MBA 638 – Operations Management
Professor Bellos – Spring 2022
· This exam is open book/notes/cases/slides/BB/video-lectures.
· No collaboration/communication with other students, use of Internet (other than to access Bb) or unauthorized materials (i.e., materials not provided through the course’s Bb or not mentioned on the Syllabus) is allowed.
· Submit your paper (as a Word document or PDF) through Blackboard by Sunday 02/06/2022 at 11:59 pm EST. Late exams will not be accepted.
· You may use a calculator or Excel. You may write and/or type. If you write, please write legibly and scan (no phone pictures).
· Show your work. Blank answers on the Word document (or PDF) will receive no credit.
· Remember to put units on your answers.
The Honor Pledge:
On my honor, I have neither given nor received unauthorized aid on this exam.
Part I –Quantitative Analysis (61 points)
1. (33 points) Managing the Pets-R-awesOMe Call Center
Tim Woods, a recent GMU MBA grad and serial entrepreneur, has opened Pets-R-awesOMe, an online pet store. He and his team are experimenting with call center staffing.
a) (13 points) The current call center format has two lines: one for customers who want to place an order and one for customers who want to report a problem. Each line is served by one specialized customer service representative. The call center is staffed so that at any given time, there is one representative taking customer orders and one representative addressing customer problems. On average, there is a new customer who wants to place an order every two minutes, exponentially distributed. Similarly, there is a new customer needing to address a problem every two minutes, exponentially distributed. The call center staffers are fast and can on average complete one call of either type in 75 seconds, with a standard deviation of 30 seconds. Each call center staff member is paid $15 per hour. The estimated cost of a customer waiting for a representative is $20 per hour due to lost goodwill and negative word of mouth.
Fill in the next table. (Don’t forget the units.) Show your work on the table or below.
What type of queuing system is this?
Average inter-arrival time
Average service time
# of servers
Avg. # of customers in the line
Avg. # of customers in the system
Avg. time a customer waits in the line
Avg. time a customer waits in the system
Probability the system is empty
b) (10 points) One option Pets-R-awesOMe is considering for its call center is to cross-train the two staff so they can both take orders or solve problems. In this case, all customers (i.e., those wishing to place an order and those wanting to report a problem) will join a single line and will be served by the first operator available. Each staffer after cross-training will be paid $16 per hour and will serve customers at the same rate as in part a). Arrivals are not expected to change for each type of call. The opportunity cost of waiting for a representative will still be $20 per hour.
Should Pets-R-awesOMe implement this system or keep the existing call center format (part a)? Justify your answer by calculating the total cost of each option. Please show your work.
c) (10 points) Another option is to invest in technology to augment the staffers’ capabilities in the dedicated server configuration of part a). In this case, they estimate that it will take on average 60 seconds to complete each customer call with a standard deviation of 24 seconds. Arrivals are not expected to change for each type of call. The technology is on a subscription basis, and the cost will be $10 per hour, in addition to the $15 per hour for each staff member. The opportunity cost of waiting will still be $20 per hour of waiting for a representative.
Should Pets-R-awesOMe implement this system or keep the existing call center format (part a)? Justify your answer by calculating the total cost. Please show your work.
2. (11 points) Managing the Process at Pets-R-awesOMe
Tim and his team are trying to develop some additional metrics. They have started to offer personalized dog training tools, called Poka-Yoke Collars, and it has turned into one of their most popular items, so demand is very large. The orders are sent from retail stores on Fridays and then filled on Fridays. The orders are received at a continuous rate of 40 per hour from 7 am until 11 am, the order cut-off time. There is an unlimited order buffer for any orders waiting. The personalization step starts at 7 am and operates continuously until all orders are personalized. The personalization takes 4 minutes per Poka-Yoke Collar, and all orders are for a single item.
a) (3 points) Draw an inventory build-up diagram (triangle) for the process. Please label it appropriately.
b) (8 points) Fill in the following information based on your diagram. If you need to show work, show it below.
Maximum number of orders waiting for personalization
Time the number of orders waiting for personalization reaches its maximum
Time the number of orders waiting for personalization goes to zero
Average number of orders waiting for personalization
Average time an order spends waiting for personalization
3. Managing the damaged order process at Pets-R-awesOMe (17 points)
Pets-R-awesOMe has developed a specific process to track and resolve orders reported damaged through shipping by customers. For some reason, there are large numbers of these. The following process is used to handle such issues. There is one employee per step.
To ensure that no claims “fall through the cracks” the process adheres to “lean principles.” Specifically, a claim for an order is handed from one station over to the next one only when the next station is ready to process the order (i.e., the stations are not allowed to have an inbox where orders accumulate).
a) (3 points) What is the throughput time (i.e., flow time)?
b) (4 points) What is the average inventory of orders in the system?
c) (5 points) What is the minimum time it would take to process a rush order (i.e., a high-priority complaint)?
d) (5 points) If you were to enable an inbox (only one) where claims about orders can “wait,” would you place this inbox right before: i) Station B or ii) Station C? Why?
Part II – Short-Answer Questions (22 points)
1. (2 points) What is an example of a Poka-yoke that Tim Woods and Pets-R-awesOMe could implement? What would your example Poka-yoke accomplish?
2. (6 points) Pets-R-awesOMe is considering making the ordering of Poka-Yoke Collars (i.e., the personalized dog training tools) available online only. The company is thinking of redesigning their website so that customers can use online tools to customize the dog training tools to their liking. Please identify two types of customer-induced variability (examples and classification) that the company may face in this case. What strategies can Pets-R-awesOMe use to manage the types of variability you identified? Please connect your answers to the “Breaking the trade-off between efficiency and service,” framework by F. Frei.
