Simulation Modeling

Simulate:

duplicate features, appearance, characteristics of a real system -math models & physical models

Uncertain Outputs can affect (2):

1) performance (unsatisfactory/inefficient) 2) Risk (loss sales/customers/profit)

Simulation Advantages:

-easy & flexible -analyze large & complex real-world situations -allows user to ask "what-if?" -doesnt affect real-world -identifies important component -"time compression" is possible -allows inclusion of real world complications

Simulation Disadvantages:

-good sims = $$ & timely -doesnt give optimal solutions, runs trial & error so each run has diff results -requires generation of all conditions & constraints -each model is unique, not transferrable to other problems

Monte Carlo (Risk):

-models uncertainty by replicating it many times w diff values -2-step process (formulate/build & input model) -gives info on underlying distribution

Analogue (performance):

-product design & testing -space walks -"games"

System (performance):

-used to analyze system performance & effects of changes on system performance -continuous systems (weather) -discrete systems (logistics, production)

3 types of Simulation Modeling:

1) Analogue (performance) 2) Monte Carlo (risk) 3) System (performance)

Simulation Process (7):

1) Define problem 2) Introduce problem's variables 3) Construct math model 4) Set up possible courses of action (COAs) to test 5) Run experiment 6) Consider results, make any needed modifications 7) Decide which COA to take

Random Variables & Probability Distribution Options (4):

1) Discrete vs. Continuous 2) Symmetric vs. Skewed 3) Bounded vs. Unbounded 4) Positive vs. Not necessarily positive

Simulation Modeling (4) Aspects:

1) Replicates system/process 2) Many applications & approaches 3) Been around awhile (war dances, kids games) 4) Applications Vary (SimCity, Ed Teller's H-bomb)

Continuous Uniform Distribution (b/t a & b)(Excel):

=a+(b-a)*rand()

Discrete Uniform Distribution (b/t a & b)(Excel):

=int(a+(b-a)*rand()) OR =randbetween(a,b)

Discrete General Distribution (2+ outcomes)(Excel):

=lookup(rand(),range 1,range2) -range 1=lower limit & range2 = has variable values

Normal Distribution (mean =u, std. dev.= sigma)(Excel):

=norminv(rand(),u, sigma) -weights it based on location

Random Number (Excel):

=rand()

T/F: Simulations give optimal solutions

FALSE

Uncertain Inputs & Outputs represented by

RANDOM VARIABLES

T/F: Each run of a simulation has diff results

TRUE

Discrete Random Variables:

may assume one of a fixed set of values (integers=whole #s)

Continuous Random Variables:

may assume one of an infinite # of values in a specified range (1/4)

Simulation Models tell you...

most likely scenario

Decisions:

typically involve the FUTURE; future involves UNCERTAINTY & RANDOMNESS