Q&A Hero

Q: Spreadsheet simulation modeling is quite similar to the other modeling applications in that it begins with input variables and then relates these with appropriate Excel formulas to produce output variables of interest.

Q: One of the primary advantages of simulation models that they enable managers to answer what-if questions about changes in systems without actually changing the systems themselves.

Q: It is simple to generate a uniformly distributed random number with a minimum and maximum other than 0 and 1. For example, the formula =150+100 RAND() generates a number uniformly distributed between a. 100 and 150 b. 150 and 250 c. 50 and 100 d. 50 and 250

Q: Which of the following statements are true? a. The @RISK contains a number of functions such as RISKNORMAL and RISKDISCRETE that make it easy to generate observations from the most important probability distributions. b. You can specify any cell or range of cells in your simulation model as output cells. When you run the simulation, @RISK automatically keeps summary measures (averages, standard deviation, percentiles, and others) from the values generated in these output cells across the replications. c. @RISK has a special function, RISKSIMTABLE, which allows you to run the same simulation several times, using a different value of some key input variable each time. d. All of the above

Q: Suppose you run a simulation model several times with different order quantities. What can we infer about the the quantity that maximizes the output, the company's profit? a. This quantity is the optimal order quantity. b. This quantity might be the optimal order quantity, but we also need to consider the company's attitude toward risk. c. This is not necessarily the optimal order quantity, because it may have produced the largest profit by luck. d. We can"t infer anything.

Q: Many companies have used simulation to determine which of several possible investment projects they should choose. This is often referred to as a. risk analysis b. @RISK investment c. unbounded risk d. None of the above

Q: If a model contains uncertain outputs, it can be very misleading to build a deterministic model by using the means of the inputs to predict an output. This is called the: a. Law of Large Numbers. b. Flaw of Averages c. Law of Inevitable Disappointment d. Central Limit Theorem

Q: When n is reasonably large and p isn"t too close to 0 or 1, the binomial distribution can be well approximated by which of the following distributions? a. Uniform distribution b. Normal distribution c. Triangular distribution d. None of these options

Q: Which of the following statements is true regarding the Triangular distribution? a. It is a discrete distribution with a minimum, maximum and most likely value b. It is more flexible and intuitive than the normal distribution c. It is a symmetric distribution d. All of these options

Q: Which of the following statements is true regarding the Normal distribution? a. It is always the appropriate distribution in simulation modeling b. It does not permit negative values c. There is a 95% chance that values will be within 2 standard deviations of the mean d. All of these options

Q: If we want to model the time it takes to serve a customer at a bank, we will probably choose a. symmetric distribution b. positively skewed distribution c. negatively skewed distribution d. All of these options

Q: If we want to model the monthly return on a stock, we might choose a. symmetric distribution around 0 b. positively skewed distribution c. negatively skewed distribution d. All of these options

Q: In order to generate random numbers in Excel from a discrete distribution with a finite number of possible values and corresponding probabilities, we can use a. only the RAND function b. only the VLOOKUP function c. only the VLOOKDOWN function d. the RAND function along with a VLOOKUP function

Q: Which of the following statements are false regarding the numbers generated by the RAND function in Excel?a. The numbers are random between 0 and 1b. The numbers are probabilistically dependent c. The numbers are probabilistically independentd. The numbers are uniformly distributed between 0 and 1

Q: Assume that x is a random number between 0 and 1, and that the number of units expected to be sold is uniformly distributed between 300 and 500. Then, sales are given by the expressiona. 300 + xb. 500 - xc. 300 + 200 xd. 500 - 200 xe. 300 + 500 x

Q: Which of the following statements is (are) false regarding the numbers generated by the RAND function in Excel? a. Approximately 10% of the numbers will be between 0.0 and 1.0 b. Approximately 20% of the numbers will be between 0.50 and 0.70 c. Approximately 40% of the numbers will be between 0.20 and 0.60 d. Approximately 60% of the numbers will be between 0.15 and 0.75 e. All of these options are false

Q: The RAND() function in excel models which of the following probability distributions: a. Normal(0,1) b. Uniform(0,1) c. Normal(-1,1) d. Uniform(-1,1).

