MGerald Glynn manages the Michaels Distribution Center. After careful examinatio
ID: 383017 • Letter: M
Question
MGerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are
Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.)
The minimum number of workers is _____ workers. (Enter your response as a whole number.)
Specify the workforce schedule for each employee by indicating the day offs (other days are considered to be work days.) Make sure to give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week, with Monday being considered as the first day of the week.)
Day Monday tueday Weds Thursday friday saturday sunday requirements 4 2 4 3 7 3 5Explanation / Answer
Total requirement over 7 days = 4+2+4+3+7+3+5 = 28 worker days
Working days per worker = 5
Therefore, theoretical number of workers required = Total requirement / working days per worker = 28/5 = 5.6 workers
However maximum number of workers on any day is 7 (on Friday). Therefore, we need at least 7 workers.
Now, locate in the 7 day requirement, any two consecutive days having the lowest requirement. There are two such pairs, Monday-Tuesday or Tuesday-Wednesday having lowest requirement (=4+2).
Start with Monday-Tuesday and assign days off to three (=7-4=3) workers to ensure that 4 workers are available on both days.
The other pair of consecutive days having lowest requirement is Tuesday-Wednesday. Assign days off to worker 4 and 5 on both of these days.
Next lowest requirement pair of consecutive days is Weds-Thursday, which require = 4+3 workers. Two workers (4 and 5) ahev already been given off on Tuesday-Weds. Requirement on Weds is 4, so only one worker can be given off on Weds-Thursday. Worker 6 is assigned off on Weds-Thursday
Next lowest requirement pair of consecutive days is Sat-Sunday, which require = 3+5 workers. So worker 7 is assigned off on Sat-Sunday
The final schedule is following. 1 indicates worker working and blank indicates off days
Minimum number of workers = 7 workers
Day Monday Tueday Weds Thursday Friday Saturday Sunday Requirement 4 2 4 3 7 3 5 Worker 1 1 1 1 1 1 Worker 2 1 1 1 1 1 Worker 3 1 1 1 1 1 Worker 4 1 1 1 1 1 Worker 5 1 1 1 1 1 Worker 6 1 1 1 1 1 Worker 7 1 1 1 1 1Related Questions
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