Modeling Mid Term

The objective function in a minimal spanning tree problem is to:

Determine the set of arcs that connect all the nodes in a network.

In a typical path problem, the supply node flow constraint RHS is equal to:

-1

The following functional relationship must be represented in a spreadsheet. How many output (or target) cells are there? Y = f(X1 , X2 , ... , Xk )

1

For a formulation with 3 structural variables, X1, X2, and X3. and 4 constraints corresponding to resources, the basic solution will consist of ___________ variables

4

The term "heuristic" means that

A feasible and (hopefully) good solution is found quickly using a rule of thumb.

Regression analysis is:

A modeling technique for analyzing the relationship between a continuous (real-valued) dependent variable Y and one or more independent variables X1, X2, ...Xn.

The net supply for each node in the network is indicated by:

A negative number next to each node.

In the model: Y = f(X1, X2, ..., Xk) +ε, the term ɛ is called

A random disturbance, or error

In a basic feasible solution

A solution to the system of equations can be obtained using a given set of basic variables (while the nonbasic variables are all set equal to zero)

The Answer Report includes:

A summary of the original and final (optimal) value of the objective cell and the decision variables.

What is the end result of the problem identification step?

A well-defined statement of the problem.

A standard form of an LP problem requires that

All constraints are of "=" type.

The term "a linear combination of the decision variables (X1 , X2 , ... , Xk )" means that

All decision variables are of power 1.

Changes or estimation errors might occur in: The objective function coefficients (the cj). b. The constraint coefficients (the aij). c. The RHS values for the constraints (the bi). d. All of the above.

All of the Above

The Sensitivity Report includes: a. Analysis of the changes in the objective function coefficients. b. Analysis of the changes in the RHS values. c. Analysis of the changes in the constraint coefficients. d. All of the above.

All of the Above

Common types of problems discussed in chapter 2 for which optimization can be used include: a. Product mix. b. Manufacturing. c. Financial planning d. All of the above.

All of the above

One advantage of calculating a confidence interval for a prediction, or prediction interval, of a new value of Y for a given value of X is a. That a prediction interval provides a lower bound on the fitted point value. b. That a prediction interval provides an upper bound on the fitted point value. c. That a prediction interval provides a confidence level (e.g. 95%) associated with the lower and upper bounds on the fitted point value. d. All of the above are advantages of constructing a prediction interval.

All of the above are advantages of constructing a prediction interval.

The "R Square" statistic in regression: a. Provides a goodness-of-fit measure. b. Is referred to as the coefficient of determination. c. Ranges in value from 0 to 1. d. All of the above are correct

All of the above are correct

Optimization problems involve the following element(s) a. Decisions. b. Constraints. c. Objective. d. All of the above

All of the above.

The goals of modeling efforts include a. Communication. b. Reliability. c. Auditability. d. All of the above.

All of the above.

Representing the decision variables requires

Allocating a separate cell in a spreadsheet to each decision variable.

If it is auditable, the model will

Allow a manager to retrace the steps followed to generate the different outputs from the model in order to understand the model and verify results.

Data Envelopment Analysis (DEA) is

An LP-based methodology for determining how efficiently various units within a company operate.

Analytic Solver Platform (ASP) is

An advanced software that has added capabilities that enhance the performance of the basis Excel solver.

A feasible region of the problem is

An area where all problem constraints are satisfied

What are the two common types of errors in human judgment?

Anchoring and framing

Suppose you want to find the minimum shipping cost using a transportation problem formulation. Further, you want to not ship any product from source i to destination j. When modeling this situation you should:

Assign a large cost, cij = M, to the shipment quantity (Xij) between source i and destination j.

Any shortest path problem can be modeled as a transshipment problem by:

Assigning a supply of 1 to the starting node, a demand of 1 to the ending node, and a demand of 0 to all other nodes in the network.

Decision makers expect that good decisions will always lead to good outcomes. Why is this not always the case?

Because unforeseeable circumstances beyond your control sometimes lead to bad outcomes even though the decision was sound

The TREND( ) function in Excel can be used to

Calculate the estimated values for linear regression model

Analytic Solver Platform (ASP) in robust optimization problems

Can accommodate uncertainties in constraint coefficients

In the statement MIN Z = c1X1 + c2X2 + ... + cnXn the symbol cn represents

Contribution to the objective function of 1 unit of product n

Each __________ must be placed in separate cells in the spreadsheet.

Decision variable.

The balance of flow constraints:

Define a relationship between inflow and outflow for each node in a network.

Structural variables are

Denoted as X1, X2, ... Xn.

Finding the optimal solution by enumerating the corner points of the feasible region requires

Determining the value of the objective function for each corner point of the feasible region.

A transshipment node can have:

Either a net supply or demand, but not both

The objective function relationship in the problem Z = f(X1 , X2 , ... , Xk ) must be

Either minimized or maximized.

The reduced cost for a variable is

Equal to the per unit amount the product contributes to profits minus the per unit value of the resources it consumes.

The shadow prices of resources:

Equate the marginal value of the resources consumed with the marginal benefit of the goods being produced.

Resources in excess supply

Have a shadow price of zero

What is the step immediately following completion of the problem formulation step?

Implementing this formulation as a spreadsheet model

The "robust solution" to an LP problem is

In the interior of the feasible region

If the allowable increase for a constraint is 10 and we add 11 units of the resource what happens to the objective function value?

Increase by unknown amount

A transportation problem:

Is a special case of transshipment problem.

Consider the set of simultaneous constraints x1 ≥ 5 and x1 ≤ 3. The feasible region for this problem

Is an empty set, because no values of x1 will simultaneously satisfy both constraints.

The transshipment problem:

Is the most general type of network flow problems.

Adjusted R2 statistic is recommended in multiple regression because:

It accounts for the number of independent variables included in a regression model.

What is a Physical Model

It is a real representation of an object, such as a car, that is built to a smaller scale for evaluation and testing purposes.

What is a solver?

It is an add-on to a spreadsheet, such as Excel, that is used to solve optimization problems.

What is Optimization

It is an area in business analytics that finds the most efficient way of using limited resources to achieve the objectives.

What is a good decision?

It is one that uses a structured, data-driven, and model-based process to make decisions

A constraint is binding if:

It is satisfied as a strict equality in the optimal solution.

What is business analytics?

It is synonymous to management science

In the following functional relationship, how many independent variables are there? Y = f(X1 , X2 , ... , Xk )

K

In the constraint f(X1 , X2 , ... , Xk ) ≤ b, the term "b" represents

Limited resource availability.

Linear programming (LP) involves creating and solving optimization problems with

Linear objective functions and linear constraints

Increasing the upper limits (or reducing the lower limits) to expand the range of feasible solutions is referred to as

Loosening

Nonnegativity conditions are examples of

Lower bounds on the decision variables.

The objective in most network flow problems is to:

Minimize the total cost, distance, or penalty that must be incurred to solve the problem.

What is the major benefit of modeling?

Models allow us to gain insight and understanding about the object or decision problem under investigation

Transportation problem is an example of a category of problems that can be modeled as __________ problems.

Network flow

Solution to a feasible LP problem will be found in

One or more extreme (corner) points of the feasible region

You must make a decision regarding job sequencing. Suppose that for a number of reasons there is only one option to proceed. This problem is not suitable for optimization because

Optimization requires that there must be decision alternatives.

The first step in implementing LP problems in a spreadsheet is:

Organize the data for the model on the spreadsheet

The proper sequence of steps in implementing the model in Excel presented in the textbook is:

Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.

In the equation: Yi = 𝛽0 + 𝛽1X1 i + 𝜀i, 𝛽0 and 𝛽1 are known as:

Population parameters

What is the purpose of implementation step in the problem solving process?

Preparing a message that is understood by various stakeholders in an organization and persuading them to take a particular course of action

Your company produces 10 different products. Each product uses resources, such as money, material and labor that have limited availability. You are responsible for developing a mathematical model to determine how many units of each product to produce to minimize the total production cost. What type of model is this?

Prescriptive

When Shadow price is greater than 0

Profit can increase due a binding constraint

When Shadow price is 0

Profit will not increase since it is a non binding constraint

The equipment replacement problem is a type of problem that can be modeled as a(n):

Shortest path problem.

In the following total cost (TC) equation, "F" is the fixed cost, "c" is the variable cost per unit and "Q" is the quantity produced. Which is (are) the dependent variable(s)

TC

In the following total cost (TC) equation, "F" is the fixed cost, "c" is the variable cost per unit and "Q" is the quantity produced. Which is (are) the dependent variable(s)?

TC

The "task pane" and "engine" are terms associated with

The Analytic Solver Platform (ASP).

A solution to an LP problem is degenerate when

The RHS values of any of the constraints have an allowable increase or allowable decrease of zero.

The regression sum of squares (RSS) represents

The amount of variation in Y around its mean that the regression function can account for

The difference (Yi - ) is referred to as

The estimation error, or residual, for observation i.

Multicollinearity is the term used to describe the situation when:

The independent variables in a regression model are correlated among themselves

One major limitation of a graphical approach to solving linear programming problems is

The number of decision variables cannot be more than 2

If you use the simplex method to solve any minimum cost network flow model having integer constraint RHS values, then:

The optimal solution automatically assumes integer values.

The problem, in which we need to determine the shortest (or least costly) route or path through a network from a starting node to an ending node is called:

The path problem.

A measure of the accuracy of the prediction obtained from a regression model is given by

The standard deviation of the estimation errors, also known as the standard error, Se.

The arcs in a network indicate:

The valid paths, routes, or connections between the nodes in a network flow problem.

Alternate optimal solutions to LP problems exist when

There can be more than one feasible point that maximizes (or minimizes) the value of the objective function.

In multiple linear regression models:

There can be more than one independent variable and all terms in the regression model must be linear

Suppose that 100 units of a resource are available for use. You found the optimal solution to the problem and determined that all 100 units of the resource are used. The constraint corresponding to the use of this resource is

Tight

The first often neglected step in formulating linear programming (LP) problems is

Understanding the problem.

In a transshipment problem formulation, the decision variables are of the form:

Xij, which is the number of items shipped (or flowing) from node i to node j.

An element of unsystematic or random variation in the dependent variable is expressed by ___________ in equation f(X1, X2, ..., Xk) + ε

ε