Question

After an all-night study session the day before their last final exam, four students decide to stop by for some much - needed coffee at the campus Starbucks. They arrive at 8.30am and are dismayed to find a rather long line. Fortunately for the students, a Starbucks executive happens to be in line directly in front of them. From her, they learn the following facts about this Starbucks location: (I) There are three employee types: - There are two cashiers, taking all orders, preparing non-beverage food items, grinding coffee, and pouring drip coffee. - There is a single frozen drink maker who prepares blended and iced drinks. - There are espresso drink makers, preparing espressos, lattes, and steamed drinks. (II) There are typically four types of customers: - Drip coffee customers order only drip coffee. This requires 30 seconds of the cashier's time to pour the coffee. - Blended and iced drink customers order a drink that requires the use of the blender. These drinks take on an average 120 seconds of work of the frozen drink maker. - Espresso drink customers order a beverage that uses espresso and/or steamed milk. On an average, these drinks require 90 seconds of work of the espresso drink maker. - Ground coffee customers buy one of Starbucks' many varieties of whole bean coffee and have it ground to the specification at the store. This requires a total of 90 seconds of the cashiers time. (III) Each customer spends on average 20 seconds with the cashier to order and pay. (IV)The customers arrive uniformly at the following rates from 7 a.m. (when the store opens) until 10 a.m. (when the morning rush is over) with no customers arriving after 10 a.m.: - Drip coffee customers: 60 per hour - Blended and iced drink customers: 25 per hour - Expresso Drink customers: 45 per hour - Ground coffee Customers: 5 per hour Answer the following questions based on these facts: a. (10 points) Create a process flow diagram. Show the path of each type of customer. b. (3 points) Calculate the capacity (in minutes/hr) at each station (cashier, frozen drinks, espresso). c. (9 points) Calculate the total workload (in minutes) at each station given the customer arrival rates. d. (6 points) Calculate the utilization and implied utilization at each station? e. (4 points) Assume that approximately 10 percent of all customers order food which requires an additional 60 seconds of the cashier's time per transaction. Recalculate the utilization of cashier. f. (6 points) From their conversation with the executive, the students learn that Starbucks is considering a promotion on all scones (half price!), which marketing surveys predict will increase the percentage of the customers ordering food to 35% (the overall arrival rates of customers will not change). However, the executive is worried about how this will affect the waiting times for customers. How do the levels of the implied utilization change as a response to this promotion?

Answer 1

a. The process flow diagram illustrates the flow of customers through three stations: Cashier, Frozen Drinks, and Espresso.

b. Capacity at each station:

- Cashier: 120 customers/hour

- Frozen Drinks: 30 drinks/hour

- Espresso: 40 drinks/hour

c. Total workload at each station:

- Cashier: 0.5 hours/hour

- Frozen Drinks: 60 hours/hour

- Espresso: 67.5 hours/hour

d. Utilization and implied utilization:

- Cashier: Utilization = 50%, Implied Utilization = 100%

- Frozen Drinks: Utilization = 83.33%, Implied Utilization = 100%

- Espresso: Utilization = 112.5%, Implied Utilization = 100%

e. With food orders: Cashier Utilization = 55%, Implied Utilization = 100%

f. Implied utilizations may exceed 100% due to increased food orders, impacting service times.

Step-by-step explanation:

a. The process flow diagram outlines customer paths, branching based on their order types: drip coffee, blended/iced drinks, espresso drinks, and ground coffee. Each path represents the cashier, frozen drinks, and espresso stations.

b. Capacity is calculated as the inverse of the average service time. For example, the cashier's capacity is 60 minutes/hour divided by 20 seconds/customer, yielding 120 customers/hour.

c. Workload is the product of arrival rate and service time. For the cashier, it's 60 customers/hour * 20 seconds/customer = 0.5 hours/hour.

d. Utilization is the ratio of workload to capacity. Implied utilization considers the time spent by the cashier on additional tasks. For the cashier, utilization is 0.5 hours/hour divided by 1 hour/hour, resulting in 50%.

e. With food orders, the cashier's workload increases to 66 seconds/customer, yielding a utilization of 55%.

f. Increased food orders due to the scone promotion raise implied utilizations above 100%, potentially causing delays. This impact should be carefully managed to maintain customer satisfaction.