Q: We can think of the uniform distribution as: a. the "I have no idea" distribution. b. a skewed distribution. c. only modeling positive values. d. nonnegative.

Q: One important special use of bounded distributions is when the only possible values are: a. less than zero. b. uniformly distributed around the mean. c. skewed to the right. d. nonnegative.

Q: A probability distribution is bounded if there are values A and B such that: a. A and B represent the 95% confidence interval b. A and B are the mean and standard deviation, respectively. c. A and B are the mean and variance, respectively. d. no value can be less than A or greater than B.

Q: We sometimes use discrete distributions in place of continuous distributions: a. because they are more accurate. b. because they are more simple. c. when we don"t know the mean and variance of the distribution. d. when we need to generate a histogram

Q: A continuous probability distribution is characterized by a: a. mean and a standard deviation. b. mean and a variance. c. density function. d. histogram

Q: Which of the following statements are true? a. A probability distribution is symmetric (around some point) if the distribution to the left of the point is a mirror image of the distribution to the right of the point. b. We say a distribution is skewed to the right (or positively skewed) if the "longer tail" is the right tail. c. We say a distribution is skewed to the left (or negatively skewed) if the "longer tail" is the left tail. d. All of the above

Q: Which of the following statements are false regarding the graph of a continuous probability distribution? a. It is characterized by a density function, a smooth curve. b. It is a series of spikes c. The height of the density curve above any point is not actually a probabilitythat is, it is not necessarily between 0 and 1. d. Heights above the density function indicate relative likelihoods but are not necessarily values between 0 and 1.

Q: Some important characteristics of probability distributions in general include the following distinctions: a. Discrete versus continuous b. Symmetric versus skewed c. Bounded versus unbounded d. Positive (or nonnegative) versus unrestricted e. All of these options

Q: Which of the following statements is correct regarding the graph of a discrete probability distribution? a. It is a series of spikes. b. The height of each spike is the probability of the corresponding value. c. There is an empty space between adjacent spikes. d. All of these options

Q: Which of the following statements are false? a. A probability distribution is discrete if it has a finite number of possible values. b. A probability distribution is continuous if its possible values are essentially some continuum. c. An example of a discrete probability distribution is the amount of rain that falls during the month of June in Michigan. d. None of these options

Q: The "building blocks" of all spreadsheet simulation models are: a. deterministic inputs b. random numbers between 0 and 1 c. decision variables d. probability distributions

Q: Simulation models are particularly useful for: a. forecasting. b. obtaining deterministic outputs. c. evaluating constraints. d. asking what-if questions.

Q: The deterministic (non-simulation) approach, using best guesses for the uncertain inputs, is: a. better to use in complicated real world applications. b. a good estimate of what the answer will be using a simulation approach. c. generally not the appropriate model. d. the preferred approach when there is correlation between input variables.

Q: Each different set of values obtained for the uncertain quantities in a simulation model can considered to be: a. the mean of the probability distribution. b. a scenario. c. a best guess. d. all of these options.

Q: Which of the following statements is true regarding a simulation model? a. It explicitly models decision-making under uncertainty b. It explicitly incorporates uncertainty in one or more input variables c. It provides probability distributions for all outputs, rather than expected values d. All of these options

Q: The transportation model is a special case of the minimum cost network flow model (MCNFM).

Q: In a transportation problem, if it costs $4 per item to ship up to 200 items between cities, and $2 per item for each additional item, the proportionality assumption of LP is satisfied.

Q: In transportation problems, shipping costs are often nonlinear due to quantity discounts.

Q: If all the supplies and demands for a transportation model are integers, then the optimal Solver solution may or may not have integer-valued shipments.

Q: Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.

Q: In blending problems, if a quality constraint involves a quotient, then the problem will be nonlinear.

Q: The optimal solution to an LP problem was 3.69 and 1.21. If and were restricted to be integers, then 4 and 1 will be a feasible solution, but not necessarily an optimal solution to the IP problem.

