OPIM 632: Homework Assignment #1 - Cachon | Terwiesch



Matching Supply with Demand: An Introduction to Operations Management

3rd Edition

Questions for Chapter 4

Last updated 3/8/12

Copyright Gerard Cachon and Christian Terwiesch: Instructors adopting our text are free to use these questions.

QUESTIONS WITH EMBEDDED ANSWERS

Furniture Face Lift refinishes old wood furniture. Their process for refinishing chairs has 8 workers and 4 stations. Each chair starts at the Stripping station, then goes to Priming, then to Painting and finally to Inspection. Where there are multiple workers within a station, each worker works independently on his/her own chair. Assume inventory buffers are allowed between each station.

|Station |Staffing |Processing time (hours per chair per |

| | |worker) |

|Stripping |3 |2.5 |

|Priming |2 |1.5 |

|Painting |2 |1.75 |

|Inspection |1 |0.8 |

What is the maximum number of chairs per hour that can be produced? Assume they start the day with inventory at each station to work on.

Answer: the average time needed to finish one chair at each station are as follows,

Capacity=staffing/activity time:

|Station |Staffing |Activity time (hours) |Capacity=staffing/activity time |

|Stripping |3 |2.5 |1.2 |

|Priming |2 |1.5 |1.333333333 |

|Painting |2 |1.75 |1.142857143 |

|Inspection |1 |0.8 |1.25 |

Painting is the bottle neck since it has the lowest capacity. The process capacity is the capacity of the bottleneck. Thus, the process capacity is 1.14 chairs/hour.

Suppose at the start of the day there is no inventory of chairs in the shop. That is, there are no chairs within any of the stations or between them in any buffer. A truck loaded with 15 chairs arrives. How many hours will it take them to complete these 15 chairs?

Answer: it takes 2.5+1.5+1.75+0.8=6.55 hours for the first chair to be produced. It takes 1/1.14 hours for each of the subsequent chairs. In total, it takes 6.55+1/1.14*14=18.8 hours to complete 15 chairs.

Suppose now that each worker is trained to do all tasks and each worker works on a chair from start to finish, i.e., each worker does Stripping, Priming, Painting and Inspection. What is the maximum capacity of the process in chairs per hour?

Answer: in this system, there will be no bottle neck, i.e., every worker is working at their full capacity. It takes each worker 2.5+1.5+1.75+0.8=6.55 hours to finish one chair. 3+2+2+1=8 works can complete 8/6.55=1.22chairs/hour.

***

The White Tooth Device Company is a manufacturer of high-end electric toothbrushes. For each toothbrush, there is a sequence of assembly steps performed by five workers. Each worker does two tasks. Inventory buffers are allowed between workers.

|Worker |Task |Time (seconds) |

|A |T1 |40 |

|A |T2 |25 |

|B |T3 |20 |

|B |T4 |15 |

|C |T5 |10 |

|C |T6 |15 |

|D |T7 |10 |

|D |T8 |20 |

|E |T9 |25 |

|E |T10 |35 |

What is the capacity of this process (toothbrushes per minute)?

Answer: the process time at each worker are: A: 65sec, B: 35sec, C: 25sec, D: 30sec, E: 60sec. Worker A is the bottle-neck. The process capacity is 60sec/65sec=0.92 toothbrushes/min.

Suppose two workers could be hired, F and G, and they take the same time to complete tasks as the current five workers. F and G can be assigned to work on the same pair of tasks as one of the current workers. For example, F could be assigned tasks T1 and T2 (just like worker A) while G is assigned T5 and T6 (just like worker C). They cannot be assigned tasks that are currently assigned to two workers. For example, F cannot be assigned to tasks T2 and T3 (because they are currently being done by workers A and B). What is the capacity of this process with workers F and G included (toothbrushes per minute)?

Answer: assign the extra one by one to the bottleneck in the process. First assign worker F to the current bottleneck A. Thus, the time to complete T1 and T2 for one toothbrush at A and F is 65sec/2=32.5 sec. Now the bottleneck is E. Assign the other worker G to be working with E. The time to complete T9 and T10 for one toothbrush is 60sec/2=30sec. The current bottleneck is B with 35sec activity time. Thus, the process capacity is 60sec/35sec=1.71 toothbrushes/min.

