decision Science MCQ by Prof. Sujeet Tambe Page 49
240. What assumption is used in the transportation model?:
a. The items to be shipped are heterogeneous.
b. Shipping cost per unit is the different regardless of the number of units shipped.
c. There is more than one route or mode of transportation being used between each
origin and each destination.
d. The items to be shipped are the same regardless of their source or
destination.
e. None of the above
241. Which of the following is needed for a transportation model?
a. A list of origins and each one's capacity or supply quantity per period
b. A list of destinations and each one's demand per period
c. The unit cost of shipping items from each origin to each destination
d. All of the above
e. Only A and B
242. The transportation model is a linear __ model.
a. Solution
b. Programming
c. Data
d. Shipping
e. Distribution