Mgmt & Science - Exam 1 Flashcards
What are the Impact of small changes in RHS of constraints on objective function value
shadow prices and ranges of feasibility
Ranges of optimality
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
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?
Current optimal solution no longer holds - problem needs to be resolved.
Shadow Price?
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.
Dual Price?
The amount of improvement in the optimal value of the objective function resulting from a 1 unit increase in a RHS of a constraint.
What is synonymous with Shadow Price?
Dual Value
Dual Price For maximization problems?
improvement translates to increase in the optimal value of the solution.
Dual Price For minimization problems?
improvement translates to decrease in the optimal value of the solution.
For minimization problems dual price is always?
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).
For maximization problems dual price equals?
shadow price (dual value).
Range of feasibility?
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.
The scientific revolution was initiated by who?
Frederic Taylor
What happens to the optimal solution when a RHS of a non-binding constraint changes and the change is within the range of feasibility?
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
Developed the simplex method?
George Danzig
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?
Current optimal solution no longer holds - problem needs to be resolved.
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?
The problem needs to be resolved - optimal solution changes and current printout no longer applies
Range of Feasibility?
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).
What happens to the optimal solution when a RHS of a non-binding constraint changes, and the change is within the range of feasibility?
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.
What happens to the optimal solution when a RHS of a BINDING constraint changes and the change is within the range of feasibility?
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
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)?
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).
Alternate Optimal Solutions?
– Multiple solutions that are different but give you the same optimal solution.
Special cases in LP models?
– Unboundness and alternate optimal solutions, and infeasibility.
What kind of error message do you see when trying to use solver for an infeasible solution?
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.
What happens to the optimal solution when a RHS of a non-binding constraint changes and the change is within the range of feasibility?
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).
Controllable
Inputs?
(Decision Variables)
Uncontrollable Inputs?
(Environmental Factors)
7 Steps of Problem Solving?
(First 5 steps are the process of decision making)
- Identify and define the problem.
- Determine the set of alternative solutions.
- Determine the criteria for evaluating alternatives.
- Evaluate the alternatives.
- Choose an alternative (make a decision).
- ——————————————————————– - Implement the selected alternative.
- Evaluate the results.
Steps in Developing a Linear
Programming (LP) Model?
Step I Define decision variables Step II Define the objective function Step III Define the constraints
Heuristics ?
simplifying strategies or rules of thumb that decision makers use when faced with complex scenarios.
Availability heuristic is?
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.
Strategies for making better decisions?
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
Mathematical Models Classified?
Single criterion (e.g. Linear Programming models)
Multiple criteria (e.g. Goal Programming models)
Stochastic models?
one or more uncontrollable inputs to the model are uncertain and subject to variation (e.g. probabilistic models)
Deterministic models?
all uncontrollable inputs to the model are known with high degree of certainty
The values of the decision variables that provide the mathematically-best output are referred to as the?
optimal solution for the model.
Reduced Cost?
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.
How to tell from a printout if alternative optimal solutions exist?
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)
