We analyzed three alternatives for maximizing the number of tables produced per day. These options involved employing either four or five individuals and determining whether they should be involved in the entire manufacturing process or work independently. Initially, we chose to merge the finishing and packaging steps as the packaging task required little time and the employee assigned to this task was not fully utilized. Hence, one employee could perform both responsibilities.
Considering the abilities and time efficiency of our team members, we made the decision to exclude Cathy from the manufacturing process. Instead, George will be solely responsible for manufacturing tables as he can assemble one in the shortest amount of time. By utilizing the Assignment method and taking into account each individual's time for each job duty, we have determined that it
...will take a total of 260 minutes to manufacture a single table. Specifically, Tom will handle assembly (60 minutes), Leon will take care of finishing and packaging (90 minutes), and Randy will handle preparation (110 minutes).
By using this method, Tom, Leon, and Randy can produce 4.36 tables in 480 minutes (the total time available divided by the longest job time) while working an eight-hour shift. Meanwhile, George can manufacture 2.09 tables during the same period. This would result in the entire team producing a total of 6.45 tables in an eight-hour workday. Our alternative option consists of adjusting assignments within the initial approach.
In our second approach, we assigned each job duty to the person who could complete it in the least amount of time. Tom was assigned preparation because he was the only one who could do it in 100 minutes or
less, which was the longest job time. George was assigned to manufacture tables on his own and Cathy was excluded from the manufacturing process. This approach resulted in a total of 270 hours, with Randy assigned to assembly (80), Leon to finishing and packaging (90), and Tom to preparation (100). With this approach, Tom, Leon, and Randy can manufacture 4.8 tables in 480 minutes, while George can manufacture 2.09 tables during the same time. This would allow the team to manufacture around 7 tables per day.
For the third option, we decided to utilize all five employees but still combine finishing and packaging as one job duty. Since it only takes three employees to manufacture a table, we concluded that George and Tom would be best utilized if they manufactured tables on their own since they are the fastest at manufacturing.
After removing George and Tom from the manufacturing process, we opted to delegate the task of preparation to Randy(110) for two reasons. Firstly, he is the fastest worker who can complete the job efficiently. Secondly, preparation is the duty that demands the most time. Subsequently, we assigned assembly to Cathy (70) and entrusted Leon (90) with finishing and packaging. This division of labor allows Randy, Cathy, and Leon to produce a total of 4.36 tables within 480 minutes. In the same timeframe, Tom can produce 1.75 tables and George can make 2.09 tables. Therefore, the combined output amounts to 8.2 tables per day.
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