Return to the case of 5 workers. Suppose the assignment of tasks to workers can change but the sequence of tasks must remain the same, workers must be assigned to consecutive tasks and each task can be assigned to only one worker. For example, worker A could do tasks T1-T3 (because they are consecutive) but cannot be assign T1,T2 and T4. If worker A is assigned to tasks T1-T3, then worker B’s first task must be T4 (worker B cannot also be assigned to task T3). Because a U-shaped line is used, tasks T1 and T10 can actually be considered consecutive tasks – worker A could be assigned tasks T10, T1 and T2. What would the maximum capacity be after possibly reassigning tasks (toothbrushes per minute)?

Answer: The total process time for one toothbrush is (40+25+20+15+10+15+10+20+25+25+35)= 215 sec. If we have 5 workers, the system can do no better than is 215/5=43sec/worker. We try to assign tasks such the process time at the slowest worker is as close as to 43sec/worker. The best we can do is the following: A: T1(40sec), B: T2 and T3(45sec), C: T4-T7(50sec), D: T8-T9 (45sec), T10(35sec). The bottleneck is worker C. The process capacity is 60sec/50sec=1.2 toothbrushes/hour.

***

Imagine US is a startup that offers high definition 3D prenatal ultrasounds for high-end customers. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses):

Activity 1: Welcome a patient and explain the procedure. (8 minutes)

Activity 2: Prep the patient (e.g., show them to the room, apply ultrasound gel). (5 minutes)

Activity 3: Take images. (14 minutes)

Activity 4: Analyze images. (12 minutes)

Activity 5: Discuss diagnostic with patient. (16 minutes)

At each location there are employees (servers) S1, S2, and S3. The assignment of tasks to servers is the following:

S1 does Activity 1.

S2 does Activities 2 and 3.

S3 does Activities 4 and Activity 5.

What is the capacity of this process (in customers per hour)?

Answer: the activity time at S1, S2, and S3 is 8 minutes, 19 minutes, and 28 minutes, respectively. S3 is the bottleneck. The capacity of the process is the capacity of the bottleneck. 60min/28min=2.14 customers/hour

Suppose 2 patients arrive every hour on average. Ignoring any “start of day” or “end of day” effects, what is the utilization of Server 1 (as a %)?

Answer: S1’s capacity is 60min /8min=7.5 customers/hour, and the demand rate is 2 customers /hour, which is smaller than the process capacity 2.14 customers/hour. Thus, the system is demand constrained. The utilization of S1 is: 2/7.5=26.67%

Suppose each activity can be done by any server and any server can do any set of activities. However, each activity is done by only one server. For example, a feasible assignment includes: S1 does activities 1 and 5, S2 does activities 2 and 4, and S3 does activity 3. Of course, the original assignment of servers to activities is also feasible. What is the maximum capacity of the process (in customers per hour)?

Answer: the total activity time = 8 + 5 + 14 + 12 + 16=55min. A perfectly balanced line will have each server working 55/3=18.3min. The best we can do is to combine the 8min task with the 12min task, 5min task with the 14min task. Thus, the capacity of the process will be 60min/20min=3 customers/hour.

Now suppose each activity can be assigned to more than one server, each activity can be done by any server and any server can do any set of activities. What is the maximum capacity of the process (in customers per hour)?

Answer: we assign all the tasks to each server. There will be no idle time in this case. The process capacity is 60min/55min*3 = 3.27 customers/hour

***

A process requires 6 tasks, A, B, C, D, E and F, that must be performed in that order. Currently there are 3 employees that are equally skilled at each task. Employee 1 is assigned tasks A and B, employee 2 is assigned tasks C and D and employee 3 is assigned tasks E and F. The task times (all in seconds) are given in the process diagram below. For example, task A requires 90 seconds.

[pic]

Suppose the system started without any work in process inventory (i.e., an empty system). How long would this process take to produce 10 units (in seconds)?

Answer: The first unit takes 270 seconds. The next 9 units take 9 x 130 seconds = 1170. The total time is 270 + 1170 = 1440.

Suppose now the 3 employees can be assigned to any task, but employees must be assigned to consecutive tasks (e.g., an employee cannot be assigned tasks B and D). What would be the processes’ maximum capacity (units per hour)?

Answer: If you assign task A to employee 1, tasks B and C to employee 2 and tasks D, E and F to employee 3, then employee 2 is the bottleneck with a capacity of 1/(40+60) = 1/100 units per second. There are 3600 seconds in an hour so the process can produce 1/100 x 3600 = 36 units. However, if you assign every task to each employee, then each employee takes 270 seconds per unit, or one unit produced every 90 seconds, which yields 3600 / 90 = 40 units per hour.

