Scottsville Textile Mill
Assignment 1
Scottsville Textile Mill
As per the report a model has been developed which can be used to schedule production for the Scottsville Textile Mill and at the same time how many yards of each fabric must be purchased from another mill has been determined. All the discussion and analysis of the report has been included below.
Table 4.16
Monthly demand, selling price, variable cost, and purchase price data for Scottsville Textile Mill Fabrics Fabric | Demand (yards) | Selling price ($/yard) | Variable Cost ($/yard) | Purchase Price ($/yard) | 1 | 16500 | 0.99 | 0.66 | 0.80 | 2 | 22000 | 0.86 | 0.55 | 0.70 | 3 | 62000 | 1.10 | 0.49 | 0.60 | 4 | 7500 | 1.24 | 0.51 | 0.70 | 5 | 62000 | 0.70 | 0.50 | 0.70 |
Table 4.17
Loom production rates for the Scottsville Textile Mill | Loom Rate (yards/hour) | Fabric | Dobbie | Regular | 1 | 4.63 | - | 2 | 4.63 | - | 3 | 5.23 | 5.23 | 4 | 5.23 | 5.23 | 5 | 4.17 | 4.17 |
Fabrics 1 & 2 can be manufactured only on the dobbie loom.
Solution:
Decision variables xij≔ Number of yards produced by loom j on product i, i=1,2,…,5, j=1,2 yi: Number of yards purchased purchased from another mill, i=1,2,…,5.
Parameters:
Di : demand of product i.
Rij: Loom rate spi: selling price of product i vci: varying cost of product i pi: purchase price of product i
Max i=15spi(j=12xij+yi)-i=15vcij=12xij-i=15pi*yi
s.t.
j=12xij+yi≥Di, i=1,2,…,5 (Demand) i=15x1j/Ri1≤8*24*30 (production capacity of Dobbie) i=15x2j/Ri2≤30*24*30(production capacity of Regular) xij≥0 i=1,2,…,5, j=1,2 x21=x22=0 (Fabrics 1 and 2 can be manufactured only on the dobbie loom)
Answers
1. The final production schedule and loom assignments for each fabric: Decision variables x_ij:=number of yards loom j produce product i | y_i:=number of yard product i is purchased | Fabric | Dobbie | Regular | | 1 | 4668.8 | 0 | 11831.2 | 2 | 22000 | 0 | 0 | 3 | 0 | 27707.80815 | 34292.19185 | 4
Scottsville Textile Mill
As per the report a model has been developed which can be used to schedule production for the Scottsville Textile Mill and at the same time how many yards of each fabric must be purchased from another mill has been determined. All the discussion and analysis of the report has been included below.
Table 4.16
Monthly demand, selling price, variable cost, and purchase price data for Scottsville Textile Mill Fabrics Fabric | Demand (yards) | Selling price ($/yard) | Variable Cost ($/yard) | Purchase Price ($/yard) | 1 | 16500 | 0.99 | 0.66 | 0.80 | 2 | 22000 | 0.86 | 0.55 | 0.70 | 3 | 62000 | 1.10 | 0.49 | 0.60 | 4 | 7500 | 1.24 | 0.51 | 0.70 | 5 | 62000 | 0.70 | 0.50 | 0.70 |
Table 4.17
Loom production rates for the Scottsville Textile Mill | Loom Rate (yards/hour) | Fabric | Dobbie | Regular | 1 | 4.63 | - | 2 | 4.63 | - | 3 | 5.23 | 5.23 | 4 | 5.23 | 5.23 | 5 | 4.17 | 4.17 |
Fabrics 1 & 2 can be manufactured only on the dobbie loom.
Solution:
Decision variables xij≔ Number of yards produced by loom j on product i, i=1,2,…,5, j=1,2 yi: Number of yards purchased purchased from another mill, i=1,2,…,5.
Parameters:
Di : demand of product i.
Rij: Loom rate spi: selling price of product i vci: varying cost of product i pi: purchase price of product i
Max i=15spi(j=12xij+yi)-i=15vcij=12xij-i=15pi*yi
s.t.
j=12xij+yi≥Di, i=1,2,…,5 (Demand) i=15x1j/Ri1≤8*24*30 (production capacity of Dobbie) i=15x2j/Ri2≤30*24*30(production capacity of Regular) xij≥0 i=1,2,…,5, j=1,2 x21=x22=0 (Fabrics 1 and 2 can be manufactured only on the dobbie loom)
Answers
1. The final production schedule and loom assignments for each fabric: Decision variables x_ij:=number of yards loom j produce product i | y_i:=number of yard product i is purchased | Fabric | Dobbie | Regular | | 1 | 4668.8 | 0 | 11831.2 | 2 | 22000 | 0 | 0 | 3 | 0 | 27707.80815 | 34292.19185 | 4