Exercise. Build More Docks?

A firm operates a docking facility for container ships in Shanghai, China. At present, the facility consists of two identical docks. Ships typically arrive during the night. The number of ships that arrive during a single night varies from night to night, as given in the distribution below. Each dock can unload one ship during the day. Ships unable to unload must wait until the following day. The cost of delaying a ship (called a demurrage charge) is $10,000 per day. A new dock will cost $5 million a year, including amortized construction costs, maintenance, and operating costs.

Nightly Arrivals	Frequency
0	0.30
1	0.30
2	0.20
3	0.10
4	0.05
5	0.05

First, build a model to simulate daily arrivals over 365 days for the current two-dock system, and calculate the daily demurrage charge. Then sum the demurrage charge over all 365 days to estimate the average annual demurrage charge. Once the model is built, run your simulation for 1000 iterations. The annual demurrage charge is the output variable.

• In the Lesson example, a uniform distribution was used. Here you should choose the "Discrete Distribution" option after clicking 'Distribution'. The distribution window will open with default discrete values and probabilities listed. Change the X-table input to reference the "Night Arrivals" in column A and the P-table input to reference the "Frequencies" in column B. (Click in the parameter input cell and then click the little 'red arrow' icon see image that will appear to enter a cell range. Don't include the labels at the top of each column.)
• Another important difference between the Lesson example and this one is here we need to generate 365 random numbers, not just 1!
• Include a cell to initialize the system with the number of ships waiting from "the day before" your simulation begins (but before new ships arrive the first night). Set this number to 0 for now.

Second, can you justify adding additional docks? Answer this using the RiskSimTable() function to simulate 1000 iterations for the Decision Variable (number of docks) set to 2, 3, and 4. Which result is best?