Question

4. Furniture Face Lift (15 points) Furniture Face Lift refinishes old wood furniture. Their process for refinishing chairs has 10 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 4 Processing time (hours per chair per worker) 2.4 1.6 1.72 0.92 Stripping Priming Painting Inspection 1 2 3 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. 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 14 chairs arrives. How many hours will it take them to complete these 14 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 1

Computation of maximum number of chairs that can be produced per hour:

А B C = A/B Station Staffing Processing Time Chairs completed in an hour Stripping 4 2.4 1.67 Priming 1 1.6 0.63 Painting 2 1.72 1.16 Inspectior 3 0.92 3.26 6.72 Nm

Let me explain. At the first station, there are 4 workers and each worker takes 2.4 hours on a chair. Therefore, chairs completed in one hour = no. of workers * 1/time taken and that gives us 1.67. This is at the first station.

Similarly, we can calculate the no. of chairs completed per hour at every station. But a chair is said to be fully finished when it goes through all the processes. So the maximum no. of chairs completed per hour is 3.26 i.e., the no. of chairs completed at the inspection station per hour. Since there is inventory at each station at the beginning, the inspection station would not have to wait for the other stations to finish processing.

Since there are no chairs as inventory or in buffer, each station will have to wait for the previous station to finish processing. Therefore we must add the time taken at all stations.

14 chairs A B C = 14*B/A Station Staffing Processing Time Total processing time Stripping 4 2.4 8.4 Priming 1 1.6 22.4 Painting 2 1.72 12.04 Inspectior 3 0.92 4.29 47.13 Nm

At the first station, it takes 2.4 hours per person per chair. So it would require a person 14*2.4 = 33.6 hours to complete. But since there are 4 people, it gets divided by 4 so 33.6/4 = 8.4hours.

Similarly, total processing time is calculated and added up to get an answer of 47.13 hours

When we add up the processing time per chair per person in all the stations (2.4+1.6+1.72+0.92) we get 6.64 hours. So if a person is doing all the processes on a chair himself, he will take 6.64 hours to complete it. No, of chairs produced by him per hour = 1/6.64 = 0.15. But since there are 10 workers, no. of chairs produced per hour goes up to 0.15*10 = 1.5. Its actually 1.51 due to round off.

Maximum capacity of the process is 1.51 chairs per hour.

Hope this helps :)