Consider the fish problem from Homework 7 with the following changes:

• a per fish, per day holding cost is incurred based upon the end of day inventory;

• a lost sales cost is incurred per customer not satisfied;

• the owner plans to operate the business for another 75 days

• fish left in the tank at the end of the time horizon are worth a salvage price/fish;

For each of the questions below solve a Markov process with rewards to determine net revenue. Assume the nominal

parameters of this model are:

• The maximum number of fish in the tank is 12.

• The selling price to customers is $20/fish.

• The Fuel Surcharge is $20/fishing day.

• The fisherman charges $4/fish.

• The Holding Cost is $1/fish/day.

• The Lost Sales Cost is $25/fish.

• The Salvage Price is $12/fish.

1. Using the nominal parameters above, determine the expected reward of the process for each state over periods

0 to 75.

2. Determine the steady state gain.

3. Change the capacity of the tank to 10 and redo questions 1 and 2. Explain the change in steady state gain.

4. Now, reset the capacity back to 12 and change the Holding Cost to $0/fish/day and redo questions 1 and 2.

Explain the change in steady state gain.

5. Change the Holding Cost back $1/fish/day and change the Lost Sales Cost per Fish to $0 and redo questions 1

and 2. Explain the change in steady state gain.

6. Change the Lost Sales Cost per Fish back to $25 and set the Fuel Surcharge to $0 and redo questions 1 and 2.

Explain the change in steady state gain.

7. Go back to the original parameters and change the demand mass function to the following and redo questions

1 and 2. What is the expected demand for the original mass function vs. the new one? Explain why the steady

state gain becomes negative in spite of the increase in expected demand.

Homework 8- ISE 362: Discrete Time Markov Processes

Due: 9 October 2020 (11:55pm)

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