BUAD 311 Practice Problem Set 2 Solution PDF

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assignment solution for the assignment on the assignment of the assignment with the solution to operation
Max capacity = bottleneck capacity = 45 groups per hour→1 group every 1.333 mins

The number of minutes it takes for 138 groups to be processed:
(138 groups * 1.3333 min...

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

Practice Problem Set #2: Little’s Law Solutions 1. Avis is a car rental company and is located 3 miles from the Los Angeles airport (LAX). Avis dispatches a bus from its office to LAX every 2 minutes. The average traveling time (a round trip) is 20 minutes. How many Avis buses are traveling to and from LAX? The flow rate is 30 buses per hour. The flow time is 20/60 =1/3 hours FT = WIP/FR FT*FR = WIP 30*1/3 = 10 10 buses are traveling to and from LAX.

2. Safety regulations require that the time between airplane takeoffs (on the same runway) be at least 3 minutes. When taking off, the run time of an airplane on the runway is 45 seconds. On average, planes wait 4 minutes and 15 seconds for take-off. On average there are 15 planes taking off per hour. How many planes are either on the runway or waiting to take off? FR = 15 plans per hour. FT = (0.75 +4.25)/60 = 1/12 of an hour WIP = FT*FR = 15*1/12 = 1.25

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

3. In Children’s Hospital in Seattle there are on average 60 births per week. Mothers and newborns stay, on average, two days before they leave the hospital. How many new mothers are staying in Children’s Hospital? FR = 60 per week FT = 2/7 weeks WIP = FT *FR = 60*2/7 = 120/7 = 17.1 On average there are 17.1 new mothers.

4. In the last university senate meeting the faculty representative complained about shortage of space in the faculty club. The representative claimed that a large fraction of the faculty has to wait a long time, sometimes more than 30 minutes until a table becomes available. At present the faculty club can seat 100 customers. A study conducted lately found that during lunch time the arrival rate is 150 customers per hour. The study also found that a person spends in the club, after he/she is seated, 75 minutes on average. a. If the management of the club wants to satisfy the faculty what should be the capacity of the club? FR = 150 customers per hour. FT = 1.25 hours WIP = FR*FT = 150*1.25 = 187.5 customers or 188 seats.

b. The club management is short of resources and is unable to add new capacity. The club management suggests introducing a self-service system. They believe that the new service will result in the faculty staying in the club for only 40 minutes. Will the self-service system solve the problem? WIP = FR*FT = 150*2/3 = 100 customers or 100 seats. This will solve the problem.

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

5. A call center employs 1000 agents. Every month 50 employees leave the company and 50 new employees are hired. a. How long on average does an agent work for this call center? Flow Rate = 50 people/month WIP = 1000 people Average working time = Flow Time = WIP/FR = 1000/50 = 20 months

Suppose the cost of hiring and training a new agent is $1000. The manager of this call center believes that increasing agents’ salary would keep them working longer term in the company. The manager wants to increase the average time that an agent works for the call center to 24 months. b. If an agent works for the call center for 24 months on average, how much can the company save on hiring and training costs over a year? Hint: First determine the current annual cost for hiring and training, then determine the new annual cost for hiring and training. Current annual cost for hiring and training: Flow Rate = 50 people/month = 600 people/year Annual hiring and training cost is 600*1000=$600,000 New annual cost for hiring and training: Average working time = Flow Time = 24 months = 2 years Flow Rate = WIP/FT = 1000 people/ 2 years = 500 people/ year Annual hiring and training cost is 500*1000=$500,000 Annual saving on hiring and training cost is $100,000.