Q: The LP relaxation of an integer programming (IP) problem is the same model as the IP model except that some integer constraints are omitted.

Q: If Solver fails to find an optimal solution to an integer programming problem, we might be able to find a near optimalsolution by increasing the tolerance setting.

Q: Solver may be unable to solve some integer programming problems, even when they have an optimal solution.

Q: Integer programming (IP) models are optimization models in which all of the variables must be integers.

Q: If an LP problem is not correctly formulated, Solver will automatically indicate that it is infeasible when trying to solve it.

Q: Multiple optimal solutions are quite common in linear programming models.

Q: When we solve a linear programming problem with Solver, we cannot guarantee that the solution obtained is an optimal solution.

Q: Many of the most successful applications of optimization in the real world have been in the areas of scheduling, blending, logistics and aggregate planning.

Q: In nonlinear models, which of the following statements are correct? a. Only the objective function is not a linear function of the decision variables b. Only the constraints are not linear functions of the decision variables c. The objective function and/or the constraints are not linear functions of the decision variables d. All of these options

Q: The binary variables in the fixed cost models correspond to: a. the number of units or products produced b. the total profit c. the amount of labor hours d. a process for which a fixed cost occurs

Q: Any integer program involving 0 " 1 variables with constraint(s) is called a knapsack problem. a. three b. two c. one d. zero

Q: In aggregate planning models, which of the following statements are correct? a. The number of workers available influences the possible production levels b. We allow the workforce level to be modified each month through the hiring and firing of workers c. We eventually allow demand to be backlogged; that is, demand need not be met on time d. All of these options

Q: In a minimum cost network flow model, the flow balance constraint for each demandnode takes the form a. Flow out Flow in + Net supply b. Flow in Flow out + Net demand c. Flow in = Flow out d. Flow in Flow out + Net demand e. Flow out Flow in + Net demand

Q: In a minimum cost network flow model, the flow balance constraint for each supplynode takes the form a. Flow in Flow out + Net supply b. Flow out Flow in + Net demand c. Flow in = Flow out d. Flow out Flow in + Net supply e. Flow in Flow out + Net demand

Q: The flow balance constraint for each transshipmentnode, in a minimum cost network flow model, takes the form a. Flow in Flow out + Net supply b. Flow out Flow in + Net supply c. Flow in = Flow out d. Flow out Flow in + Net supply e. Flow in Flow out + Net demand

Q: In a typical minimum cost network flow model, the nodes indicate a. roads b. rail lines c. geographic locations d. rivers

Q: A minimum cost network flow model (MCNFM) has the following advantage relative to the special case of a simple transportation model: a. a MCNFM does not require capacity restrictions on the arcs of the network b. the flows in a general MCNFM don"t all necessarily have to be from supply locations to demand locations c. a MCNFM is generally easier to formulate and solve d. All of these options

Q: Transportation and transshipment problems are both considered special cases of a class of linear programming problems called a. minimum cost problems b. minimum cost network flow problems c. supply locations network problems d. demand locations network problems

Q: In a transshipment problem, shipments a. can occur between any two nodes (suppliers, demanders, and transshipment locations) b. cannot occur between two supply locations c. cannot occur between two demand locations d. cannot occur between a transshipment location and a demand location e. cannot occur between a supply location and a demand location

Q: In formulating a transportation problem as linear programming model, which of the following statements are correct? a. There is one constraint for each supply location b. There is one constraint for each demand location c. The sum of decision variables out of a supply location is constrained by the supply at that location d. The sum of decision variables out of all supply locations to a specific demand location is constrained by the demand at that location e. All of these options

Q: In a network representation of a transportation problem, the arcs generally represent: a. warehouses b. geographic locations c. flows d. capacities

Q: In a network representation of a transportation problem, the nodes generally represent: a. warehouses b. geographic locations c. flows d. capacities

Q: The decision variables in transportation problems are: a. profits b. costs c. flows d. capacities

