1. What are the problems facing Jason Mah and the Café D. Pownd?
There are several problems facing Jason Mah and Café D Pownd. One serious problem, which arose from lack of space, was the confusion building in the queues since people had no idea which line they were in. There were times when people had been lining up in the interactive cooking line for several minutes when they actually wanted to be in the pre-cooked line. Another problem was the long lines tended to create a wall of people in front of the soft drink machines, becoming burdensome even with as few as 20 people waiting for service. In order for people to get drinks, they had to barge through a line of people. Usually this confusion caused spills and was annoying for people waiting in line and the people trying to get to the soda machine. There was also the issue that the customers might use other alternative options for meals if the long wait time was not resolved at Café D Pownd. The residents had other options for meals. Suites in Cambridge Hall and Nottingham Hall were equipped with furnished kitchens, and residents could also order a wide variety of food for delivery to the residence from local restaurants using their residence meal plans.
2. What are Mah’s constraints?
Mah’s major constraint is the lack of space that the cafeteria has. The general layout of the serving area was not appropriate since a lot of things were forced into a small area. Besides the poor layout, Mah faced the problem of finding a way to accommodate a large number of people in a small are. Another constraint that Mah had was the fact that cafeteria was very inefficient during the peak period between 5-6:30 pm. Roughly 366.66 residents were expected to be served during this short window. Out of 550 students, two thirds showed up to the cafeteria during the peak period. Another major constriction for Mah is, he hoped to resolve the situation without any major investments or disbursements.
3. Construct a process-flow diagram for the Café D. Pownd.
4. Use Microsoft Excel to construct frequency histograms for the customer interarrival times, precooked food service times, interactive service times, and cashier service times. For customer interarrival times, use class limits of 0.00, 0.15, 0.30, 0.45, 0.60, 0.75, 0.90, 1.05, and 1.20. For precooked food service times, use class limits of 0.00, 0.50, 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00, 4.50, and 5.00. For interactive service times use class limits of 4, 5, 6, 7, and 8. For cashier service times, use class limits of 0.00, 0.50, 1.00, 1.50, 2.00, 2.50, and 3.00. Find the mean and standard deviation of these histograms. What sort of distributions do these random variables appear to have? (Hint: compare them to the exponential, uniform, and normal probability distributions.)
*Frequency histograms can be found on the attached page.
Customer interarrival time- 0.26
Precooked food service time- 1.03
Interactive service time-5.98
Cashier service time- 0.40
Customer interarrival time- 0.24
Precooked food service time- 1.20
Interactive service time- 1.08
Cashier service time- 0.54
5. Would you have collected data differently than Jason Mah?
Yes, I would have collected data differently than Jason Mah. I would have timed each customer from the time they walked into the cafeteria to the time they finished paying at the cashier. I would also take a sample from the entire day instead of only the peak times, to more accurately depict the wait time for service throughout the day. Only timing the peak hours may be bias, since that would only show the busiest time at Café D Pownd.
6. What is the arrival rate of customers desiring (made-to-stock) pre-cooked food?
Precooked service line attracted twice as many students as the interactive line. Out of 35 students, 26.25 students went to pre-cooked or interactive line. Since, twice as many students went to the pre-cooked like, out of 35 students, 17.5 students went to the pre-cooked line.
35 students x 25% self service = 8.75 (self service/directly to cashier) 35-8.75= 26.25 (pre-cooked or interactive line)
8.75×2 (twice as many students went to the pre-cooked line) =17.5 (pre-cooked line)
Sum of all arrivals = 8.95 minutes
8.95×25% = 2.24 minutes for all self service arrivals
8.95-2.24= 6.71 minutes for all interactive and pre-cooked arrivals 6.71/3=2.24×2=4.47 minutes for all customers desiring pre-cooked food 8.95/35 = 0.26 seconds
The arrival rate of customers desiring pre-cooked food is every 0.26 seconds
7. What is the arrival rate of customers desiring (made-to-order) interactive food?
The arrival rate of customers desiring interactive food is 8.75 customers.
