Gerald Glynn manages the Michaels Distribution Center. After careful examination

Question

Gerald 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 Th Su Requirements 4 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 7 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.) Employec Days off

Explanation / Answer

M Tu Wed Thu Fri Sat Sun

Requirement 4 3 7 3 6 4 2

Let's find two consecutive days where the total requirement is the lowest. Saturday+Sunday=6 and Sunday+Monday=6. Since there is a tie, we would give the first worker (Worker 1) Saturday and Sunday off.

M Tu Wed Thu Fri Sat Sun

Worker 1    X X

Net Requirement 3 2 6 2 5 4 2

Now Sun+Mon have the lowest total requirement, so we can give worker 2 off on Sunday and Monday

Worker 2 X          X

Net Requirement 3 1 5 1 4 3 2

Now Mon+Tu have the lowest net requirement. So, Worker 3 can take Mon+Tu off

Worker 3 X X         

Net Requirement 3 1 4 0 3 2 1

Now, Thu+Fri and Sat+Sun have the lowest net requirement. We will prefer Sat+Sun off for Worker 4

Worker 4          X X

Net Requirement 2 0 3 0 2 2 1

Now, Mon+Tu=2 and Thu+Fri=2 have the lowest net requirement. We will prefer Mon+Tu as they are in the start of the week.

Worker 5 X X            

2 0 2 0 1 1 0

Again Sat+Sun is the lowest along with Thu+Fri. We will prefer Sat+Sun

Worker 6       X X

Net Requirement 1 0 1 0 0 1 0

Thu+Fri=0. So, Thu+Fri is given preference

Worker 7    X X   

Net Requirement 0 0 0 0 0 0 0

Days Off

Worker Days Off

1 Saturday+Sunday

2 Sunday+Monday

3 Monday+Tuesday

4 Saturday+Sunday

5 Monday+Tuesday

6 Saturday+Sunday

7 Thursday+Friday

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