Q: Which of the following is nota required input for a typical transportation problem? a. Capacities (or supplies) b. Demands c. Unit shipping (and possibly production) costs d. Distance from origins to destinations

Q: A typical transportation problem requires which of the following sets of input numbers: a. Capacities, demands and flows b. Capacities, demands and unit shipping costs c. Supplies, demands and flows d. Supplies, demands and arcs

Q: The objective in transportation problems is typically to: a. maximize profits b. maximize revenue c. minimize costs d. maximize feasibility

Q: The problem which deals with the direct distribution of products from supply locations to demand locations is called a(n) a. transportation problem b. assignment problem c. network problem d. transshipment problem

Q: To specify that must be at most 75% of the blend of, , and , we must have a constraint of the form a. b. c. d. e.

Q: The constraints in a blending problem can be specified in a valid way and still lead to which of the following problems? a. Unboundedness b. Infeasibility c. Nonlinearity d. None of these options

Q: Which of the following statements is a type of constraint that is often required in blending problems? a. Integer constraint b. Binary constraint c. Quality constraint d. None of these options

Q: If refers to the number of hours employee works in week, then to indicate that the number of working hours of 4 employees in week 3 should not exceed 160 hours, we must have a constraint of the form a. b. c. d.

Q: Which of the following statements are false? a. Solver does not offer a sensitivity report for models with integer constraints b. Solver's sensitivity report is not suited for questions about multiple input changes c. Solver's sensitivity report is used primarily for questions about one-at-a time changes to input d. None of these options

Q: Rounding the solution of a linear programming to the nearest integer values provides a(n) a. integer solution that is optimal b. integer solution that may be neither feasible nor optimal c. feasible solution that is not necessarily optimal d. infeasible solution

Q: Which of the following is true regarding multiple optimal solutions? a. All solutions have the same values for the decision variables b. All solutions have the same value for the objective function c. All solutions have the same shadow prices d. All of these options

Q: A common characteristic of integer programming models is that they: a. are easy to solve graphically b. produce the same answer and standard linear programming models c. often produce multiple optimal solutions d. all of these options

Q: Workforce scheduling problems are often integer programming models, which means that they have: a. an integer objective function b. integer decision variables c. integer constraints d. all of these options

Q: Many organizations must determine how to schedule employees to provide adequate service. If we assume that an organization faces the same situation each week, this is referred to as a. static scheduling problem b. dynamic scheduling problem c. transportation scheduling problem d. All of these options

Q: Which of the following does not represent a broad class of applications of linear programming models? a. Blending models b. Financial portfolio models c. Logistics models d. Set covering models e. Forecasting models

Q: The market manager is concerned about variability in the fat content of beef, noting that it actually can be as high as 20% and as low as 5%. For the model in Question 117, perform a sensitivity analysis to determine the effect, first on the amount of beef used, and then on the revenue. What do the results indicate? Should the manager be concerned?

Q: What happens to the revenue when the optimal plan changes to the one given in Question 118?

Q: NARRBEGIN: SA_117_120 A meat market manager for a large grocery store is preparing a processing plan to stock the shelves with sausage, ground meat, and jerky, which he can prepare from beef, pork and venison. Sausage and ground meat can be made of any mix of the beef, pork and venison, as long at the fat contents are below 15% for sausage and 10% for ground meat. Sausage sells for $5/pound and ground meat sells for $3/pound. Jerky, which sells or $10/pound, is made in a drying process from beef or venison. In the drying process, there is a 50% loss in weight for jerky made from beef (e.g., one pound of beef yields 0.5 pounds of beef jerky) and a 30% loss in weight for jerky made from venison. The market can sell at most 500 pounds of sausage, 1000 pounds of ground meat, and 100 pounds of jerky before their expiration dates. There are currently 1,000 pounds of beef (10% fat content), 500 pounds of pork (8% fat content), and 200 pounds of venison (2% fat content) available for processing. NARREND Suppose that later in the year, venison will be out of season, but the market will be able to obtain an additional 300 pounds of pork for the same costs. Develop a processing plan in that case. How does the solution change?