Note: For all these problems assume Poisson arrivals and exponential service time
M83 Steve Jobs is a computer technician in an investment company. He responds to a variety of complaints from investment advisors regarding their computers performance. He receives an average of one computer every 55 minutes to repair. It takes him an average of 45 minutes to repair any of these computers. Steve believes that adding a second repair technician would significantly improve his department's efficiency. He has a friend, Steve Wozniak, who is looking for a job. He estimates that adding an assistant, but still keeping the department running as a singleserver system, would allow computer2 to be repaired in half the time, an average of 22.5 minutes to repair these computers. The investment advisors earn $35 for the company, on average, while the computertechnicians earn $18 per hour. An investment advisor who does not have access to his computer is unable to generate revenue for the company. a] Consider the performance of the office before the new technician is added. On average, how many computers [to the nearest 0.01 computers) are in the system given the arrival and service rates? b] Consider the performance of the office before the newtechnician is added. On average, how many hours (to the nearest 0.01 hour) does each computer spend in the system given the arrival and service rates? c] Consider the performance of the office before the newtechnician is added. Based on the average number of computers in the system, what is the total system cost [technicians cost and waiting cost) per hour (to the nearest thour)? d] Consider the performance of the office m the new technician is added. On average, how many computers [to the nearest 0.01 computers) are in the system given the arrival and service rates? e) Consider the performance of the office after the new technician is added. [in average, how many hours (to the nearest 0.01 hour) does each computer spend in the system given the arrival and service rates? f] Consider the performance of the office after the new technician is added. Based on the average number of computers in the system, what is the total system cost (technicia ns cost and waiting cost} per hour [to the nearest 0.01 Slhour)? g] Based on your cost analysis - is it worth it to add another technician? MBA A chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for theirjobs. The warehouse receives a request for supplies, on average, every three minutes. The average request requires 2.75 minutes to fill a request. Maintenance employees are paid $21.50 per hour and warehouse employees are paid $16 per hour. The warehouse operates 8 hours per day. a] Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day [to the nearest S) if there is only 1 warehouse employees working? b] Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day [to the nearest 5} if there are 2 warehouse employees working? c] Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day [to the nearest S} if there are 3 warehOuse employees working? :1] What is the optimal number of warehouse employees to staff the warehouse? M85 Use Little's Flow equations to solve the following problems. a] b] 1') A car rental company at a major airport has 70% of its fleet of 200 cars rented each day on average. Cars are rented for an average of 4 days. Howr mam;r rentals are processed each day on average? A wealth management company is able to process 300 customer statements (bills) per day. The average processing time is six {6) days. What is the average number of statements {bills} the company has in process at anytime? An accounting firm is capable of processing 20 E2 tax forms per day and the average number of forms on hand in the office is 64 forms. What is the average processing time per EZ tax form? A custom machine shop can process 25 orders per day. The average processing time is 4 days. What is the average number of orders that are in process at any time? A manufacturer's average workinprocess inventory for Part 1234 is 1,250 parts. The workstation produces parts at the rate of 150I parts per day. What is the average amount of time a part spends at the workstation? The average number of hotel rooms occupied per day during the month of March is 225. Rooms are booked on average for 2.5 days. On average, how many new bookings occur each day
