Question

Build a schedule for the following staffing requirements, giving workers two consecutive days off per cycle (not including Sunday). Assume that 4 days of work is full time.
Day Mon Tue Wed Thu Fri Sat
Staff needed 3 4 2 3 4 5

Answer 1

Answer:

Explanation:

The following process is used to schedule staffing requirements.

Start appointing workers in a way that two days contain the lowest amount of staff required are designated first.

Then, we minus 1 from each cell except for the selected pair of days.

After that, we lookout for pairs of days that contain the least amount of staff requirements.

We will then repeat the above process until the staffing requirements are fully met.

OUTPUT:

$\ A\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B\ \ \ \ \ \ \ \ \ \ \ C\ \ \ \ \ \ \ \ \ \ \ D\ \ \ \ \ \ \ \ \ \ \ E\ \ \ \ \ \ \ \ \ \ \ F\ \ \ \ \ \ \ \ \ \ \ G$

$1 \ \ \ \ Day \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mon \ \ \ \ \ \ \ \ \ \ \ Tue \ \ \ \ \ \ \ \ \ \ \ Wed \ \ \ \ \ \ \ \ \ \ \ Thur \ \ \ \ \ \ \ \ \ \ \ Fri \ \ \ \ \ \ \ \ \ \ \ Sat$

$2 \ \ \ \ Staff \ needed \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ 5$

$3 \ \ \ \ Worker \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ \mathbf{2 \ \ \ \ \ \ \ \ \ \ \ 3} \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ 5$      

$4 \ \ \ \ Worker \ 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{ 2 \ \ \ \ \ \ \ \ \ \ \ 3} \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ 4$

$5 \ \ \ \ Worker \ 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ \mathbf{1 \ \ \ \ \ \ \ \ \ \ \ 2} \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ 3$    

$6 \ \ \ \ Worker \ 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ \mathbf{1 \ \ \ \ \ \ \ \ \ \ \ 2} \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 2$

$7 \ \ \ \ Worker \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \mathbf{0 \ \ \ \ \ \ \ \ \ \ \ 1}$

$8 \ \ \ \ Worker \ 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ 1$

$9 \ \ \ \ No \ working^* \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ 5$

10    *count the number of workers after excluding highlighted cells and 0 values.

Day      Minimum number of workers needed

$Mon \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3$

$Tue \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4$

$Wed \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2$

$Thur \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3$

$Fri \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4$

$Sat \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5$