Please describe the process of excel
Sol:
Decision Variables:
Let, Xij = number of hours operator I is assigned to work on day j
Where,
i = 1, 2,…, 6 for the operators K.C., D.H., H.B., S.C., K.S., N.K. respectively
j = 1, 2,..,5 for the days Mon. to Fri. respectively
Subject To:
The objective of the problem is to minimize total cost of labor:
Min. Z = $25(X11 + X13 + X15) + $26(X22 + X24) + $24(X31 + X32 + X33+X35) +
$23(X41 + X42 + X43 + X45) + $28(X51 + X53 + X54) + 30(X64 + X65)
Subject to:
Number of hours per day availability of operators:
Operator |
Mon |
Tue |
Wed |
Thus |
Fri |
K.C. |
X11 <= 6 |
X13 <=6 |
X <= 6 |
||
D.H. |
- |
X22 <= 6 |
- |
X24 <= 6 |
|
H.B. |
X31 <= 4 |
X32 <= 8 |
X33 <= 4 |
X35 <= 4 |
|
S.C. |
X41 <=5 |
X42 <= 5 |
X43 <= 5 |
X45 <= 5 |
|
K.S. |
X51 <= 3 |
X53 <= 3 |
X54 <= 8 |
||
N.K. |
X64 <= 6 |
X66 <= 2 |
Minimum Number of hours guaranteed for each operator:
Operator |
|
K.C. |
X11 + X13 + X15 >= 8 |
D.H. |
X22 + X24 >= 8 |
H.B. |
X31 + X32 + X33+X35 >= 8 |
S.C. |
X41 + X42 + X43 + X45 >= 8 |
K.S. |
X51 + X53 + X54 >= 7 |
N.K. |
X64 + X65 >= 7 |
Number of hours the lab is open:
Day |
|
Mon |
X11 + X31 + X41 + X51 = 14 |
Tues |
X22 + X32 + X42 = 14 |
Wed |
X13 + X33 + X43+X53 = 14 |
Thus |
X24 + X44 + X54 = 14 |
Fri |
X15 + X35 + X45 + X65 = 14 |
Non-negativity Constraint: all Xij >= 0
Optimal Solution:
NUMBER OF WORKING HOURS PER DAY (Xij) |
Hours per week |
||||||
Operator |
Mon |
Tue |
Wed |
Thus |
Fri |
||
K.C. |
2 |
0 |
3 |
0 |
4 |
9 |
|
D.H. |
0 |
2 |
0 |
6 |
0 |
8 |
|
H.B. |
4 |
7 |
4 |
0 |
4 |
19 |
|
S.C. |
5 |
5 |
5 |
0 |
5 |
20 |
|
K.S. |
3 |
0 |
2 |
2 |
0 |
7 |
|
N.K. |
0 |
0 |
0 |
6 |
1 |
7 |
|
Total Weekly Cost = $1,755
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