Decision Sciences Trivia Quiz

The solution of a transportation problem is feasible if the number of occupied cells is equal to m + n - 1. This means that the total number of supplies (m) and destinations (n) minus one should be equal to the number of occupied cells. This condition ensures that all supplies are allocated to destinations and there are no unoccupied cells.

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 each variable multiplied by a constant coefficient. The objective is to minimize the value of the expression 4X + 3Y + 6Z.

The correct answer is Hungarian Method. The Hungarian Method is a combinatorial optimization algorithm that is used to solve the assignment problem. It is specifically designed to find the optimal assignment of tasks to resources, such as assigning jobs to workers or assigning machines to tasks, with the objective of minimizing the overall cost or maximizing the overall profit. The Hungarian Method uses a step-by-step approach to iteratively improve the assignment until an optimal solution is found. It is widely used in various industries and has been proven to be an efficient and effective method for solving assignment problems.

The property of the optimum assignment matrix is that it will have at least one zero in each row and column. This means that each row and column will have at least one element that is assigned to a task or job with zero cost or value. This property is important in optimization problems where the goal is to minimize the total cost or maximize the total value of assignments. By having at least one zero in each row and column, it ensures that all tasks or jobs are assigned and no resources are left unutilized.

The correct answer is "Objective of linear programming" because in linear programming, the objective is to maximize or minimize a certain quantity, such as profit or cost, subject to a set of constraints. The objective function represents the goal that the decision-maker wants to achieve, and the constraints represent the limitations or restrictions on the decision-making process. Therefore, the maximization or minimization of a quantity is the objective of linear programming.

Jockeying refers to the customer behavior of moving from one queue to another in a multiple channel situation. This behavior can occur when customers perceive that one queue is moving faster or when they are dissatisfied with the service in their current queue. By switching queues, customers hope to reduce their waiting time or improve their overall experience. Jockeying can lead to inefficiencies in the system as it disrupts the order and fairness of the queues.

The dummy source or destinations in a transportation problem are added to satisfy the rim conditions. Rim conditions refer to the constraints that ensure the total supply equals the total demand in the transportation problem. By adding dummy sources or destinations, the problem can be balanced and the rim conditions can be satisfied. This allows for a feasible solution to be obtained.

The prohibited cell in transportation problem is considered by assigning it a cost of infinity (∞). This means that this particular cell cannot be used for transportation as it is not feasible or allowed. The cost of infinity represents an extremely high cost, indicating that it is not possible or practical to use this cell for transportation.

The correct answer is R2 = (R0 X P2) X (R0XP2). This equation represents the calculation of state probabilities at the end of the second period. The term (R0 X P2) represents the state probabilities at the end of the first period multiplied by the transition probabilities from the first period to the second period. The term (R0XP2) represents the state probabilities at the end of the first period multiplied by the transition probabilities from the first period to the second period. Therefore, multiplying these two terms together gives the state probabilities at the end of the second period.

In Monte Carlo Simulation, the solutions obtained using different sets of random numbers will be different. This is because Monte Carlo Simulation relies on random sampling to generate multiple scenarios and obtain a range of possible outcomes. By using different sets of random numbers, the simulation explores different combinations and variations, resulting in different solutions. This variability is essential in capturing the uncertainty and randomness inherent in the simulation process.

Queue discipline refers to the rules or policies that determine the order in which units or customers are served in a queue. It specifies how the units waiting in the queue are prioritized and served, such as First-Come-First-Served (FCFS), Last-Come-First-Served (LCFS), or Priority-based. Queue discipline is an important aspect of managing queues efficiently and ensuring fairness in service delivery.

A simulation model uses the mathematical expressions and logical relationships of the real system. This means that the model is designed to mimic the behavior and characteristics of the actual system being studied. By using the mathematical expressions and logical relationships of the real system, the simulation model can provide insights and predictions about the real system's performance and behavior. It allows researchers to experiment with different scenarios and make informed decisions based on the model's output.

When a worker cannot be assigned a particular job, the relevant cost item is replaced by a very large number (M). This is done to indicate that it is not feasible or desirable to assign that worker to that job. By replacing the cost item with a large number, it effectively makes the cost of assigning that worker to that job extremely high, discouraging such an assignment.

In the queue model notation (a/b/c) : (d/e), the variable c represents the number of services. This refers to the number of parallel servers available in the system that can provide service to the arriving customers. It indicates the capacity of the system to handle multiple customers simultaneously.

The utilization factor is a measure of how effectively a system or resource is being used. It is calculated by dividing the arrival rate (the rate at which customers or entities enter the system) by the service rate (the rate at which the system can process or serve those entities). This ratio provides insight into how busy or congested the system is. A higher utilization factor indicates a higher level of utilization and potentially longer waiting times for entities in the system.

In the (M/M/1) : (∞/FCFS) model, the system length Ls is given by ϱ / 1-ϱ. This formula represents the average number of customers in the system at any given time. The symbol ϱ represents the traffic intensity, which is the ratio of the arrival rate (λ) to the service rate (µ). When the traffic intensity is high (close to 1), the system length increases, indicating that there are more customers in the system waiting for service. When the traffic intensity is low (close to 0), the system length decreases, indicating that there are fewer customers in the system. Therefore, the formula ϱ / 1-ϱ accurately calculates the system length in this model.

The analysis of a Markov Process involves studying the probabilities of transitioning between different states in a system. By understanding these probabilities, one can describe the future behavior of the system. This is because the Markov Process assumes that the future behavior only depends on the current state and not on the history of the system. Therefore, by analyzing the Markov Process, one can gain insights into how the system is likely to evolve over time.

In a multiple channel system, each server having the same service rate means that they are capable of processing the same number of requests per unit of time. This ensures that the workload is evenly distributed among the servers, preventing any server from being overloaded while others remain underutilized. Having the same service rate also allows for better efficiency and faster processing of requests, resulting in improved overall system performance.

The first step in solving an operations research problem is model building. This involves creating a mathematical representation of the problem, which includes defining the decision variables, objective function, and constraints. By building a model, we can understand the problem structure and identify the key elements that need to be considered in finding a solution. This step sets the foundation for further analysis and optimization of the problem. Obtaining alternate solutions, interpreting the variables, and formulating the problem come after model building and rely on the initial model created.

The single server queuing method assumes that service times are exponentially distributed, not Poisson distributed. The exponential distribution is commonly used to model the time between arrivals or the time between service completions in a queuing system. In contrast, the Poisson distribution is used to model the number of arrivals in a given time interval. Therefore, the statement "Service times are Poisson distributed" is not an assumption of the single server queuing method.