Mathematics Simulation Programming Assessment
Problem:
A room has 10 cotton spinning looms. Once the looms are set up, they run automatically. The setup time is exponentially distributed, with
mean 10 minutes. The machines run for an average of 40 minutes, also exponentially distributed. Loom operators are paid $10 an hour, and
looms not running incur a cost of $40 an hour.
• How many loom operators should be employed to minimize the total cost of the loom room?
• How many people should be employed so that no loom waits more than 1 minute for an operator?
• How many operators should be employed to ensure that, on average, at least 7.5 looms are running at all times?
Task 1:
Simulation Construct the computer program in a general-purpose language (e.g., C, Java, Phyton)
1. Specify the Event-graph
2. Describe design choices:
• How do you advance the time?
• How do you represent the system state?
• How do you process the events?
• How do you compute the statistics?
3. Make a flowchart for each implemented routine (timing, event handling, statistics etc...)
Task 2:
Experiments Design the set of experiments to run:
1. What type of simulation?
2. How many repetitions do you need for obtaining 95% confidence?
3. Collect data (raw data should be included in the Report)
Task 3:
Output Analysis
1. For each measure of interest calculate:
• Sample Average
• Sample Variance
• Confidence Interval half-width
2. Validate the output obtained from the simulation