3. (2 points) In this course, we have talked about the queuing benefits of pooling. Why do you think in practice grocery stores or retailers like Pets-R-awesOMe may be hesitant to pool the waiting lines and instead they use configurations with multiple lines each served by a dedicated server?
4. (2 points) How do you think the pandemic has affected call center operations? In particular, the different types of variability that the call centers face and their ability to manage those types of variability?
5. (10 points) In your view, how do you think businesses can use the principles/concepts/methods we have discussed in this course so far to adjust to the post-COVID-19 reality or even get prepared for the next “black swan” event?
Ideally, your answer will meaningfully and succinctly draw on as many as possible principles/concepts/methods we have discussed and attempt to make connections between them.
Part III – Objective Questions (17 points)
1. (3 points) Consider the two processes shown below. Which one will have on average the higher total production outcome (i.e., total number of products produced in a given time period)?
a) Process A
b) Process B
c) They will have the same hourly production outcome.
a) Process A
b) Process B
c) On average, they will have the same total production outcome.
2. (2 points) What happens in Process B above if the buffer size increases from 2 to 10?
a) Throughput time increases
b) Throughput time decreases
c) Starving increases
d) Throughput rate decreases
e) Nothing changes
3. (2 points) Assume that there are on average 45 students in my undergraduate class for every quiz. It took me 90 minutes to grade all responses to Quiz 1. After several Grande Americanos from Starbucks, it took me 50 minutes to grade all responses to Quiz 2. What was the percent change in my productivity?
4. (2 points) On a typical weekday in January, 4200 customers visit the local Wal-Mart. It is estimated that, on average, there are 350 customers in the store. Assuming that the store is open 14 hours a day, how much time does the average customer spend in the store?
a) 7 min
b) 20 min
c) 14 hours
d) 1.167 hours
e) None of these
5. (2 points) The cycle time is always at least as long as the throughput time.
6. (2 points) All else the same, which curve in the figure below has less variability?
a) System A
b) System B
7. (2 points) In a pull system, if demand is below capacity, what is the utilization of the slowest machine?
a) Less than 100%
c) More than 100%
d) None of the above
8. (2 point) In a G/G/3 system, the arrival rate λ should never exceed the service rate μ.
That’s the end!
M/M/1 0.80000000000000016 0.80500000000000016 0.81000000000000016 0.81500000000000017 0.82000000000000017 0.82500000000000018 0.83000000000000018 0.83500000000000019 0.84000000000000019 0.8450000000000002 0.8500000000000002 0.8550000000000002 0.86000000000000021 0.86500000000000021 0.87000000000000022 0.87500000 000000022 0.88000000000000023 0.88500000000000023 0.89000000000000024 0.89500000000000024 0.90000000000000024 0.90500000000000025 0.91000000000000025 0.91500000000000026 0.92000000000000026 0.92500000000000027 0.93000000000000027 0.93500000000000028 0.94000000000000028 0.94500000000000028 0.95000000000000029 0.95500000000000029 0.9600000000000003 0.9650000000000003 0.97000000000000031 0.97500000000000031 0.98000000000000032 3.2000000000000037 3.3232051282051325 3.4531578947368464 3.5904054054054102 3.7355555555555608 3.8892857142857196 4.0523529411764763 4.2256060606060677 4.4100000000000072 4.6066129032258143 4.8166666666666753 5.0415517241379408 5.2828571428571536 5.5424074074074188 5.8223076923077048 6.1250000 000000142 6.4533333333333491 6.810652173913061 7.2009090909091107 7.6288095238095455 8.1000000000000245 8.6213157894737122 9.2011111111111425 9.8497058823529766 10.580000000000041 11.408333333333381 12.355714285714342 13.449615384615448 14.726666666666743 16.236818181818276 18.050000000000114 20.267222222222365 23.040000000000184 26.606428571428818 31.363333333333674 38.025000000000496 48.020000000000785 M/D/1 0.80000000000000016 0.80500000000000016 0.81000000000000016 0.81500000000000017 0.82000000000000017 0.82500000000000018 0.83000000000000018 0.83500000000000019 0.84000000000000019 0.8450000000000002 0.8500000000000002 0.8550000000000002 0.86000000000000021 0.86500000000000021 0.87000000000000022 0.87500000000000022 0.88000000000000023 0.88500000000000023 0.89000000000000024 0.89500000000000024 0.90000000000000024 0.90500000000000025 0.91000000000000025 0.91500000000000026 0.92000000000000026 0.92500000000000027 0.93000000000000027 0.93500000000000028 0.94000000000000028 0.94500000000000028 0.95000000000000029 0.95500000000000029 0.9600000000000003 0.9650000000000003 0.97000000000000031 0.97500000000000031 0.98000000000000032 1.6000000000000019 1.6616025641025662 1.7265789473684232 1.7952027027027051 1.8677777777777804 1.9446428571428598 2.0261764705882381 2.1128030303030338 2.2050000000000036 2.3033064516129071 2.4083333333333377 2.5207758620689704 2.6414285714285768 2.7712037037037094 2.9111538461538524 3.0625000000000071 3.2266666666666746 3.4053260869565305 3.6004545454545553 3.8144047619047727 4.0500000000000123 4.3106578947368561 4.6005555555555713 4.9248529411764883 5.2900000000000205 5.7041666666666906 6.1778571428571709 6.7248076923077242 7.3633333333333715 8.1184090909091378 9.0250000000000572 10.133611111111183 11.520000000000092 13.303214285714409 15.681666666666837 19.012500000000248 24.010000000000392 Utilization
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