In early spring 2021, a team of health care innovators, operational leaders, and information technology experts met in Denver, Colorado. The goal is to create a new model for drive-through vaccination sites capable vaccinating 10,000 people in two days. The process designed by the team consists of the following four steps: 

 

I. Appointment verification. Upon arrival to the vaccination site, cars are directed to one of 6 lanes. (Assume that there is one patient per car). In each lane, a line attendant verifies appointments and hands out welcome packets. This greeting stage takes an average of 20 seconds.

II. Registration. At the end of each lane, there are 3 staff members checking the patients in. (The total number of registration stations is therefore 18.) On average, the registration process takes 1 minute and 30 seconds.

III. Vaccination. After registration, cars are directed into one of 16 vaccination tents. Each tent has a team of two vaccinators who confirm identities, ask screening questions, manage vaccination supplies, and administer and document vaccines. With the two vaccinators working together, this process takes an average of 1 minute and 30 seconds for each patient.

IV. Observation. Once vaccination is completed, patients are directed to the observation site, where they will wait for 15 minutes before being discharged. There are a total of 505 parking spots available. (1a) Which one of the four steps is the bottleneck, and how many patients can this site vaccinate in each hour?

(1b) The vaccination site planned to operate from 8am to 2pm each day. What is the demand rate (i.e. patients to vaccinate per hour), if 5,000 patients need to be vaccinated per day? (1c) The team is considering adding one volunteer to each of the 16 vaccination tents to help with screening questions and paperwork. This reduces the time each car spends at the vaccination tent from 1.5 minutes to 1 minute. What would be the new capacity of the process?

(1d) Assume that the change in (c) is implemented. Which step is the new bottleneck, and what would you do to meet the demand of 5,000 patients per day?

Question 2. The salad store in Morningside Heights is among the first fastcasual restaurant chains to create its own app and allow customers to order ahead on its website. Recently, the company redesigned the store for digital volume, with one salad production line in the front serving walk-in customers (who order their salads in person in the store), and an extra salad production line in the back, fulfilling online orders only. During lunch hours, 3 workers make salads at the front for walk-in customers, while 2 workers fulfill online orders in the back. Each salad takes an average of 4 minutes to prepare, and the standard deviation of this preparation time is 3 minutes. (The preparation times for walk-in and online orders have the same distribution.) The interarrival time for walk-in customers is 1.5 minutes on average, and the average interarrival time for online orders is 3 minutes. Assume that customers and online orders arrive randomly, such that the coefficient of variation of the interarrival times is 1 for both lines.

(2a) How many minutes on average does a customer need to wait in line, if the customer walks into the store to order a salad in person?

(2b) If the customer places an order online instead, how many minutes does it take for the customer to get the salad, after the customer placed the order? Note that this includes both (i) the time the order waits "in line" and (ii) the time it takes for a worker to prepare the order.

(2c) The store is considering redesigning its work flow again, merging the two salad production lines into a single line, and have all 5 workers prepare walk-in and online orders in a first-come-first-serve manner. If this change is implemented, what is the new waiting time? Hint: Once the two production likes are merged, the average interarrival time for orders (walk-in and online combined) will be 1 minute. This is because:

The interarrival time for walk-in customers is 1.5 mins, meaning that in each hour, 60/1.5=40 walk-in orders arrive. The interarrival time for online orders is 3 mins, meaning that in each hour, 60/3=20 online orders arrive. In total, 40+20 = 60 orders arrive in each hour, thus the new average interarrival time is 60/60 = 1 minute. Assume that the coefficient of variation of the new interarrival times is 1.

(2d) (2 points) In addition to the average waiting times, what other factors should the store consider when making the decision on whether to merge the two salad production lines? What do you think are the pros and cons?