Seattle Coffee, founded in 1992, has experienced an enormous success within the last few years. Due...

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Seattle Coffee, founded in 1992, has experienced an enormous success within the last few years. Due to high demand for their products and the rise in the competition, the company is considering ways to streamline its operation in order to ensure a high-quality service delivery and maintain its market shares. In addition to coffee beverages and food items, the company sells whole bean coffee and coffee related hardware and equipment (e.g., espresso machines, grinders, mugs, etc.) in its stores. The demand breakdown and the average retail sale per customer for each merchandise is summarized below: Merchandise Type Coffee Beverages/Food Whole Bean Coffee Coffee Related Equipment Merchandise breakdown (%) 68 22 10 Ave. $ Amount per Transaction $6 $15 $30 As a part of a pilot project, the company is considering analyzing the waiting times in one of its smaller stores. Currently, the store has one employee who handles all transactions (this includes making and selling beverages and food products as well as selling coffee beans and equipment). After some preliminary data collection on the arrival rates and transaction times, it was concluded that the arrivals of customers to the store follow a Poisson distribution with a mean rate of 40 per hour. The transaction time was approximated with an exponential distribution with an average of 3 minutes. Furthermore, the result of a study indicated that customers did not join the queue when they saw 4 people in the queue (line plus service) and thus, their sale is lost to competition. (This behavior is only an approximation of the real behavior of customers and is made here for convenience. Also, for simplicity, assume that each customer buys only one of the three merchandise types in a visit). a) Identify the type of the queue which best approximates this situation and find the fraction of customers lost to competition and the average lost revenue per hour. b) What is the average throughput rate of the system? The operations analyst for the company is considering setting up a new counter at the corner of the store with a new employee. This new counter will only handle the sale of the coffee beans and coffee products. With this addition, the existing employee will be in charge of making and/or selling coffee beverages and food items. In this set up, the average transaction time for a beverage/food and the whole bean coffee/equipment queues will be 2 and 5 minutes, respectively (Assume that service times are exponential). If the hourly wage for the new employee is $22 and we assume that a customer would not join a queue if s/he finds 4 people in that queue, as before: c) Calculate the average revenue lost per hour for each of the two queues, and the average incremental total cost per hour (lost revenue plus wages are viewed as cost). Seattle Coffee, founded in 1992, has experienced an enormous success within the last few years. Due to high demand for their products and the rise in the competition, the company is considering ways to streamline its operation in order to ensure a high-quality service delivery and maintain its market shares. In addition to coffee beverages and food items, the company sells whole bean coffee and coffee related hardware and equipment (e.g., espresso machines, grinders, mugs, etc.) in its stores. The demand breakdown and the average retail sale per customer for each merchandise is summarized below: Merchandise Type Coffee Beverages/Food Whole Bean Coffee Coffee Related Equipment Merchandise breakdown (%) 68 22 10 Ave. $ Amount per Transaction $6 $15 $30 As a part of a pilot project, the company is considering analyzing the waiting times in one of its smaller stores. Currently, the store has one employee who handles all transactions (this includes making and selling beverages and food products as well as selling coffee beans and equipment). After some preliminary data collection on the arrival rates and transaction times, it was concluded that the arrivals of customers to the store follow a Poisson distribution with a mean rate of 40 per hour. The transaction time was approximated with an exponential distribution with an average of 3 minutes. Furthermore, the result of a study indicated that customers did not join the queue when they saw 4 people in the queue (line plus service) and thus, their sale is lost to competition. (This behavior is only an approximation of the real behavior of customers and is made here for convenience. Also, for simplicity, assume that each customer buys only one of the three merchandise types in a visit). a) Identify the type of the queue which best approximates this situation and find the fraction of customers lost to competition and the average lost revenue per hour. b) What is the average throughput rate of the system? The operations analyst for the company is considering setting up a new counter at the corner of the store with a new employee. This new counter will only handle the sale of the coffee beans and coffee products. With this addition, the existing employee will be in charge of making and/or selling coffee beverages and food items. In this set up, the average transaction time for a beverage/food and the whole bean coffee/equipment queues will be 2 and 5 minutes, respectively (Assume that service times are exponential). If the hourly wage for the new employee is $22 and we assume that a customer would not join a queue if s/he finds 4 people in that queue, as before: c) Calculate the average revenue lost per hour for each of the two queues, and the average incremental total cost per hour (lost revenue plus wages are viewed as cost).

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