Q1. What is the fastest way to manufacture Old Oregon tables using the original crew? How many could be made per day?
Each of the four employees is capable of building a table from start to finish on their own; however, some employees are more efficient in accomplishing one task than others. To determine the fastest way to manufacture Old Oregon tables with the original crew, the linear programming method in order to decide the most efficient solution for job pairings. Therefore, by calculating the difference in time between each of four steps of manufacturing: preparation, assembly, finishing and packaging operation for each employee, the following information is produced:
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Person | Time from Preparation to Assembly | Time from Assembly to Finishing | Time from Finishing to Packaging | Packaging Time |
Tom | 100 | 160 | 90 | 25 |
George | 80 | 160 | 60 | 10 |
Leon | 110 | 200 | 80 | 10 |
Cathy | 120 | 190 | 100 | 25 |
Using the original crew, Tom will work on the preparation, Cathy will work the assembly process, George on the finishing, and Leon on the packaging which yields 240 minutes (as represented in the table below). Therefore, to determine the number of tables that can be manufactured in a day, the number of minutes spent in each workday is divided by 240 (while taking into consideration that each table is manufactured in sequential order as stated above i.e. one process must be completed before the other can be initiated).
Hence, for an 8 hour per day, one-shift operation:
8 hours * 60 minutes = 480 minutes – 60 minutes break time
= 420 minutes
PERSON | PROCESS | COST |
Tom | Prep | 100 |
George | Finishing | 60 |
Leon | Pack | 10 |
Cathy | Assembly | 70 |
Total | 240 |
Q2. Would production rates and quantities change significantly if George would allow Randy one of the four functions and make one of the original crew the backup person?
Adding Randy would not add any significantly value to the production rate of the tables by much; however, with Randy there would be a 10 minute reduction in total time to complete all four production functions. In fact, adding Randy would necessitate the creation of a dummy position; as such, I do not recommend adding Randy, as the results do not yield any significant gains.
Optimal Cost ($230) | Preparation | Assembly | Finishing | Packaging | Dummy |
Tom | 100 | Assign 60 | 90 | 25 | 1 |
George | Assign 80 | 80 | 60 | 10 | 1 |
Leon | 110 | 90 | Assign 80 | 10 | 1 |
Cathy | 120 | 70 | 100 | 25 | Assign 1 |
Randy | 110 | 80 | 100 | Assign 10 | 1 |
Q3. What is the fastest time to manufacture a table with the original crew if Cathy is moved to either preparation or finishing?
The table below shows when Cathy is moved to Preparation.
| Preparation | Assembly | Finishing | Packaging | |
| Tom | 0.00 | 1.00 | 0.00 | 0.00 |
| George | 0.00 | 0.00 | 1.00 | 0.00 |
| Leon | 0.00 | 0.00 | 0.00 | 0.00 |
| Cathy | 1.00 | 0.00 | 0.00 | 0.00 |
| Randy | 0.00 | 0.00 | 0.00 | 1.00 |
In the above scenario, it would require 250 minutes to manufacture one table. Leon becomes the back up in this scenario. The longest time for a job is 120 minutes for preparation.
The table below shows the results when Cathy is move to finishing.
| Preparation | Assembly | Finishing | Packaging | |
| Tom | 0.00 | 1.00 | 0.00 | 0.00 |
| George | 1.00 | 0.00 | 0.00 | 0.00 |
| Leon | 0.00 | 0.00 | 0.00 | 0.00 |
| Cathy | 0.00 | 0.00 | 1.00 | 0.00 |
| Randy | 0.00 | 0.00 | 0.00 | 1.00 |
In this scenario it would require 250 minutes to complete one table. The longest time for a job being 100 minutes.