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

6. (Spring 2016 Midterm 1 question) At the domestic terminal for United Airlines, all passengers must check in, obtain a boarding pass, and go thru TSA Security screening before they can go to their flight departure gate. Currently, 1000 people per hour arrive at the United domestic terminal. [Advance Check-In] Forty percent of passengers check in online and obtain a boarding pass in advance. They can go directly to Security when they arrive at the airport, but twenty-five percent of them still have luggage to check, and must first stop at the luggage counters before going through Security. The rest go straight to Security. [Airport Check-In] Sixty percent of passengers get their boarding pass at the airport. Half of them stop first at a cluster of automated kiosks to obtain their boarding passes. It takes an average of 6 minutes get a pass, including wait time plus using the kiosks. After printing their pass, they can go directly to Security, but one third of them still have luggage to check, and must first stop at the luggage counters before going through Security. The remaining passengers go directly into the single line at the luggage counters before going to Security to check luggage and confirm they have a boarding pass, or to obtain one along with their luggage receipts. On average, 80 passengers are waiting or being serviced at the luggage counters. [Security] Once they have a boarding pass, all passengers must go through Security. 20% of the passengers have TSA Trusted Traveler status; they zip thru Security (with much less hassel) in an average of only 4 minutes. The remaining passengers go through Security in an average of 10 minutes. HINT: Draw a process flow diagram for this process. a. On average, how many passengers are tied up using the automated kiosks to obtain a boarding pass? FR(kiosk) = 300 passengers/hr FT(kiosk) = 6 min By Little’s Law: WIP(kiosk) = FR(kiosk) * FT(kiosk) = 300 passengers/hr * 6min * (1hr/60min) = 30 passengers b. On average, how many passengers are tied up in Security? FR(security) = 1000 passengers/hr FT(security) = 10min*0.8 + 4min*0.2 = 8.8 min By Little’s Law: WIP(security) = FR(security) * FT(security) = 1000 passengers/hr * 8.8min * (1hr/60min) = 146.7 passengers c. Ignoring other incidental delays, what is the average time a passenger needing to check luggage will spend before going thru Security (in minutes)? FR(luggage) = 500 passengers/hr WIP(luggage) = 80 passengers By Little’s Law: FT(luggage) = WIP(luggage) / FR(luggage) = 80 passengers / 500 passengers/hr = 0.16 hour = 9.6min

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

d. Ignoring other incidental delays, on average, how many minutes is a passenger required to spend at the airport before they are able to go on to their flight departure gate? FR(system) = 1000 passengers/hr WIP(system) = WIP(kiosk) + WIP(luggage) + WIP(security) = 30+80+146.7 = 256.7 passengers By Little’s Law: FT(system) = WIP(system) / FR(system) = 256.7 passengers / 1000 passengers/hr = 0.2567 hour = 15.4min Alternatively: WIP(kiosks) + WIP(luggage) = 30 + 80 = 110. Overall flow rate is 1000 per hour or 1000/60 = 16.66666 per minute. So FT = (110/1000) hours or 110/16.66666 = 6.6 minutes before entering Security. FT(Security) is 8.8 minutes. So total time spent before going to your gate is 6.6 + 8.8 = 15.4 minutes. The hard way: (200/1000) spend 6 mins in kiosks before heading for Security. WIP(luggage) = 80 and FR(luggage) = 500/hr = 8.33333/min, so FT(luggage) = 80/8.33333 = 9.6 mins. Thus, 100 spend 6 mins at kiosks PLUS another 9.6 in luggage = 15.6 mins. Also, (400/1000) go directly to luggage and spend the 9.6 mins there. So (200/1000)[6] + (100/1000)[15.6] + (400/1000)[9.6] = 6.6 mins before heading to Security, where you spend an additional 8.8 mins, for a total of 15.4 minutes.

e. The United Operations team wants to improve the traveler’s experience by adding the capability to check luggage at the kiosks as well, by yourself. You get a boarding pass, luggage tags and receipts, and can then just drop your luggage on a conveyor as you head for Security. In tests, with this additional capability in place, there are only 50 people, on average, tied up in the luggage check process. All of the kiosk users self-serve their luggage check in; that is, NO kiosk users go to luggage check after getting their passes and luggage tags from the kiosk. But the average time at the kiosks rose from 6 minutes to 7 minutes. Under this new arrangement, what now would be the total number of minutes that a passenger would expect to spend at United before moving on to their flight departure gate? New WIP(kiosk) = FR(kiosk) * FT(kiosk) = 300 passengers/hr * 7min * (1hr/60min) = 35 passengers New WIP(system) = New WIP(kiosk) + New WIP(luggage) + WIP(security) = 35+50+146.7 = 231.7 passengers By Little’s Law: FT(system)

