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Scottsville Textile Mill Case: Production Schedule and Loom Assignment

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Scottsville Textile Mill Case: Production Schedule and Loom Assignment
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 (Selling-Purchasing) |

|1 |0.33 (0.99-0.66) |0.19 (0.99-0.8) |

|2 |0.31 (0.86-0.55) |0.16 (0.86-0.7) |

|3 |0.61 (1.1-0.49) |0.5 (1.1-0.6) |

|4 |0.73 (1.24-0.51) |0.54 (1.24-0.7) |

|5 |0.2 (0.7-0.5) |0 (0.7-0.7) |

Working Hour

Dobbie: 8*24*30=5760 hours Regular: 30*24*30=21600 hours

Hour per yard

|Fabric |Dobbie |Regular |

|1 |1/4.63=0.216 | / |

|2 |1/4.63=0.216 | / |

|3 |1/5.23=0.19 | 0.19 |

|4 |1/5.23=0.19 | 0.19 |

|5 |1/4.17=0.24 | 0.24 |

Objective Function

Max Profit

Max 0.33X1+0.31X2+0.61X3+0.73X4+0.2X5+0.61X6+0.73X7+0.2X8+0.19X9+0.16X10+0.5X11+0.54X12+0X13

S.T.

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

[pic]

[pic]

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
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