Question

A mortgage service office has the following four activities involved in approving a loan application. Note that a working day is 8 hours and there are 60 minutes in one hour.

Activity	Time (minutes)
A. Property survey	20
B. Credit report	15
C. Title search	30
D. Final decision	25

• Solution inputs are numbers only, no symbols. Percentage is kept as 0.76 instead of 76%.
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. If each activity is performed by a different person, with four employees, what would be the maximum number of loan applications the office can process per day?    And what is the office's direct labor utilization (DLU) ?  

2. Activities B and C are combined together and assigned to two employees, while the other two employees are responsible for activities A and D respectively. What would be the maximum number of loan applications the office can process per day?    And what is the office's direct labor utilization (DLU) ?  

3. The office now has only three employees, activities B and C are combined together and assigned to one employee, while the other two employees are responsible for activities A and D respectively. Under this setting, what would be the maximum number of loan applications the office can process per day?    And what is the office's direct labor utilization (DLU) ?  

4. The office now has only three employees, activities A, B and C are combined together and assigned to two employees, while the other employee is responsible for the last activity D . Under this setting, what would be the maximum number of loan applications the office can process per day?    And what is the office's direct labor utilization (DLU) ?  

5. With three employees, every employee can perform any activity and more than one activity. Under this setting, What would be the maximum number of loan applications the office can process per day?   And what is the office's direct labor utilization (DLU) ?  

There are seven tasks in an assembly line, from which a product with a relative stable demand is produced. The time needed for each task (in minutes) and the relationships among tasks are in the graph below (note that activity C is linked to activity D). The assembly line operates 8 hours a day. The daily customer demand for the product is 100 units. Please design/balance this assembly line, so that supply and demand would be matched the most efficiently way possible.

• A (5) ----> B (3) ----> D (1) ----> E (1) -----> F (2) ------> G(4)
• C (2)------------------>

1. What is the desired cycle time (in minutes) of the balanced assembly line? (Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24)  
2. Assumed the desired cycle time is 5 minutes, please used the assumed CT value to calculate the minimum number of workstations needed (round up to an integer number) for line-balancing, in order to achieve the best process efficiency.  
3. Assumed the desired cycle time is 5 minutes, please used the assumed CT value to balance the assembly line using the greatest positional weight rule. Which tasks would be assigned to the last workstation? (Letter only, NO space or comma between letters, e.g., ABDE)

Answer 1

1.

Activity	Processing Time (P)	Number of resources (N)	Capacity per day = 8*60*N/P
A. Property survey	20	1	24
B. Credit report	15	1	32
C. Title search	30	1	16
D. Final decision	25	1	19.2

Cycle time = Max(20, 15, 30, 25) = 30 minutes

Capacity = Min(24, 32, 16, 19.2) = 16 per day

DLU = Total direct labor content / (Cycle time * # workers) = 90 / (30*4) = 0.75 or 75%

2.

Activity	Processing Time (P)	Number of resources (N)	Capacity per day = 8*60*N/P
A	20	1	24.00
B & C	45	2	21.33
D	25	1	19.20

Cycle time = Max(20, 45/2, 25) = 25 minutes

Capacity = Min(24, 21.33, 19.20) = 19.2 per day

DLU = Total direct labor content / (Cycle time * # workers) = 90 / (25*4) = 0.90 or 90%

3.

Activity	Processing Time (P)	Number of resources (N)	Capacity per day = 8*60*N/P
A	20	1	24.00
B & C	45	1	10.67
D	25	1	19.20

Cycle time = Max(20, 45, 25) = 45 minutes

Capacity = Min(24, 10.67, 19.2) = 10.67 per day

DLU = Total direct labor content / (Cycle time * # workers) = 90 / (45*3) = 0.67 or 67%

4.

Activity	Processing Time (P)	Number of resources (N)	Capacity per day = 8*60*N/P
A, B, & C	65	2	14.77
D	25	1	19.20

Cycle time = Max(65/2, 25) = 65/2 = 32.5 minutes

Capacity = Min(14.77, 19.2) = 14.77 per day

DLU = Total direct labor content / (Cycle time * # workers) = 90 / (32.5*3) = 0.92 or 92%