= WIP(system) / FR(system) = 231.7 passengers / 1000 passengers/hr = 0.2317 hour = 13.9min

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

7. (Fall 2017 Quiz 1 question) Trojan Scooters manufactures kick scooters. The firm’s assembly process has three workstations. See the process flow diagram below.

Yes

Station A

Station B

Standard design? Station C No

Station A: At this workstation, a worker can assemble the fork, steering support and handle for a scooter in 20 minutes. The workstation has 4 workers. Station B: At this workstation, a worker can assemble the wheel, brake, steering mechanism and deck for a standard design scooter in 20 minutes. The workstation has 2 workers. Station C: At this workstation, a worker can assemble the wheel, brake, steering mechanism and deck for a custom design scooter in 30 minutes. The workstation has 3 workers. Suppose that the market demand is 4.5 standard scooters per hour and 5.4 custom scooters per hour, and we find that the average work-in-process inventory at the stations A, B, and C are 4.4, 2.2, 3.3 scooters, respectively. On average, how long does a scooter stay in Trojan Scooters?

FT = WIP / FR = (4.4 + 2.2 + 3.3) / (4.5 +5.4) = 1 hour Or FT = WIP / FR = 4.4 / (4.5 +5.4) = 0.444 hour FT = WIP / FR = 2.2 / 4.5 = 0.489 hour FT = WIP / FR = 3.3 / 5.4 = 0.611 hour 0.444 + 4.5/(4.5 +5.4) *0.489 + 5.4/(4.5 +5.4)*0.611 = 1 hour

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

8. (Fall 2017 Midterm 1 question) You are managing room reservations at the Radisson Hotel in Los Angeles for events at USC. Room reservations are divided as follows: 70% request a room with single bed, 20% request a room with two beds and 10% request a room with three beds. The average nightly rates for single-bed rooms, two-bed rooms, three-bed rooms are $250, $300, $350, respectively. Rooms with a single bed are booked for 3 days on average, rooms with two beds are booked for 4 days on average and rooms with three beds are booked for 6 days on average. The average number of booked rooms with single bed is 120. a. What is the arrival rate of single-bed room reservations per week? FR = WIP/FT = 120/3 = 40 per day = 280 per week

b. What is the arrival rate of reservations (for rooms of any type) per week? 70% of X reservations per week is 280 single-bed room reservations per week è 280 = .70 X è X = 280 / .70 = 400 reservations per week

c. What is the arrival rate of two-bed room reservations per week? 400 * 20% = 80 reservations per week

d. What is the average number of booked rooms with two beds? WIP = FR*FT = 80 * (4/7) = 45.7

e. What is the arrival rate of three-bed room reservations per week? 400 * 10% = 40 reservations per week

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USC Marshall School of Business BUAD 311 Operations Management

Practice Problem Set #2

f. What is the average number of booked rooms with three beds? WIP = FR*FT = 40 * (6/7) = 34.3

g. What is the weekly revenue at Radisson? 280*3*250+80*4*300+40*6*350 = 390000 Or (120*250+45.7*300+34.3*350)*7 = 390000

h. Suppose you offer a discount on three-bed rooms. As a result, some customers who would otherwise have booked the other room types decide to book the three-bed rooms instead. The total number of weekly reservations remains the same. Will the average number of booked rooms increase or decrease? Justify your answer. WIP = FR * FT. Notice that increasing the percentage of three-bed room reservation increases flow time. Given that the total flow rate is kept fixed, by Little’s law, the WIP increases.

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