Management 101 - Homework

The field of management science:

- Approaches decision making rationally, with techniques based on the scientific method - Concentrates on the use of quantitative method to assist in decision making - Is another name for decision science and operations research

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B then:

-0.5A + 0.5B -0.5C <= 0

Infeasibility means that the number of solutions to the linear programming model that satisfies all constraints is

0

If a basic transportation problem (with no capacity constraints for arcs) has four origins and five destinations, the LP formulation will have

9 Constraints Supply: 4 constraints saying only ____ can be assigned to _____ Demand: 5 constraints saying ____ can be accepted to _____

The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means

Agent 3 can be assigned to 2 or less tasks

Decision criteria

Are the ways to evaluate the choices faced by the decision maker

A transportation problem with 3 sources and 4 destinations will have 7 decision variables

False

Alternative optimal solutions occur when there is no feasible solution to the problem

False

Any change to the objective function coefficient of a variable that is positive in the optimal solution will change the optimal solution

False

Decision variables limit the degree to which the objective in a linear programming problem is satisfied

False

Frederick Taylor is credited with forming the first MS/OR interdisplanary team in the 1940's

False

Only binding constraints form the shape (boundaries) of the feasible region

False

The dual price associated with a constraint is the change in the value of the solution per decrease in the right-hand side of the constraint

False

There is a dual price for every decision variable in a model

False

Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time

False

Revenue management methodology was originally developed for the banking industry

False - for an Airline

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution

False - it could affect the optimal solution

Uncontrollable inputs are decision variables for a model

False - the decision variables are controllable

The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.

False. It is an interative process.

Deterministic

Known for sure like tax rate

How do you interpret a dual price for a constraint?

Say the dual price is 2.33 This would mean the objective function will increase by 2.33 units for every additional unit on the right-hand side of the constraint

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

Standard form

Range of feasibility

The range in which a resource can increase/decrease before the dual price changes.

Range of optimality

The range that the objective coefficient of X can vary before a new solution becomes optimal. i.e. You subtract the allowable increase and allowable decrease from the current value. And thus, the optimal solution will not change as long as the profit contribution of each Fliptop model is between ___ and ___.

The problem which deals with the distribution of goods from several sources to several destinations is the

Transportation problem

For any constraint, either its slack/surplus value must be zero or its dual value must be zero

True

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

True

In portfolio models, risk is minimized by diversification

True

Portfolio selection problems should acknowledge both risk and return

True

Revenue management methodology can be applied in the case of nonperishable assets

True

The assignment problem is a special case of the transportation problem in which all supply supply and demand values equal one

True

The direction of flow in the shortest route problem is always out of the origin node and into the destination node

True

The first step in the decision making process is to identify the problem

True

The standard form of a linear programming problem will have the same solution as the original problem.

True

When a route in a transportation is unacceptable, the corresponding variable can be removed from the LP formulation

True

The constraint 5x1 - 2x2 <= 0 passes through the point (x1= 20, x2 = 50)

True, just separate unknown variables and plug in the point

The shortest-route problem is a special case of the transshipment problem

True: 1 supply 1 demand

Stochastic

Unknown like demand

If a dual price/shadow price is zero, does this make sense?

Yes it does make sense, as it means that the overall profit will not change if more molding time etc. is made available. This is due to the fact that it is a non-binding constraint. If there is slack, that means there is a value of 0 for the dual price.

A cost that is incurred no matter what values the decision variables assume is

a sunk cost

Inputs to a quantitative model

are uncertain for a stochastic (unknown) model stochastic/probabilistic: unknown deterministic: known for sure

A negative dual price for a constraint in a minimization problem means

as the right-hand side increases, the objective function value will decrease

In a transshipment problem, shipments

can occur between any two nodes

The difference between the transportation and assignment problem is that

each supply and demand value is 1 in the assignment problem

Media selection problems usually determine

how many times to use each media source

Slack

is the amount by which the left side of a <= constraint is smaller than the right side

A model that uses a system of symbols to represent a problem is called

mathematical

Blending problem arise whenever a manager must decide how to

mix two or more resources to produce one or more products

Sensitivity analysis information in computer output is based on the assumption of

one coefficient change

Management science and operations research both involve

quantitative approaches to decision making

The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

reduced cost

The overall goal of portfolio models is to create a portfolio that provides the best balance between

risk and return

Decision variables

tell how much or how many of something to produce, invest, purchase, hire etc.

A constraint with a positive slack value

will have a dual price of zero Slack only occurs in non-binding constraints Dual values are zero for non-binding constraints because you don't use all the available resource in the first place anyway.