Mr. K’s Hair Salon

Mr. K’s is a very popular hair salon. It offers high-quality hair-styling and physical relaxation services at a reasonable price, so it always has unlimited demand. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parenthesis):

Activity 1: Welcome a guest and offer homemade herb tea. (10 minutes)

Activity 2: Wash and condition hair. (10 minutes)

Activity 3: Neck, shoulder, and back stress release massage. (10 minutes)

Activity 4: Design the hair style and do the hair. (25 minutes)

Activity 5: Check out the guest. (5 minutes)

Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following:

S1 does Activity 1.

S2 does Activities 2 and Activity 3.

S3 does Activities 4 and Activity 5.

Which server is the bottleneck of the process?

S1 can process 1/10 customers per minute.

S2 can process 1/20 customers per minute.

S3 can process 1/30 customers per minute.

S3 has the lowest capacity and is hence the bottleneck.

What is the utilization of server 2?

Since we assume that there is unlimited demand, the flow rate is equal to the capacity of the process, i.e., 2 customers per hour.

The capacity of S2 is 3 customers per hour.

The utilization at S2 is 2/3= 66.7%.

What is the average labor utilization of the servers? Assume the process operates at its capacity.

labor content = 10+20+30 = 60 min.

total idle time = 20+10 = 30 min.

Average labor utilization = 60/(60+30) = 2/3 = 66.7%

Assume a wage rate of $18 per hour. What are the direct labor costs for one guest?

Direct labor costs = (Total wages) / (flow rate)

There are three employees with a wage of $18/hr implying that the total wages per hour are given by 18x3 = $54/hr.

We deduce that

Direct labor costs = 54/2 = $27

To increase the service rate, Mr. K’s is considering two alternatives:

Alternative I: To hire a new employee to help any one (and only one) of the servers without changing the tasks performed by each server.

Alternative II: To redesign the assignment of tasks to servers. For this, Mr. K’s is evaluating to reassign Activity 5 from S3 to S1.

What would be the costs of direct labor of serving one guest under each of the two alternatives? Assume that the system operates at its capacity.

Under Alternative I, the additional worker would help S3 and under this case the bottleneck would become S2 with a capacity of 3 customers/hr.

Direct labor costs = (18*4)/3 = $24

Under Alternative II, S3 would still be the bottleneck but the new capacity of S3 will be of 60/25=2.4 customers/hr.

Direct labor costs = (18*3)/2.4 = $22.5

One Hour Loan

One Hour Loan offers customized loans. Customers call a toll free number with a specific loan request, and obtain a response within an hour. One Hour Loan’s business process includes five activities which must be conducted in the sequence described below. (The time required for each activity is shown in parenthesis):

Activity 1: Answer customer call and record key information. (4 minutes)

Activity 2: Gather and format the information (obtain credit scores, organize customer specific needs) for analysis (5 minutes)

Activity 3: Analyze the information: Check the credit worthiness, and decide loan amount and APR to offer. (7 minutes)

Activity 4: Perform final checks on loan offer (2 minutes)

Activity 5: Call customer back with the new loan offer and close. (4 minutes)

The whole process is conducted by three workers in a worker paced line. The assignment of tasks to workers is the following:

W1 does Activity 1.

W2 does Activities 2 and 3.

W3 does Activities 4 and 5.

What is the bottleneck of the process?

W2 is the bottleneck.

How much time will it take to process 100 loans? (Assume that the process starts with an empty production line)

See the following calculations: [pic]

What is the utilization of worker 3? (You can assume that the process operates at capacity and you do not have to consider any empty system effects).

See the following calculations

[pic]

What is the average labor utilization of the workers? Assume the process operates at its capacity and there are no empty system effects.

See the following: [pic]

What are the direct labor costs for one loan application? Assume a wage rate of $20 per hour.

See the following calculations: [pic]

To increase the production rate, One Hour Loan is considering two alternatives:

Alternative I: To hire a new worker to help any one (and only one) of the workers without changing the tasks performed by each worker.

Alternative II: To redesign the assignment of tasks to workers. For this, the company is evaluating to re-assign Step 2 from W2 to W1.

Suppose that Alternative I is chosen. Which worker should the new employee assist?

Should assist W2 because he is the bottleneck.

What would be the costs of direct labor of one loan application under the solution depicted above? Assume there is sufficient demand (system operates at its capacity) and there are no empty system effects.

To compute the cost, we calculate: [pic]

What would be the direct labor costs for Alternative II?

To compute the cost, we calculate: [pic]

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