Question 1 (25 points)

You have been asked to compute the capacity of the four resources at a local burger joint.

• On average, 80% of customers eat at the restaurant and 20% order to go. To simplify the analysis, assume that each customer only places a single order.
• The menu consists of burgers, fries, milk shakes, and soft drinks. On average, 90% of customers order a burger and 60% of customers who order a burger also order fries. For drinks, 40% of customers order a milk shake and 50% order a soft drink. The remaining 10% do not order a drink.
• All customers place their orders at the registers. For those who choose to dine in, the food and drinks are delivered to the table by the waitstaff. Patrons who place a to-go order wait at the register and pick up their order.
• Placing an order takes on average 3 minutes if the customer pays with a credit card and 4 minutes if the customer pays with cash. 90% of customers pay with a card and 10% pay with cash. There are two cashiers taking orders.
• Burgers and fries are prepared in the kitchen where three line cooks work. On average a burger takes 6 minutes to prepare, and an order of fries takes 3 minutes.
• Milkshakes are prepared at the milkshake bar where one staff member works. On average, it takes 5 minutes to prepare a milkshake. The same staff member also prepares the soft drinks, and this step takes 1 minute per drink.
• The waitstaff takes on average 10 minutes to serve each customer at various steps in the process. There are two waitstaff working at the restaurant.
• On average 5% of the dine-in customers send their burgers back to be recooked because the meat is undercooked. Recooking takes 2 minutes at the kitchen.

1. Compute the capacities of the cashiers, line cooks, milkshake bar, and the waitstaff in customers per hour.
2. Which resource is the bottleneck and what is the capacity of the restaurant?
3. The restaurant decides to redesign the order taking process. Under the new process, the cashier will only take the to-go orders and all to-go orders will be paid by card. The cashier will also process the payment (collected by waitstaff) for the dine-in customers. Dine-in customers pay either by credit card (90%) or cash (10%). Dine-in customers will place their orders and pay at the table. This will increase the average processing time for the waitstaff to 14 minutes (including the time to take orders and collect checks). As part of the redesign effort, the restaurant plans to train one of the cashiers as waitstaff reducing the number of cashiers to one and increasing the waitstaff to three. What is the capacity of the restaurant after the redesign is implemented?

Question 2 (25 points)

Consider a small pharmacy which administers vaccines in a separate area of the store. Patients arrive at a rate of 30 per hour according to a Poisson process. All patients first need to check in and sign the necessary paperwork. The service time at this step is exponentially distributed with a mean of 4 minutes and there are 3 people working at the check in desk. The site offers two different types of vaccines. 80% of the patients prefer vaccine A. Vaccine A administration takes on average 8 minutes (service time exponentially distributed) and there are 4 stations where it can be administered. 20% of the patients prefer vaccine B. Vaccine B administration takes on average 5 minutes (service time exponentially distributed) and there is 1 station where it can be administered. After receiving their shots, all patients need to proceed to a room where they will be monitored for adverse effects on average for 15 minutes (exponentially distributed). The monitoring room has 10 seats. For the monitoring room, assume that any time spent waiting to get a seat does not count towards the 15-minute monitoring time.

1. a. What are the average throughput times (Ws) at the check-in desk, vaccine A stations, vaccine B station, and waiting area, respectively?
2. b. On average, what is the total number of patients waiting to get a seat at the monitoring area?
3. c. Now just focus on the check-in desk and the vaccine administration stations. Assume that patients incur a cost of $20 per hour they spend at the pharmacy. If the hourly cost of adding one more staff member is $15, at which step (check in, vaccine A, vaccine B) would you add an additional staff member to achieve the biggest benefit, i.e., the reduction in patient waiting cost per hour minus the hourly cost of a staff member? Does adding an additional server at that step justify the cost (i.e., $15 per hour)?

Month	Demand
1	154
2	166
3	164
4	167
5	158
6	224
7	227
8	220
9	238
10	212

Question 3(10 points)

Develop a three-period moving average forecast for periods 4-11. Calculate the MFE,MAD and MAPEusing data and forecasts for periods 4-10

Question 4(20 points)

Develop two exponential smoothing forecasts: one with alpha = 0.4 and another with alpha = 0.7 for periods 2-11 . Assume your forecast for period 1 was 155. Calculate the MFE, MAD, and MAPEvalues using data and forecasts for periods 2-10 for both forecasting models. Which model is a better fit? Why?

Question 5 (20 points)

You are given the task of forecasting demand for snow shovels for a local retailer. As anticipated, you observe that demand is highly seasonal. The following table gives the quarterly demand data for the years 2017 to 2020.

Quarter	2017	2018	2019	2020
1	116	109	126	121
2	79	91	93	103
3	11	12	27	31
4	33	35	44	70

Using regression analysis as the first step, develop a forecasting model with quarterly seasonal indices. Then please forecast demand for each of the quarters for the year 2021. You may use the following values for the intercept and slope of your regression line.

Intercept	68.3546
Slope	0.0619

In your answer, please provide the quarterly regression forecasts for 2017-2020, the seasonal indices for each quarter, and your final seasonal forecasts for 2021. A final answer without these intermediate steps will not receive full credit.