CRU Computer Rentals is a national computer rental company that purchases CPUs, monitors, printers and other peripherals

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CRU Computer Rentals is a national computer rental company that purchases CPUs, monitors, printers and other peripherals and rents them out for the long- or short-term. The flow of orders and units through the CRU system is as follows. After a customer reaches a sales specialist, the sales specialist checks the Available for Rent inventory in the company's central distribution center (DC) and sends the requested units to the Configuration department. After the units are configured to meet the customer's requirements, they are shipped to the customer. At the end of the rental term, the customer packages the units and ships them back to the company's main warehouse. Sometimes the units are returned by customers prior to the end of the rental term because they are broken or need repair. All returned units are received at the main warehouse in the Receiving department. Upon arrival, each unit is classified as either defective (status D) or not defective (status ND). Status ND units are put into storage to be worked on by the Pre-Configuration department, and status D units are put into storage to be worked on by the Repairs group. Historically, 30 percent of the units received have been classified as status D and 70 percent of the units received have been classified as status ND at Receiving. When a technician in the Pre-Configuration department is ready to work on a unit, it is taken from storage and brought to the technician. The technician runs a quick check to see that it is truly not defective; historically, 15 percent of status ND units have turned out to be defective. In other words, they should have been classified as status D at Receiving, but were not classified correctly. In this case, the technician changes the status of the unit to status D and returns it to the storage of the Repairs group. If the unit works, the technician reformats the hard drive, does some basic cleaning and puts the unit back into storage in the company's central DC as Available for Rent. When a technician in the Repairs group is ready to work on a status D unit, it is picked up from storage and brought to the technician. The technician then repairs the unit, potentially replacing some parts, and then makes it Available for Rent. The overall repair process, between the time a technician starts working on the unit and the time it becomes Available for Rent, takes on average 1/3 weeks. About 1,000 units are rented per week. The average rental term (duration of time the unit is with the customer) is eight weeks. There are, on average, 500 units waiting at Receiving, 1,000 units in status D (but not yet processed by the Repair group), and 1,500 units in status ND. In addition, CRU policy requires holding enough Available for Rent inventory in the company's central DC to cover two weeks of demand. For simplicity, assume that the time to classify the unit in the Receiving department, the time to configure the unit at the Pre-Configuration and Configuration stages and the shipment times are all almost equal to zero. (Note that the capacities of these staff are not infinity, so there are buffers in front of them.)

(a) Draw a process flow diagram of CRU's operations. [10 pts]

(b) What is the total number of units owned by CRU? Out of those, what is the average fraction of units that are with the customers, i.e., being rented at any given point in time? [15 pts]

(c) How much time, on average, elapses between the time a customer sends a unit back to CRU and the time it is Available for Rent in the central DC?