I8-3 (Restaurant work scheduling problem). The famous Y. S. Chang Restaurant is
ID: 3155721 • Letter: I
Question
I8-3 (Restaurant work scheduling problem). The famous
Y. S. Chang Restaurant is open 24 hours a day.
Waiters and busboys report for duty at 3 A.M., 7 A.M.,
11 A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an
8-hour shift. The following table shows the minimum
number of workers needed during the six periods
into which the day is divided. Changs
scheduling problem is to determine how many waiters
and busboys should report for work at the start of
each time period to minimize the total staff required
for one days operation. (Hint: Let Xi equal the
number of waiters and busboys beginning work in
time period i, where i = 1, 2, 3, 4, 5, 6.)
PERIOD TIME NUMBER OF WAITERS AND BUSBOYS REQUIRED
1 3 A.M.-7 A.M. 3
2 7 A.M.-11 A.M. 12
3 11 A.M.-3 P.M. 16
4 3 P.M.-7 P.M. 9
5 7 P.M.-11 P.M. 11
6 11 P.M.-3 A.M. 4
* ADDITIONAL CONSTRAINT Total number of workers to start the shifts must be less less than or equal to 31.
I have this one mostly done I just can't get the solver to work, everything comes up zeros, this is my first time using solver and I think I may have the data inputed wrong.
Explanation / Answer
Solution:
Given that PERIOD TIME NUMBER OF WAITERS AND BUSBOYS REQUIRED
1 3-7am 3
2 7-11am 12
3 11-3pm 16
4 3-7pm 9
5 7-11pm 11
6 11-3am 4
Let xi = the number of persons beginning work at the start of time period I (i= 1,2,3,4,5,6)
We will have to minimize x1+x2+x3+x4+x5+x6
Constraints:
X1+x6 3
X1+x212
X2+x316
X3+x49
X4+x511
X5+x64
Period 1 2 3 4 5 6 Time 3-7am 7-11am 11-3pm 3-7pm 7-11pm 11-3am Number of waitress and busboys required 3 12 16 9 11 4 2 7