Final Flashcards
Purpose of Simulation
To analyze large and complex real-world situations
Simulations:
Duplicate features, appearance, and
characteristics of a real system
Analogue Simulation
(Performance)
-Product design and testing
-Space walks
-“games”
Monte Carlo Simulation
(Risk)
-Models the uncertainty or randomness of a system by “replicating” it many times with different values for random inputs
-Provides knowledge of the underlying distribution of the uncertain events and a better understanding of the distribution of possible outcomes and the risk involved
2-Step Process of Monte Carlo Simulation
- Formulate (build your model)
- Input the model into your software (i.e. EXCEL)
System Simulation
(Performance)
-Typically used to analyze “system performance” and the effects of
changes on “system performance”
-Continuous systems (weather, wind flow)
-Discrete systems (production, logistics, transportation, service)
Simulation advantages
-Straight forward and flexible
-Can analyze large and complex real-world situations
-Allows the user to ask “What-if?”
-Simulations do not interfere with real-world system
-Identifies important component thru simulation interactions
-“Time compression” is possible
-Allows the inclusion of real world complications
Simulation disadvantages
-Good simulations can be expensive and time consuming
-Does not generate optimal solutions, but runs trial and error
approach yielding different results with each run
-Requires the generation of all conditions and constraints
-Each model is unique; not transferable to other problems
Probability Distributions
- Normal vs. Uniform
- Discrete vs. Continuous
- Symmetric vs. Skewed
- Bounded vs. Unbounded
- Positive vs. not necessarily positive
Discrete vs. Continuous Random Variables
Discrete random variables – may assume one of a fixed set of values
* Ex: Integers
- Continuous random variables – may assume one of an infinite number of values in a specified range
- Ex: the amount of gasoline in a gas tank (gallons, centimeters)
Profit Equation
𝜋 = 𝑠𝑥 − 𝑣𝑥 − 𝑓
Break-even point is when
Total Costs = Revenue
How to find indifference points
Set the two profit equations equal
Maximax
(Optimistic)
Max of Max’s
Maximin
(Pessimistic)
Max of Min’s
Minimax Regret
Minimum opportunity loss
Regret of outcome = (Best payoff per outcome) - (Actual payoff per outcome)
Criterion of Realism (Hurwicz)
Use coefficient of Realism
Realism Payoff = (alpha x Max.) + ((1-alpga) x Min)
Equally Likely (LaPlace) Criterion
Choose highest alternative average payoff
Ex. 0.5(100000)+0.5(200000)
Expected Monetary Value
Given p=0.9
Ex. 0.9(100000) + 0.1(200000)
Expected Opportunity Loss
EMV but for opportunity loss
(Choose lowest)
EVwPI =
Expected Value with perfect information
Sum of (p of outcome) x (best value of outcome)
EVPI =
The amount by which perfect information would increase our expected payoff
EVwPI - EMV
Decision Trees
Right to Left
Values on the right, than probabilities, find EMV, Calculate at circle, Decision at squares.
Unbounded Solutions always result from
A modeling error
Any change to the RHS of a non-redundant constraint will
Change the feasible region
Shadow Price
Indicated the amount by which the objective function value (solution) changes given a unit increase in the RHS value of the constraint
How to find indifference point for allowable increase/decrease
Set profit of normal equation equal to profit at adjacent point
Shadow Price
Change in Objective Function Value if we increase one constraint by 1 unit.
How to find shadow price
-Add 1 unit to 1 constraint
-Solve for new corner point
-Calculate new objective function value
-Compare to original Objective function value
-New OFV - Old OFV
Allowable increase/decrease only apply to
Objective function coefficient
Never Final value
What happens if LHS=RHS
Binding constraint
Shadow price doesn’t equal 0
What happens if LHS doesn’t equal RHS
Shadow Price equals 0
Nodes
(Circles) A specific point or location in a network
Arcs
Lines that connect nodes
Origins
A location that creates goods (factory)
Destinations
A location that consumes goods (stores)
Transshipment
A location through which goods pass on their way to or from other locations (warehouse)
Node Flow Balance Constraint
(Total Flow into Node) - (Total Flow Out of Node) = Net Flow
