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A MILP model for one dimensional cutting stock problem with adjustable leftover threshold . . .
Table 7. Solution by 1D Solution in matrix form

O 1 O 2 O 3 O 4 O 5 O 6 O 7 O 8 O 9
B 1
B 2 ✓ ✓ ✓
B 3 ✓ ✓ ✓
B 4 ✓ ✓
B 5 ✓
B 6
Figure 3. Visualization of OptiCutter’s cutting plan
5.2.5. Overview
5.2.3. Solution by 1D Solutions
Table 8. shows the comparison of obtained cut-
We used 1D Solutions desktop version to find the ting plans. We can see that 40 cm of waste ap-
optimal cutting plan. Here we have the option pears for software OptiCutter and 1D Solutions,
to set the 45 cm waste limit. This software can while the other two tools found a cutting plan
load data from .csv file too. The file contains the without waste. Despite the fact that 1D Solu-
stock and order details with length but waste limit tions gives the oportunity to set the waste limit,
should set manually. The obtained result shows a it seems to ignore it moreover the number of cuts
cutting plan consisting of 8 cuts, with a total of is also higher in its cutting plan.
40 cm of waste and 4 bars.
Table 6. Solution by 1D Solution in matrix form

O 1 O 2 O 3 O 4 O 5 O 6 O 7 O 8 O 9
B 1
B 2
B 3 ✓ ✓ ✓
B 4 ✓ ✓
B 5 ✓ ✓
B 6 ✓ ✓
Figure 5. Cutting plan
Table 8. User input comparison
Table 6. shows the matrix form of the obtained
cutting plan, and Fig. 4. presents the visualiza-
tion of it. OptiCutter 1D Solutions Optimalon MACROPT-1D
Cuts: 6 8 6 6
Waste: 40 cm 40 cm - -
Waste cost: 4000$ 4000$ 0$ 0$
Total cost: 6400 $ 7200$ 2400$ 2400$
Used qty: 4 4 4 4

6. Computational tests

In order to better investigate the issues raised in
the numerical example, simulations were carried
Figure 4. Cutting plan
out. The key questions of the experiment are:
5.2.4. Solution by Optimalon (1) What is the ranking of plans given by the
different software when considering only
We used Optimalon Excel add-in. After installing
the number of cuts and when considering
the extension, a new button willappear on the Ex-
cuts and the amount of waste together?
cle toolbar. Here we have to select and mark the
(2) Does 1D Solutions always ignore the waste
part of the workbook that contains the stock, the
limit?
orders and their length. The waste limit can also
(3) Optimalon and our implementation seem
be set manually. Optimalon gives a solution that
equally effective in the example. Are there
requires 6 cuts, 4 bars are involved and there is
cases where they give different results?
no waste. Table 7. and Fig. 5 present the cutting
plan. For testing, we generated 20 random inputs
and applied the same waste limit (W = 45), cut
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