BA 302 - Simulation

• Learning outcomes:
• Explain the need for simulation of business processes. What does simulation give you that the waiting line equations do not give you?
• Understand the difference between physical and computational simulation models.
• Understand that both are 'models.'
• Understand how a simulation model's stochastics can be modeled with random numbers.
• Know how to model discretely distributed stochastics with random numbers (random number assignment).
• Be able to explain the notion of 'Monte Carlo' simulation.
• Be able to analyze and evaluate simulation model results.

• Recognize the need/opportunity for simulation.
  

 

---

 

• Recall some performance measures of processes:
• Queue time.
• Waiting time.
• Idle time (slack time).
• Process time.

• With queuing (waiting line) models we have equations to compute their averages.
• !!! However, recall that averages tell only half the story ==> Must get an idea of (future) variation as well ==> simulation !!!
  
• Simulation:
• A model which represents both the structure and the dynamics of a system (deterministic or stochastic).
• Must have good correspondence.
• Must be simple enough to execute in reasonable time (parsimony).

• Can be physical (material based): e.g.,

  

• Can be mathematical/logical (information based); e.g.,

  

  

• Problem: can you think of some applications of simulation?
• Simulation goals:
• Imitate the relevant aspects of a real-world situation, either physically or mathematically.
• Study properties and operating characteristics and changes without actually having to experience them (what-if analysis).
• Make recommendations based on the results of the simulation.
• Advantages:
• Can analyze large, complex real-world problems for which no closed-form analytical solutions exist (both stochastic and deterministic).
• Can include real-world complications which most other techniques cannot.
• Enables 'time compression.'
• Allows 'what if' questions.
• Allows study of relationships in a system.
• Does not interfere with the real-world system.
• Allows inclusion of uncertainty (stochastics) into the system (we will do this with the homework exercise).
  

• Disadvantages:
• Can be time consuming; implies an investment in time and effort.
• Model and data must have good correspondence.
• Does not yield optimal solution (simulation ≠ optimization).
  
• Requires managerial input & support.
• Must be careful generalizing results to other situations.

• Approach:

• Simulation model components:
• Governing equations/principles: structure and dynamics of the system.
• Initial conditions: starting/initial state of the system.
• Decision variables: variables and values to be tested.

 

• Simulation of stochastic systems: Monte Carlo simulation: simulation that models future uncertainty (≠ scenario analysis):
• Overall approach:
• Simulate (run the model) many times; each time with a different 'future.'
• Each time, randomly select a 'future' from a probability distribution of future possibilities.
• After running many of these futures, consider the mean, minimum, maximum and variation of the results.

• E.g., simulation of barge unloading operation:
• Barges coming down the river to our dock to be unloaded.
• Barge arrival rate (number of barges arriving per unit of time) is λ
• ==> Barge mean inter-arrival time 1/λ.
• Barge mean service rate (number of barges unloaded per unit of time) is μ.
• ==> Barge mean unloading time = 1/μ.
• However, actual barge inter-arrival times vary.
• However, actual barge unloading times vary.
• ==> Sometimes we have extra capacity (idling); sometimes demand outstrips capacity (queue).
• To estimate the effect of a capacity change on waiting time variation(!!), we may want to simulate the system.
  
• Simulation 1: simple, discrete distributions.
• Historic/observed arrival data:




• Historic/observed unloading data:




• We must simulate random variation of inter-arrival and unloading times within the boundaries of these data:
• Build cumulative distribution for each variable.
• Establish interval of random numbers for each variable (see above).
• Generate random numbers to get values for each variable for each time step.
• Simulate a series of runs (trials) using those random numbers.

  
  

• Example: Barges arriving and unloading (discrete distributions) (Excel spreadsheet; requires Analysis Toolpack to be installed):
• Both inter-arrival and unloading times taken from discrete distributions.
• Couple things to notice:
• Model page contains the 'model;' i.e., the variables and their relationships with each other.
• Model represents one possible future of 20 barges arriving.
• Inter-arrival and unloading times are determined through random numbers.
• The translation of each random number is covered on the Distributions page.
• The mapping of the random number to the inter-arrival time or unloading time on the Model is done through a VLOOKUP.

• The Multiple Run page simulates 50 runs of the model; i.e., 20 barges each ==> 50 alternative futures.
• F9 runs the entire spreadsheet ==> 50 alternative futures of 20 barges arriving.
• Notice how through simulation we get some idea of the variation of performance data.

• Simulation 2: However, in reality barge arrivals and unloading do not follow a discrete probability distribution; instead, they follow a continuous distribution.
• Example: Barges arriving and unloading (continuous distributions) (Excel spreadsheet; requires Analysis Toolpack to be installed):
• Both inter-arrival and unloading times taken from negative exponential distributions.
• Both continuous distributions still 'honor' the discrete (observed) data.
• Excursion: how can we make a negative exponential distribution from discrete data?
• Equation for negative exponential distribution:
• P = 1 - e^−μt  where:
  

• μ = mean service rate
• t = service time

• ln(1 - P) = ln(e^−μt)
• ln(1 - P) = -μt ln(e)
• ln(1 - P) = -μt
• -t = 1/μ ln(1 - P)
• 1/μ = mean service time ==> can compute from discrete data:
  
• 1/μ = Σ{t * P(t)} / n ==> see Distributions sheet

• Replace P with a random number between 0 and 1 ==> (1−P) becomes a random number between 0 and 1.

• In the Model, replaced VLOOKUP with mean service time (1/μ) * ln(random number between 0 and 1): LN(RAND()).
  
• Check to see if we indeed get negative exponentially distributed numbers:
• Copy (Paste Values...) the Model numbers to a new sheet.
• Do a few more runs (F9) and add Multiple Runs data to the new sheet.
• Make a histogram of the new sheet data ==> hey presto!

• Homework Simulation: Note that the above examples of barge unloading have no capacity component; i.e., barges get served, one after another but the models do not offer ways to experiment with increasing or reducing capacity. The simulation model you work with in your homework DOES have capacity built in, and you are asked to use the model to decide whether or not to increase process capacity.

 

---

 

Test Questions:

• What are some of the advantages and disadvantages of simulation?
• Explain why both physical and computational simulation models are 'models.'
• What do we mean with the term 'Monte Carlo simulation'? How is a Monte carlo simulation different from a scenario simulation?
• What does a simulation model give you that a waiting line equation does not give you?
• Which of the barge unloading models must be preferred? The discrete one or the continuous one? Why?
• Suppose you have a simulation model but you do not like its outcomes. Could you not keep running it (try new combinations of random values) until you find a case that you like better?