Sum of all arrivals = 8.95 minutes
8.95×25%=2.24 (minutes for all self service arrival)
8.95-2.24= 6.71 (minutes for all interactive and pre-cooked arrivals) 6.71/3=2.24 (minutes for all customers desiring interactive food) 8.95/8.75= 1.02
The arrival rate for customers desiring interactive food is every 1.02 minutes.
8. What is the combined service rate of the two pre-cooked food servers?
The combined service rate of the two pre-cooked food servers is 1.03 minutes. This is the average of the 35 samples taken.
36.21/35= 1.03 minutes
9. What is the combined service rate of the two interactive food servers?
The combined service rate of the two interactive food servers is 5.98 minutes. This is also derived from the 35 samples presented and is the mean of the interactive service times.
10. Given the arrival rate of customers desiring pre-cooked food and the combined service rate of the two pre-cooked food servers, what is the expected customer waiting time in line?
The expected waiting time in line for customers desiring pre-cooked food is 37 seconds.
1.03 minutes = 63 seconds (service rate for pre-cooked meals) Arrival rate for customers desiring pre-cooked meals is every 26 seconds.
63 seconds-26 seconds=37 second waits
11. Given the arrival rate of customers desiring interactive food and the combined service rate of the two interactive food servers, what is the expected customer waiting time in line?
The expected waiting time in line for customers desiring interactive food is 4.96 minutes.
The arrival rate for customers desiring interactive food is every 1.02 minutes The service rate of the two interactive food servers is 5.98 minutes
5.98-1.02=4.96 minute wait
12. If you were Jason Mah, what course of action would you take in order to resolve the problems facing the Café? What kind of analysis would you carry out?
If I were Jason Mah I would hire two part time interactive food servers to cut the waiting time in line for customers desiring interactive food. It seems as though customers are getting tired of waiting close to 6 minutes in line to be served and they are thinking of seeking other alternatives for meals. The part time employees would work during the peak times to alleviate the two full time interactive food server’s workload. This would help cut down the service time and the wait, as a result creating a better customer experience. I would also ensure that the work area for the two pre-cooked servers is large enough for them to operate efficiently since there were complaints that they operated in such close proximity. They served simultaneously and it is important that they do not slow each other down. Looking at the Café D. Pownd Layout we can see that the pre-cooked station is not placed in the most effective area. The chart attached to this paper will demonstrate a more effective layout with more work area for the servers. I would also post a description of the meals served at the pre-cooked line in order for customers to be well informed on the meals prior to reaching the servers.
From observations, Jason noticed that approximately 20 to 30 seconds of the service time was due to customer asking information about the meals offered. To help eliminate the queue build up and speed up the servers I would post a description of the meals served at the pre-cooked line in order for customers to be well informed on the meals served prior to reaching the servers.
If I were Jason Mah I would analyze how the problem with weighing salads and candy could be fixed. There was a line build up at the cash register because of the cashiers spending time to weigh salads and candy. I would also analyze what can be done about some of the pricing that was not programmed into the cash register, which again slowed down the payment line.
13. What recommendations do you have for Mah?
I would recommend for Mah to realign the layout of Café D Pownd. The second recommendation I would make is to make sure that the servers have enough space to work efficiently since they can slow each other down if they are working in a constricted space. Although I am aware that the establishment is small in size, there seems to be room for improvement with the general layout of the stations. The soda machine and the pre-cooked station have to be moved. The altered layout of Café D Pownd is attached to the paper. Posting a description of the meals served would tremendously speed up the pre-cooked line and mostly eliminate the 20 to 30 seconds that is wasted on providing customers information about the meals. I would also pre package the salads and candied with weight and pricing to speed up the payment line. Alongside, I would also program the pricing for daily specials and other items that were not recorded in the database to eliminate the time spend looking for the price of those items.