Gerald Glynn manages the Michae\'s Distribution Center. After careful examinatio

Question

Gerald Glynn manages the Michae's 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-tme staffing requirements are Day Requirements Su 7 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 weck and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. Note: I there is a te that cannot be broken by following the preforence 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.)

Explanation / Answer

Maximum number of workers required on any paid of consecutive days is 7 (M & W). Therefore, at least 7 workers are required.

2 workers are required each day on Saturday and Sunday, so, first five workers are given off on S-Su. The other two workers work on S-Su.

7 workers are required on both days Monday and Wednesday, although only 2 workers are required on Tuesday, however, it is next to Monday and before Wednesday, when all 7 workers are required. So no workers can be given off on M-T-W. So workers 6 and 7 are given off on Th-F.  

The final workforce schedule is as follows. 1 indicates that worker is working on that day, blank indicates off day.

The minimum number of workers = 7 workers

M T W Th F S Su Requirement 7 2 7 5 5 2 2 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 1

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