Homework SourseHere is a problem in which I need to have employees schedule
| Here is a problem in which I need to have employees scheduled for shifts that begin | ||||||||
| at 8:00 a.m.; Noon; 4:00 p.m.; 8:00 p.m. and Midnight. | ||||||||
| The minimum number of officers must be at least what is listed in column C. | ||||||||
| I know that a+b+c+d+e+f >=0. I don\'t know how to finish writing the objective function | ||||||||
| or to calculate the constraints. Please provide in detail the formulas so I can complete this problem. | ||||||||
| Time of Day | Min Officers | |||||||
| 8 a.m.-4 p.m. | ||||||||
| Noon-8 p.m. | ||||||||
| 4 p.m.-midnight | a+b+c+d+e+f+g | |||||||
| 8 p.m.-4 a.m. | ||||||||
| Midnight-8 a.m. | ||||||||
| RHS | ||||||||
| a | 8 a.m. - Noon | 5 | a+b>=5 | |||||
| b | Noon-4:00 p.m. | 6 | b+c>=6 | |||||
| c | 4 p.m.-8 p.m. | 10 | c+d>=10 | |||||
| d | 8 p.m.-Midnight | 7 | d+e>=7 | |||||
| e | Midnight-4 a.m. | 4 | e+f>=4 | |||||
| f | 4 a.m.-8 a.m. | 6 | f+g>=6 |
| Here is a problem in which I need to have employees scheduled for shifts that begin | ||||||||
| at 8:00 a.m.; Noon; 4:00 p.m.; 8:00 p.m. and Midnight. | ||||||||
| The minimum number of officers must be at least what is listed in column C. | ||||||||
| I know that a+b+c+d+e+f >=0. I don\'t know how to finish writing the objective function | ||||||||
| or to calculate the constraints. Please provide in detail the formulas so I can complete this problem. | ||||||||
| Time of Day | Min Officers | |||||||
| 8 a.m.-4 p.m. | ||||||||
| Noon-8 p.m. | ||||||||
| 4 p.m.-midnight | a+b+c+d+e+f+g | |||||||
| 8 p.m.-4 a.m. | ||||||||
| Midnight-8 a.m. | ||||||||
| RHS | ||||||||
| a | 8 a.m. - Noon | 5 | a+b>=5 | |||||
| b | Noon-4:00 p.m. | 6 | b+c>=6 | |||||
| c | 4 p.m.-8 p.m. | 10 | c+d>=10 | |||||
| d | 8 p.m.-Midnight | 7 | d+e>=7 | |||||
| e | Midnight-4 a.m. | 4 | e+f>=4 | |||||
| f | 4 a.m.-8 a.m. | 6 | f+g>=6 |
Solution
The objective function is to minimize the total number of employees.
Thus, minimize : a+b+c . . . + f subject to constraints:
a >= 5 ; b >=6; c >=10, d >=7 ; e >= 4; f >=6
and, a+b >=6; b+c>=10; c+d >=10;d+e >=7, e+f>=6
The last set of constraints are from the fact that, minimum requirement for a shift from 8 am to 4p.m would be the bigger of the minimum requirements of 8a.m. - Noon and Noon-4p.m. and so on.
Hope, now you can solve this. Ask if you have any doubts.
