1. Long-term averages
TheMerger and Acquisition department of a global bank has been experiencing a verystable workload over the last few years. On average, the department completes75 deals per year with an average deal completion time of 1.8 months.
Q1.1 - How many deals on average are active at any point in time?
Q1.1 - How many deals on average are active at any point intime? Deals:
2. Capacity and Queues
Mango Electronics Inc. is a Fortune 500 company that develops andmarkets innovative consumer electronics products. The development processproceeds as follows. Mango researches new technologies to address unmet market needs. Patents arefiled for products that have the requisite market potential. Patents aregranted for a period of 20 years starting from the date of issue. Afterreceiving a patent, the patented technologies are then developed intomarketable products at four independent development centers. Each product isonly developed at one center. Each center has all the requisite skills to bringany of the products to market. However, any single center has the capacity toonly work at one patent at a time. It is assumed that development centers takeon development patents on a first-come first-serve basis.Mango is granted a patent every 7 months on average with standard deviation of7 months. The average development process lasts 25 months with standarddeviation of 50 months.
Q2.1 - What is the utilization of Mango’sdevelopment facilities?
Q2.1 - What is theutilization of Mango’s development facilities? Utilization:
Q2.2 - How long does it take an averagetechnology to go from filing a patent to being launched in the market as acommercial product?
Q2.2 - How long doesit take an average technology to go from filing a patent to being launched inthe market as a commercial product? Months:
Q2.3 - How many years of patent life are leftfor an average product launched by Mango Electronics?
Q2.3 - How many yearsof patent life are left for an average product launched by Mango Electronics?Years:
IndividualAssignment 1 ()
3. Queue Buildup
Acar park in the vicinity of a football field experiences high demand duringleague games. During such days, cars begin arriving 4 hours and 30 minutesbefore the game begins and the last vehicle arrives exactly when the gamestarts. Predictably, a larger inflow of cars is observed in the period between1h before the game and 30 minutes before the game begins. During this period,cars arrive at a rate of 130 cars per hour. During the rest of the time, carsarrive at 80 vehicles per hour. Due to technical limitations of the ticketingmachines, the car park can process a maximum of 90 incoming cars per hour.The car park has an abundance (unlimited amount) of space and the flow of carsis assumed continuous/fluid and deterministic. Ignoring any unpredictablevariability in both arrivals and processing times, construct a build-up diagramto answer the following questions:
Q3.1 - What is the length of the queue of cars when it is largest?
Q3.1 - What is the length of the queue of cars when it islargest? Cars:
Q3.2 - When does the last vehicle enter the car park? (after thegame starts)
Q3.2 - When does the last vehicle enter the car park? (after thegame starts) Minutes: