1.Flight 77 has just opened for check-in. There is a dedicated check-in area for this flight, consisting of several check-in counters pulling passengers from a single queue operating on a first-in-first- out basis. The check-in counters have a total processing capacity of 80 passengers per hour. Although the airline recommends that passengers arrive between 2h and 1h30min before departure, in practice passengers begin arriving 3 hours before departure, and the last passenger arrives at the queue about 1 hour before the plane departs. During the 30-minute recommended arrival period, passengers arrive at a rate of 140 passengers per hour. During the rest of the arrival period between 3h and 1h before the flight departs (that is excluding the 30 minute recommended arrival period), passengers arrive at a rate of 50 passengers per hour. For simplicity assume that there is a single class in this flight, and that all passengers need to go through the same check-in process. Ignoring any unpredictable variability in both arrivals and processing times and assuming a continuous/fluid and deterministic flow of passengers, construct a build-up diagram to answer the following questions:
Q1.1 What is the largest number of passengers waiting in the queue at any point during the check-in process?Please explain how did you reach the answer.
Q1.2 How many passengers are still in the queue 1 hour before the flight departs? Please explain.
Q1.3 How much time before the plane’s departure will the very last passenger check-in? Please explain.
2.Mango Electronics Inc. is a Fortune 500 company that develops and markets innovative consumer electronics products. The development process proceeds as follows.
Mango researches new technologies to address unmet market needs. Patents are filed for products that have the requisite market potential. Patents are granted for a period of 20 years starting from the date of issue. After receiving a patent, the patented technologies are then developed into marketable products at five independent development centers. Each product is only developed at one center. Each center has all the requisite skills to bring any of the products to market. However, any single center has the capacity to only work at one patent at a time. It is assumed that development centers take on development patents on a first-come first-serve basis.
Mango is granted a patent every 7 months on average with standard deviation of 7 months. The average development process lasts 28 months with standard deviation of 56 months.
Q2.1 – What is the utilization of Mango’s development facilities?Please explain your calculation
Q2.2 – How long does it take an average technology to go from receiving a patent to being launched in the market as a commercial product?
Please explain your calculation
Q2.3 – How many years of patent life are left for an average product launched by Mango Electronics?Please explain your calculation
- (Little’s Law) Construction company: A construction company in Dubai regularly participates in the bidding process for large scale construction projects in the city. Over the last few years the company has enjoyed a stable success in being the lowest bidder, and hence undertaking the construction project. On average the company starts a new project every 6 months. The projects are, on average, completed in 4 years.
Q3.1 – What is the average number of projects that the contracting company is working on at any given time?
Please explain your calculation
Q3.2 – The management team is currently considering expanding the operations of the company into other regions of the Middle East. This would result in the company starting a new project every 4 months. However, they don’t want to increase the number of active projects at any given time, but rather take on shorter projects. How much shorter should the projects be to keep the average number of active projects the same as before?Please explain your calculation
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