Cutting Stock |
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| A
steel mill produces sheets of steel in 3 sizes. These sizes are 100, 80 and
55 inches. Unfortunately, |
| demand
is in 3 other sizes; 45,30 and 18 inches.How should the mill cut the sheets
to minimize waste? |
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| Possible
combinations |
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45" sheet |
30" sheet |
18"
sheet |
Waste
(inches) |
Number of sheets |
Total Waste |
| 1 |
100" sheet |
2 |
0 |
0 |
10 |
1 |
10 |
| 2 |
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1 |
1 |
1 |
7 |
1 |
7 |
| 3 |
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1 |
0 |
3 |
1 |
1 |
1 |
| 4 |
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0 |
3 |
0 |
10 |
1 |
10 |
| 5 |
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0 |
2 |
2 |
4 |
1 |
4 |
| 6 |
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0 |
1 |
3 |
16 |
1 |
16 |
| 7 |
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0 |
0 |
5 |
10 |
1 |
10 |
| 8 |
80" sheet |
1 |
1 |
0 |
5 |
1 |
5 |
| 9 |
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1 |
0 |
1 |
17 |
1 |
17 |
| 10 |
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0 |
2 |
1 |
2 |
1 |
2 |
| 11 |
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0 |
1 |
2 |
14 |
1 |
14 |
| 12 |
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0 |
0 |
4 |
8 |
1 |
8 |
| 13 |
55" sheet |
1 |
0 |
0 |
10 |
1 |
10 |
| 14 |
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0 |
1 |
1 |
7 |
1 |
7 |
| 15 |
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0 |
0 |
3 |
1 |
1 |
1 |
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Totals |
7 |
12 |
26 |
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Total |
122 |
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Demand |
150 |
200 |
175 |
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| Problem |
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| A
steel mill produces sheets of steel in three different sizes. Demand,
however, is in 3 other, smaller, sizes. |
| How should the
company cut the sheets of steel in order to minimize waste? |
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| Solution |
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| 1) There are only a limited number of ways to cut the
sheets. The variables are the number
of times we have |
| to cut a sheet
in a certain way. In worksheet Cutstock these are defined as Sheets_used. |
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| 2) The
constraints are simple and straightforward. |
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Sheets_made = Demand |
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Sheets_used >= 0 via the Assume Non-Negative option |
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Sheets_used = integer |
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| 3) The
objective is to minimize waste. This is defined on the worksheet as
Total_waste. |
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| Remarks |
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| In
some situations it may seem rather difficult to write out all the
possibilities for cutting stock as is done in |
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model. There is a technique that lets the computer do this, called column
generation. It is beyond the |
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example to fully discuss this technique. |
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