The marketing department of a company is deciding on the price to charge for a key product. In setting this price, marketing needs to consider the price that a major competitor will charge for a similar product because the competitor's price will affect the demand for the company's product. Similarly, in setting its price, the competitor will consider what the company will charge. What is an appropriate mathematical technique for analyzing such a decision?
Answer(s): A
Game or decision) theory is a mathematical approach to decision making when confronted with an enemy or competitor. Games are classified according to the number of players and the algebraic sum of the payoffs. In a two-person game, if the payoff is given by the loser to the winner, the algebraic sum is zero and the game is called a zero-sum game. If it is possible for both players to profit, however, the game is a positive-sum game. Mathematical models have been developed to select optimal strategies for certain simple games.
Because of the large number of factors that could affect the demand for its new product, interactions among these factors, and the probabilities associated with different values of these factors, the marketing department would like to develop a computerized model for projecting demand for this product. By using a random-number procedure to generate values for the different factors, it will be able to estimate the distribution of demand for this new product. This method of estimating the distribution of demand for the new product is called
Simulation is a technique in which a probabilistic process is first modeled. The inputs to the model are then varied a large number of times to estimate the distribution of possible outcomes from the model of the variable of interest. Simulations that use a random-number procedure to generate values for the inputs are referred to as Monte Carlo simulations.
An account executive has just designed a Monte Carlo model to estimate the costs of a particular type of project. Validating the model could include all except
Answer(s): D
The Monte Carlo technique is used in a simulation to generate the individual values for a random value. An essential step in the simulation procedure is to validate the mathematical model used. This process involves not only searching for errors but also verifying the assumptions. It also should provide some assurance that the results of the experiment will be realistic. This assurance is often obtained using historical datA. If the model gives results equivalent to what actually happened, the model is historically valid. There is still some risk, however, that changes could make the model invalid for the future. The model should not be implemented until this validation process is complete.
A large fishing operation has information on the interval, time, and probabilities of shrimp schools staying beneath their fishing boats. In order to use this information to predict when and where to send their boats, which of the following techniques should be used?
Simulation Monte Carlo simulation) is a technique for experimenting with logical/mathematical models using a computer. Despite the power of mathematics, many problems cannot be solved by known analytical methods because of the behavior of the variables and the complexity of their interactions. However, the performance of a quantitative model under uncertainty may be investigated by randomly selecting values for each variable in the model based on its probability distribution) and then calculating the value of the solution. If this process is performed many times, the distribution of results from the model will be obtained.
Which of the following is not true about simulation models?
Simulation is a technique for experimenting with logical/mathematical models using a computer. The simulation procedure has five steps: define the objectives, formulate the model, validate the model, design the experiment, and conduct the simulation and evaluate the results. A simulation uses the laws of probability to generate values for random variables. Thus, simulation models are probabilistic, not deterministic.
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