MBA II Semester - 204 - Decision Science

Network models have an advantage in terms of project planning, scheduling, and controlling. This means that using network models allows for effective planning of project activities, creating a schedule that outlines the sequence and duration of tasks, and providing a means to monitor and control the progress of the project. By utilizing network models, project managers can ensure that projects are well-planned, efficiently scheduled, and effectively controlled to achieve successful outcomes.

The correct answer is that all of the alternatives are true. This means that analysis of a Markov process can describe the future behavior of the system, optimize the system, and lead to higher order decision making. Markov processes are mathematical models that can be used to analyze and predict the behavior of systems that have a finite number of states and where the future state depends only on the current state. By studying the probabilities of transitioning between states, Markov processes can provide valuable insights for optimizing the system and making informed decisions.

The objective function in a linear programming problem represents the quantity that needs to be minimized or maximized. In this case, the objective function "Min 4X + 3Y + 6Z" is a valid objective function because it is a linear combination of the decision variables X, Y, and Z, with coefficients 4, 3, and 6 respectively. The objective is to minimize the value of the objective function.

Queue discipline refers to the rules or algorithms used to determine the order in which units or entities are served in a queue. It defines how the units in the queue are prioritized and allocated service. The manner in which units receive their service, such as First-Come-First-Serve (FCFS) or any other scheduling algorithm, is a part of queue discipline. Therefore, the correct answer is Queue Discipline.

The correct answer is "All of the above" because the sample space in probability theory refers to the set of all possible outcomes of an experiment or event. It includes all possible sample events, which are the individual outcomes that can occur. It also includes all the exhaustive events, which means that every possible outcome is accounted for in the sample space. Additionally, the sample space consists of events such that at least one of them must happen at a time, meaning that one or more outcomes will occur from the sample space. Therefore, all the given options are valid explanations for the correct answer.

The decision variables in a problem determine the quantity or amount of something that needs to be produced, invested, purchased, hired, or any other action that needs to be taken. These variables represent the values of the constraints and are used to measure the objective function. They are essential for each constraint in the problem as they define the specific quantities or amounts that need to be determined in order to optimize the objective.

The correct answer is "Listing of values of a variable and their probability of occurrence." This explanation is supported by the definition of a probability distribution, which involves listing the possible values of a variable along with their corresponding probabilities. It is different from a frequency distribution, which only lists the frequencies or counts of each value. The term "random distribution of probability" is not a commonly used term in probability theory.

The maximization or minimization of a quantity is the objective of linear programming because linear programming is a mathematical technique used to optimize the allocation of limited resources to achieve the best possible outcome. The objective in linear programming is to maximize or minimize a certain quantity, such as profit or cost, subject to a set of constraints. By formulating the problem as a linear programming model and solving it using mathematical algorithms, the objective can be achieved. Therefore, the objective of linear programming is to maximize or minimize a quantity.

The quantitative analysis approach requires mathematical expressions for the relationships because this approach involves using mathematical models and formulas to analyze and solve problems. These mathematical expressions help in quantifying and understanding the relationships between different variables and factors involved in the problem. By using mathematical expressions, managers can make more accurate predictions, perform calculations, and make informed decisions based on data and numerical analysis.

The coefficient of optimism alpha is required while using the Hurwicz criteria. This criteria is a decision-making method that involves considering both the best and worst possible outcomes of a decision. The coefficient of optimism, represented by alpha, determines the decision maker's level of optimism or pessimism. A high alpha value indicates a more optimistic decision maker who is more likely to choose options with higher potential payoffs, while a low alpha value indicates a more pessimistic decision maker who is more likely to choose options with lower potential payoffs.

A saddle point in a game exists when the maximum value that a player can guarantee from their strategy is equal to the minimum value that their opponent can guarantee from their strategy. In other words, it is a point where both players have found their best possible outcome. In this case, the statement "Row maximin = column minimax" means that the maximum value that a player can guarantee by choosing the best strategy for each row is equal to the minimum value that their opponent can guarantee by choosing the best strategy for each column. Therefore, a saddle point exists in the game.

A fair game refers to a situation where the value of the game is zero. In such a game, there is an equal chance for each player to win or lose, and the expected outcome for each player is balanced. This means that neither player has an advantage over the other, and the game is conducted in a fair and unbiased manner. Therefore, the given answer "Fair game" accurately describes the situation where the value of a game is zero.

PERT and CPM are both project management techniques that help in planning and scheduling activities. One of the main differences between the two is that PERT makes use of a critical path, while CPM does not. The critical path in PERT represents the longest path in a project network, which determines the minimum time required to complete the project. On the other hand, CPM focuses on determining the earliest and latest start and finish times for each activity, without considering the critical path. Therefore, the given answer correctly states that PERT makes use of a critical path, while CPM does not.

The maximin criterion represents a pessimistic approach because it focuses on maximizing the minimum possible outcome. It assumes that the worst-case scenario will occur and aims to minimize the potential loss or negative impact. This approach is cautious and conservative, prioritizing risk avoidance and ensuring that the decision or action taken can withstand the worst possible outcome.

The correct answer is "Finding the area under the normal curve between lines X=X1 and X=X2." This is because the probability P(X1

Slack refers to the amount by which the left side of a constraint in a linear programming problem is smaller than the right side. It represents the surplus or excess capacity in the system. Slack is calculated by subtracting the right side of the constraint from the left side. If the result is positive, it indicates that there is slack or unused resources.

A simulation model uses the mathematical expressions and logical relationships of the real system to mimic its behavior and make predictions. By accurately representing the real system, the simulation model can be used to study and analyze various scenarios, test different strategies, and make informed decisions. It allows us to understand how the real system functions and how it may respond to different inputs or changes.

The given correct answer, ϱ / 1-ϱ, is the formula for calculating the system length (Ls) in the (M/M/1) : (∞/FCFS) model. In this model, ϱ represents the traffic intensity or the utilization factor, which is the ratio of the arrival rate (λ) to the service rate (µ). The formula ϱ / 1-ϱ is derived from Little's Law and is used to calculate the average number of customers in the system. It shows that as the traffic intensity approaches 1, the system length increases, indicating higher congestion and longer wait times for customers.

P(A/B) indicates the probability of event A occurring given that event B has already occurred. It represents the likelihood of event A happening under the condition that event B is true.

In the queue model notation (a/b/c): (d/e), the notation "c" represents the number of services. This refers to the number of parallel servers or channels available to serve customers in the system. It indicates how many customers can be served simultaneously, which affects the overall efficiency and waiting time in the queue.