Mgmt & Science - Exam 1

Question 1

What are the Impact of small changes in RHS of constraints on objective function value

Answer 1

shadow prices and ranges of feasibility

Question 2

Ranges of optimality

Answer 2

The range of values over which an objective function coefficient next to a given decision variable can vary, without leading to a change in the values of the decision variables in the optimal solution

Question 3

What happens to the optimal solution when an objective function coefficient next to a decision variable changes, and the change is outside the range of optimality?

Answer 3

Current optimal solution no longer holds - problem needs to be resolved.

Question 4

Shadow Price?

Answer 4

The amount of change in the optimal value of the objective function per 1 unit increase in the right-hand side (RHS) of the constraint.

Question 5

Dual Price?

Answer 5

The amount of improvement in the optimal value of the objective function resulting from a 1 unit increase in a RHS of a constraint.

Question 6

What is synonymous with Shadow Price?

Answer 6

Dual Value

Question 7

Dual Price For maximization problems?

Answer 7

improvement translates to increase in the optimal value of the solution.

Question 8

Dual Price For minimization problems?

Answer 8

improvement translates to decrease in the optimal value of the solution.

Question 9

For minimization problems dual price is always?

Answer 9

negative (or reverse) of shadow price.

Example: SP = +10 Dual price = -10 (increase in the objective function value indicates lack of improvement);
Example: SP = -6 Dual price = +6 (decrease in the objective function value represents improvement, so dual price is positive).

Question 10

For maximization problems dual price equals?

Answer 10

shadow price (dual value).

Question 11

Range of feasibility?

Answer 11

Range within which a RHS of a constraint can vary without leading to a change in the value and interpretation of its shadow price

The range within which shadow price for a given constraint holds.

Question 12

The scientific revolution was initiated by who?

Answer 12

Frederic Taylor

Question 12

What happens to the optimal solution when a RHS of a non-binding constraint changes and the change is within the range of feasibility?

Answer 12

Since the dual price of 0 for the non-binding constraint holds we can assume no change in the optimal solution or objective function value

Question 14

Developed the simplex method?

Answer 14

George Danzig

Question 15

What happens to the optimal solution when an objective function coefficient next to a decision variable changes and the change is outside the range of optimality?

Answer 15

Current optimal solution no longer holds - problem needs to be resolved.

Question 16

What happens to the optimal solution when a RHS of a BINDING or NON-BINDING constraint changes and the change is outside the range of feasibility?

Answer 16

The problem needs to be resolved - optimal solution changes and current printout no longer applies

Question 17

Range of Feasibility?

Answer 17

The range of values over which the right-hand side of a constraint may vary without changing the value and interpretation of its shadow price (shadow price holds or remains valid).

Question 18

What happens to the optimal solution when a RHS of a non-binding constraint changes, and the change is within the range of feasibility?

Answer 18

Since the shadow price is 0 for the non-binding constraint we can assume no change in the optimal solution or objective function value. Changing the RHS of a non-binding constraint changes only the slack/value.

Question 19

What happens to the optimal solution when a RHS of a BINDING constraint changes and the change is within the range of feasibility?

Answer 19

Optimal solution changes (values of the decision variables will change)
Optimal value of the objective function changes - shadow price can be used to calculate the new objective function value

Question 20

What happens to the optimal solution when an objective function coefficient next to a decision variable changes, and the change is within the range of optimality (objective coefficient’s allowable increase – allowable decrease)?

Answer 20

Current optimal solution holds (values of the decision variables stay the same).
Objective function value changes (unless the decision variable had a value of 0 in the optimal solution).

Question 21

Alternate Optimal Solutions?

Answer 21

– Multiple solutions that are different but give you the same optimal solution.

Question 22

Special cases in LP models?

Answer 22

– Unboundness and alternate optimal solutions, and infeasibility.

Question 23

What kind of error message do you see when trying to use solver for an infeasible solution?

Answer 23

The Objective Cell Values do not converge, maybe you have a maximization problem instead of minimization, unboundness, constraint wrong. Most common problem is a missing constraint.

Question 24

What happens to the optimal solution when a RHS of a non-binding constraint changes and the change is within the range of feasibility?

Answer 24

Since the dual price of 0 for the non-binding constraint holds we can assume no change in the optimal solution or objective function value (changing the RHS of a non-binding constraint changes only the slack/surplus value).

Question 25

Controllable

Inputs?

Answer 25

(Decision Variables)

Question 26

Uncontrollable Inputs?

Answer 26

(Environmental Factors)

Question 27

7 Steps of Problem Solving?

Answer 27

(First 5 steps are the process of decision making)

1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criteria for evaluating alternatives.
4. Evaluate the alternatives.
5. Choose an alternative (make a decision).
   - ——————————————————————–
6. Implement the selected alternative.
7. Evaluate the results.

Question 28

Steps in Developing a Linear

Programming (LP) Model?

Answer 28

Step I
Define decision variables
Step II
Define the objective function
Step III
Define the constraints

Question 29

Heuristics ?

Answer 29

simplifying strategies or rules of thumb that decision makers use when faced with complex scenarios.

Question 30

Availability heuristic is?

Answer 30

based on the probability with which we recall certain events or instances.

If you witness a traffic accident on the way to school you are likely to assign a higher probability of accidents on that stretch of a highway.

Question 31

Strategies for making better decisions?

Answer 31

Acquiring experience and expertise
Reducing bias in judgment
Taking an outsider’s view (insider’s view tends to be more optimistic, e.g. you may believe that your house remodeling project will be completed on time and near the projected costs, while your friends may know that such projects end up being 20 – 50% over budget and overdue)
Using linear models 
Adjusting intuitive predictions

Question 32

Mathematical Models Classified?

Answer 32

Single criterion (e.g. Linear Programming models)

Multiple criteria (e.g. Goal Programming models)

Question 33

Stochastic models?

Answer 33

one or more uncontrollable inputs to the model are uncertain and subject to variation (e.g. probabilistic models)

Question 34

Deterministic models?

Answer 34

all uncontrollable inputs to the model are known with high degree of certainty

Question 35

The values of the decision variables that provide the mathematically-best output are referred to as the?

Answer 35

optimal solution for the model.

Question 36

Reduced Cost?

Answer 36

The amount by which an objective function coefficient next to a given decision variable in the objective function would have to change, for that variable to assume a positive value (>0) in the optimal solution.

Question 37

How to tell from a printout if alternative optimal solutions exist?

Answer 37

Reduced cost = 0 next to a decision variable with a value of 0 in the optimal solution.

Dual price of zero next to a binding constraint (degeneracy)