Integer or Linear Programming for a Local Textile Company E-commerce
Essay Instructions:
In this discussion board assignment, you are asked to describe a use case for integer programming or nonlinear programming that was not discussed in class. You can approach this problem in one of the following ways: You can get inspired by the examples or exercises from the selected chapters that are in e-reserve in the book by Powell and Baker: The Art of Modeling with Spreadsheets. You can also draw from your experiences in your workplace or in your personal life. For example, you can describe a use case in your work or personal life and explain how this problem can be solved using integer programming or nonlinear programming. Be as specific as possible when describing the use case. The case is of our local textile manufacturing company. The company produces three types of textile materials and each is cut into a 15-mtr roll. However, for the past week, its customers demand for these materials is in different dimensions, and the demand also varies. The demand is 15, 25, and 10 for 4-mtr, 6-mtr, and 8-mtr respectively. How will the company cut the materials in a way to minimize the wastage of textile while at the same time meet the customer demand?
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Integer Programming
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Integer Programming
The case is of our local textile manufacturing company. The company produces three types of textile materials and each is cut into a 15-mtr roll. However, for the past week, its customers demand for these materials is in different dimensions, and the demand also varies. The demand is 15, 25, and 10 for 4-mtr, 6-mtr, and 8-mtr respectively. How will the company cut the materials in a way to minimize the wastage of textile while at the same time meet the customer demand?
Solution.
The possible scenarios are; cut 4mtr 3X (waste 3 mtr), cut 6mtr 2X (waste 3 mtr), cut 8mtr once & 4 mtr 1X (waste 3 mtr), cut 8mtr 1X & 6 mtr 1X (waste 1 mtr), cut 6mtr 1X & 4 mtr 2X (waste 1 mtr),
We can formulate this first by use of a table:
Cutting design
4-mtr
6-mtr
8-mtr
Wastage per mtr
Decision variable
1
3
0
0
3
X1
2
0
2
0
3
X2
3
1
0
1
3
X3
4
0
1
1
1
X4
5
2
1
0
1
X5
Demand
15
25
10
Objective fn Minimize waste=Total mtrs of material cut-Total demand
=15(x1+x2+x3+x4+x5)-(15*4+25*6+10*8), =15(x1+x2+x3+x4+x5)-290, but since 15 and 290 are constants, the objective function is x1+x2+x3+x4+x5, subject to constraints;
3x1+x3+2x5=>15, 2x2+x4+x5=>25, x3+x4=>10, where xi=>0
See attached excel. Below is the output;