## Describe the input-output transformation and provide examples of feedbacks and controls: A shipping company

Homework Assignment 1 – Total Points: 200
ISOM 319: Operations Management

Problem 1: (15 pts) Describe the input-output transformation and provide examples of feedbacks and controls:
1) (5 pts) A shipping company
2) (5 pts) A new product development project
3) (5 pts) The cash cycle of a company

Problem 2: (15 pts) Provide a short description of the specific meaning of flow time (T), flow rate (R), and inventory level (I) for the following three scenarios.
1) A factory that makes iPhone 6s.
2) A home builder who builds single-family houses.
3) Somerset Café.

Problem 3: (20 pts) Apply Little’s Law to answer the following two questions. I=RT
1) (10 pts) Suppose that a restaurant makes 400 pizzas per week, each of which uses one-half pound of dough, and that it typically maintains an inventory of 70 pounds of dough. What is the average freshness (in terms of days) of a dough?
2) (10 pts) A branch office of an insurance company processes 10,000 claims per year. Average processing time is three weeks. Assume that the office works 50 weeks per year. How many claims are being processed at any given point?

Problem 4: (20 pts) Consider the operation of inspecting used cell phones, which includes three steps (from left to right in the graph below): (1) checking for visible physical damage, (2) inspecting for liquid damage, and (3) testing all main function. The processing rates of one employee performing each step are given in the graph. Calculate system parameters, R0, T0, and I0, of this operation. (cell phone per hour = rate)

Problem 5: (60 pts) Consider the following four-workstation production line.

Station Number of Machines Processing Time (hours)
1 1 0.05
2 6 0.25
3 3 0.2
4 2 0.167

1) (15 pts) What are the bottleneck rate, raw process time and critical inventory of this production line?
2) (15 pts) Assume that the current inventory level in this production line is 42 parts. What is the flow rate under the practical worst case? If the actual flow rate of this line is 10 jobs per hour, is the line running efficiently or not?
3) (15 pts) If we add an identical machine to Station 4 and keep the same number of inventory as in (b), i.e., 42, what is the flow rate under the practical worst case? If after adding this identical machine, the actual flow rate of the line increases to 14 jobs per hour, is the line running efficiently now?
4) (15 pts) Again, assume that the current inventory level in this production line is 42 parts. If we speed up both machines in Station 4 from each processing 6 jobs per hour to each processing 8 jobs per hour and keep the same number of inventory, what is the flow time under the practical worst case? If the actual flow time that we observed from the production line is 4 hours, is the line running efficiently now?
Problem 6: (70 pts) This question is based on the Starbucks’ Operations In-Class Exercise. Some information is modified and additional information is provided, so please read carefully.
The following information is available about the operations of a local Starbucks store.
A. There are three employees in the store:
Cashier who takes all orders and pours drip coffee.
Frozen drink maker who prepares blended and iced drinks.
Espresso drink maker who prepares espressos, lattes and steamed drinks.
B. Three types of drinks are offered:
Drip coffee: takes the cashier 20 seconds on average to pour a cup of coffee.
Blended and iced drink: takes the frozen drink maker 2 minutes on average to make one.
Espresso drink: takes the Espresso drink maker 1.5 minutes on average to make one.
C. Average customer demand rate (i.e., ) for each type of drink:
Drip coffee: 50 per hour.
Blended and iced drink: 20 per hour.
Espresso drink: 40 per hour.
We also know that each customer spends 20 seconds on average with the cashier to order and pay.
(1) (10 pts) Calculate the utilization of the three employees.

(2) (10 pts) As an effort to improve operations, the manager has cross-trained the frozen drink maker and the Espresso drink maker, i.e., now each of them can make both frozen and espresso drinks. What is the utilization of the two drink makers combined, i.e., if we consider the two drink makers as a workstation, what is the utilization of the workstation?

(3) (10 pts) Recently, the store has experienced a change in demand pattern. Specifically, the average customer demands for the three drinks are:
Drip coffee: 65 per hour.
Blended and iced drink: 15 per hour.
Espresso drink: 30 per hour.
Calculate the utilization of the cashier and the drink maker workstation (i.e., assume that cross-training is done as in Part (2)).

(4) (10 pts) Given the new demand scenario presented in Part (3), the manager has decided to shift the responsibility of pouring coffee to the two drink makers and let the cashier focus solely on taking orders and payments. Assume that each of the two drink makers also spends 20 seconds pouring a cup of coffee. Based on the average demand data in Part (3), calculate the utilization of the cashier and the drink maker workstation (i.e., assume that cross-training is done as in Part (2)).

(5) (30 pts) Given the new demand scenario presented in Part (3) and the change made in Part (4), in order to serve customers better, the manager has collected additional data to assess customers’ estimated waiting time before they can order, i.e., the waiting time before they are served by the cashier. The manager knows that the coefficient of variations of the customer demand process (i.e., the arrival process) and the cashier (i.e., the service process) are 1 and 1.3, respectively. Calculate the followings:
a. (10 pts) How long on average does a customer have to wait before ordering?
b. (5 pts) On average, how many customers are waiting to have their orders taken (DO NOT include customers waiting for their drinks)?
c. (15 pts) With the upcoming opening of a nearby office building, the manager estimates that the total demand rate (including all three types of drinks) will increase by 30%. What will be the waiting time before ordering given this 30% increase? What is the percentage increase of waiting time compared to that obtained in (a)?

Problem 7: (30 pts) The following information is available about the operations of a call center.
There are three departments in this call center:
• Sales Department that handles all calls related to placing new orders, and has 10 representatives.
• Return Department that handles all calls related to product return requests from customers, and has 8 representatives.
• Service Department that handles all other types of calls, mainly including warranty and billing issues, and has 9 representatives.
On average,
• Each representative in the Sales Department takes 5 minutes to answer one call;
• Each representative in the Return Department takes 6 minutes to answer one call; and
• Each representative in the Service Department takes 10 minutes to answer one call (regardless of call type).
On average, the call center receives 200 calls per hour, where 50% of the calls are for the Sales Department, 26% of the calls are for the Return Department, 18% of the calls are for warranty related issues, and the rest of the 6% are for billing related issues.
Calculate the utilization of the three departments.