Suppose that you have an appointment with a customer exactly one hour later. Due to your...

 

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Suppose that you have an appointment with a customer exactly one hour later. Due to your contract, there is a penalty you have to pay if you are late for the appointment. Suppose that the penalty you are going to pay is 2m TL in case you are m minutes late. Note that you don't have to pay (or receive!) anything if you arrive early. Also suppose that even if you are late for 2 minutes and 59 seconds, you will still be considered late for 2 minutes and only have a penalty cost of 4 TL. You can take the subway from your current position and with some additional walking you can be at your destination in 1 hour 5 minutes. The subway ticket is 4 TL. An alternative is walking to the ferry terminal (which will take 10 minutes), take the ferry to cross the Bosphorus (which costs 2 TL), and either walk another 20 minutes or take a taxi (which costs 10 TL) in order to reach your destination afterward. After the ferry the taxi ride will be only 5 minutes, however, you will need some time to find a taxi. Suppose that your best estimate for taxi waiting time is normally distributed with mean 5 minutes and standard deviation 1 minute at this time of the day. [Note that after the ferry you should either start walking (through the park!) or take a taxi. A mixture policy. (e.g., start walking and keep an eye on taxi, or wait for an empty taxi some time and later start walking, etc.) is not an option!]. Crossing the Bosphorus with ferry will take only 25 minutes. However, you might have to wait for the ferry when you arrive at the ferry terminal. Based on your experience you consider that the waiting time is uniformly distributed between 0 minutes and 20 minutes. Your objective is minimizing the expected total cost in TL (including both the transportation cost and the penalty cost). You decided to approximate the chance events by utilizing the Extended Pearson-Tukey Method. Draw the decision tree and determine the optimal strategy and expected cost. Suppose that you have an appointment with a customer exactly one hour later. Due to your contract, there is a penalty you have to pay if you are late for the appointment. Suppose that the penalty you are going to pay is 2m TL in case you are m minutes late. Note that you don't have to pay (or receive!) anything if you arrive early. Also suppose that even if you are late for 2 minutes and 59 seconds, you will still be considered late for 2 minutes and only have a penalty cost of 4 TL. You can take the subway from your current position and with some additional walking you can be at your destination in 1 hour 5 minutes. The subway ticket is 4 TL. An alternative is walking to the ferry terminal (which will take 10 minutes), take the ferry to cross the Bosphorus (which costs 2 TL), and either walk another 20 minutes or take a taxi (which costs 10 TL) in order to reach your destination afterward. After the ferry the taxi ride will be only 5 minutes, however, you will need some time to find a taxi. Suppose that your best estimate for taxi waiting time is normally distributed with mean 5 minutes and standard deviation 1 minute at this time of the day. [Note that after the ferry you should either start walking (through the park!) or take a taxi. A mixture policy. (e.g., start walking and keep an eye on taxi, or wait for an empty taxi some time and later start walking, etc.) is not an option!]. Crossing the Bosphorus with ferry will take only 25 minutes. However, you might have to wait for the ferry when you arrive at the ferry terminal. Based on your experience you consider that the waiting time is uniformly distributed between 0 minutes and 20 minutes. Your objective is minimizing the expected total cost in TL (including both the transportation cost and the penalty cost). You decided to approximate the chance events by utilizing the Extended Pearson-Tukey Method. Draw the decision tree and determine the optimal strategy and expected cost.

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To solve this problem and determine the optimal strategy and expected cost we can construct a decisi... View the full answer