Operation management Three questions
In-A-Jiffy Lube Inc offers both car wash and oil change services to its customers. It has 3 car wash bays, 1 service person working on oil changes, 1 person working on minor repairs and 1 cashier. Suppose arrival rate to the car wash facility is according to a Poisson Process with rate 10/hr. The arrival rate for the oil change is also a Poisson process with rate of 2/hr. While the oil change is being done, the service person also checks for some minor problems in the car. 20% of the cars tend to have a minor problem and these cars are sent to the minor repair facility. After the service is completed, all cars join a common queue to make their payment at cashier. The diagram below represents the service process at In-A-Jiffy. Car wash, Oil change and Minor repairs are exponentially distributed and take 15mins, 20mins and 30mins respectively. The payment process is also exponentially distributed and it takes 4min for the cashier to collect payment from a customer.
1. What is the average time a car coming for car wash spends in the system?
2. What is the average time a car that comes to get an oil change spends in the queue?
3. What is the average number of cars at Jiffy Lube (includes both queue and service)?
Joe Mataya’s company provides after-sales support for all the photo-copiers and high-load printers on our campus. When a machine fails, it is immediately brought to Joe’s workshop near Ozona’s on Greenville. The service (including ticketing) essentially consists of five steps, and each step is typically done by 1 person. The steps, with time required for each step in brackets, are: (i) Ticketing (15 min), (ii) Diagnosis (1 hr), (iii) Spare-part identification (30 min), (iv) Repair (2 hr) and (v) Assembly (90 min). Joe’s shop is open 8 hours a day. Assume there is no variability in processing times.
- Draw a process flow diagram and identify the bottleneck in the repair process.
- Suppose there are 800 machines all over campus. Each machine, on average, fails 9 times every year (300 working days). What should be the minimum capacity in Joe’s shop? What is the corresponding cycle time?
- How many people (in round numbers) does Joe need for each of the above 5 steps
Arthropod Inc. is a manufacturer of farm equipment delivered all over the US, Mexico and Canada. They produce two lines of machines which are popular in different locations: Centipede and Millipede. The same three steps are involved in the production of both machines, but because of design and assembly differences, the times taken for the tasks are different. They are provided in the table below.
The machines are manufactured-on-demand, meaning a machine is assembled only after an order is placed for it. The production season closely follows the farming season and goes from February 1st to September 30th of every year. There are four manufacturing cells at Arthropod, and each one of them can be configured to perform any one of the three assembly steps (A, B or C).
- In February, there is a very high demand for Centipedes, and no demand for Millipedes. How will you set up the four cells in February? In other words, how many cells will you dedicate to each of these steps? In your configuration, what is the maximum number of Centipedes that Arthropod can produce in an 8-hour shift?
- In September, the scenario would have switched completely. There is no demand for Centipedes, and there is high demand for Millipedes. Will you change the configuration of the factory? In your configuration, what is the maximum number of Millipedes that Arthropod can produce in an 8-hour shift?
- During May and June, Arthropod would like to maintain a 50-50 mix of Centipedes and Millipedes to meet the even demands for the two. What is the most number of Centipedes and Millipedes that can be produced in 8 hours, and how should the factory be configured to achieve that?Hint: The 50-50 mix implies that if Anthropod produces 1 Centipede, it should also produce 1 Millipede. So think about how much time the different steps would take if 1 Millipede and 1 Centipede has to be produced.