Scottsville Textile Mill Case

747 Words Apr 26th, 2013 3 Pages
Scottsville Textile Mill Case

MGM 350

Production Schedule and loom assignment
Decision Variable
X1: Yards of fabric 1 on dobbie loom
X2: Yards of fabric 2 on dobbie loom
X3: Yards of fabric 3 on dobbie loom
X4: Yards of fabric 4 on dobbie loom
X5: Yards of fabric 5 on dobbie loom
X6: Yards of fabric 3 on regular loom
X7: Yards of fabric 4 on regular loom
X8: Yards of fabric 5 on regular loom
X9: Yards of fabric 1 purchased
X10: Yards of fabric 2 purchased
X11: Yards of fabric 3 purchased
X12: Yards of fabric 4 purchased
X13: Yards of fabric 5 purchased
Profit Contribution per yard
|Fabric |Manufacturing (Selling-Variable) |Purchasing
…show more content…
X1+X9=16500
X2+X10=22000
X3+X6+X11=62000
X4+X7+X12=7500
X5+X8+13=62000
0.216X1+0.216X2+0.191X3+0.19X4+0.24X5≦5760
0.19X6+0.19X7+0.24X8≦21600
X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13≧0

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Project Contribution to Profit
Objective Function=62548.860
X1=4666.67, X2=22000, X3=0, X4=0, X5=0, X6=27868.421, X7=7500, X8=62000, X9=11833.333, X10=0, X11=34131.579, X12=0, X13=0
So it means Yards of fabric 1 on dobbie loom is 4666.67; Yards of fabric 2 on dobbie loom is 22000; Yards of fabric 3 on dobbie loom is 0; Yards of fabric 4 on dobbie loom is 0; Yards of fabric 5 on dobbie loom is 0; Yards of fabric 3 on regular loom is 27868.421; Yards of fabric 4 on regular loom is 7500; Yards of fabric 5 on regular loom is 62000; Yards of fabric 1 purchased is 11833.333; Yards of fabric 2 purchased is 0; Yards of fabric 3 purchased is 34131.579; Yards of fabric 4 purchased is 0; Yards of fabric 5 purchased is 0.

Additional loom time
If there is a ninth dobbie loom, the total work hours will be 6480 (9*24*30=6480), still in the range of [4756, 8316], so the optimal solution is the same. So the new objective function is 62548.86+0.648*(6480-5760) =63015.42

Objective Coefficient range
Yards of fabric 1 on dobbie loom [0.315, 0.34]
Yards of fabric 2 on dobbie loom [0.3, unlimited]
Yards of fabric 3 on dobbie loom [unlimited, 0,624]
Yards of fabric 4 on dobbie loom [unlimited, 0.714]
Yards