# 2024 Supply Chain Homework

2024 Supply Chain Homework

2024 Supply Chain Homework.

Brainy

Conceptual Questions (10 points each)
C1. Choose two firms you know from different industries. For each, briefly explain the corporate strategy, identify the order winners and the order qualifiers, and relate these to the process strategy of the firm. (No need to make explicit contrasts or comparisons across the two firms.)
C2. Identify some reasons why a firm might want to lead demand, i.e., make incremental capacity investments to stay mostly ahead of the current demand level. Similarly, identify some reasons why a firm might want to lag demand, i.e., let capacity fall behind the current demand level between incremental capacity investments.
C3. The capacity of a process is determined by the capacity of the bottleneck step, but doubling the capacity of the bottleneck step may not double the capacity of the process. Explain why this is so.
C4. Creating a production line by assigning a network of tasks to workstations is a powerful concept for operations management. What challenges can you imagine in practice with the implementation of this concept?
Quantitative Questions (12 points each)
1. (a) A truck stop on I-95 uses fuel pumps that deliver 6 gallons per minute. The truck stop operates 24 hours per day and typically serves 300 trucks each day. The average fuel purchase is 90 gallons per truck. The utilization of the pumps is only about 80% (due to variability in the arrival of trucks). How many pumps are installed at the truck stop?
(b) During the off-peak period, a supermarket has on average 140 customers per hour. Cashiers serve 60%; the rest use the self-service registers. It takes 2.4 minutes for a cashier to serve the average customer, but the utilization of cashiers is only about 70% (due to variability in the arrival of customers). How many cashiers are working during the off-peak hours?
2. Watch the video about Southwest Airlines that is posted with this assignment on Blackboard. Find appropriate publically available data about Southwest’s operations, in order to justify quantitatively the claim made at the end of the video: adding one minute to the time it takes Southwest Airlines to get an aircraft back into the air for its next flight (“turn time”) would entail a need for an additional five aircraft in their fleet.
3. The figure below shows the process flow for customers who enter a service shop. After step T1, Type A customers go to step T2 and then to any of the three stations at step T3, followed by steps T4 and T7. After step T1, Type B customers go to Step T5, then steps T6 and T7. Numbers in parentheses are minutes per customer.

(a) What is the process capacity for each type of customer?

## Parallel stations

(b) Suppose the times for the parallel stations at step T3 become significantly larger: station T3-a takes 60 minutes per customer, station T3-b takes 60 minutes per customer, and station T3-c takes 40 minutes per customer. What is the capacity for Type A customers now?

(c) If 70% are Type A customers, what is the combined capacity (i.e., total customers per hour, irrespective of type)?

(d) Let the times the stations at T3 be as shown in the figure. As in (c) suppose 70% of customer are Type A. If the arrival rate is random, but on average equal to 4.60 customers/hour, where will each type of customer typically have to wait?

4. The following table shows steps in the process at a sandwich shop.

Element
Time (secs.)
Predecessor(s)

A – Take order
25
None

B – Collect payment
20
A

C – Make sandwich
32
B

D – Get other order items
30
B

E – Get drinks
35
C, D

F – Package order
25
E

G – Deliver order
10
F

(a) If one employee performs all tasks, how many customers can be served per hour?

(b) If the shop wants to be able to serve 45 customers per hour, how many employees are needed?

## Number

(c) With the number of employees from (b), how many customers can be served per hour?

(d) Suppose you have only have the number of employees from (b). Moreover, all seven steps in the process are needed (i.e., no step can be removed) and the times for each step cannot be reduced. Find a plausible way reconfigure the process in order to increase the capacity.

(e) If any number of employees can be used, but each task must be assigned to a single employee, what is the capacity? What is the smallest number of employees needed to reach this capacity?

5. Consider the following assembly network. The desired output is at least 40 units per hour. (a) What is the theoretical minimum number of workstations?

## Longest work element rule

(b) Use the longest work element rule to balance the assembly line: show which elements are assigned to each workstation. What is the capacity? What is the efficiency?

(c) Use the shortest work element rule to balance the assembly line: show which elements are assigned to each workstation. What is the capacity? What is the efficiency?

Element
Time (seconds)
Predecessor(s)

A
40
None

B
30
A

C
80
A

D
20
B

E
60
C

F
15
C

G
25
C

H
10
D, E

I
75
F

J
45
G

K
15
J, H, I

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