Development of Optimal Cutting Plan using Linear ... - ijimt

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International Journal of Innovation, Management and Technology, Vol. 1, No. 5, December 2010ISSN: 2010-0248OptionStock Size(cm)L×WTABLE IV: YIELD(S) FOR CUTTING DIFFERENT SIZED ITEMS (ARCHERTOOL/LINGO8.0)Item Size (cm)LP Model Yield or Area utilization with Fibre Direction ConstraintLongitudinalTransverseL × W L × WPiecesPieces1 12 2% Yield% Yieldq11 300x150 30x15 20x10 100 0 100% 100 0 100%2 300x150 40x20 70x40 49 2 99.56% 42 4 99.56%3 300x150 25x15 15x10 120 0 100% 120 0 100%4 300x150 30x15 15x10 100 0 100% 100 0 100%OptionStock Size(cm)L×Wq2TABLE V: YIELD(S) FOR CUTTING DIFFERENT SIZED ITEMS (ITEMIZER9)Item Size (cm)LP Model Yield or Area utilization with Fibre Direction ConstraintLongitudinalTransverseL × W L × WPiecesPieces1 12 2% yield% yieldq11 300x150 30x15 20x10 100 0 100% 100 0 100%2 300x150 40x20 70x40 49 2 99.56% 42 4 99.56%3 300x150 25x15 15x10 120 0 100% 120 0 100%4 300x150 30x15 15x10 100 0 100% 100 0 100%q2q1q1q2q2V. VERIFICATION/VALIDATION OF MATLAB ALGORITHMAND LP MODELResults from the MATLAB algorithm have been comparedand found consistent with those from ArcherTool, LINGO8.0and ITEMIZER9.In order to further verify/validate the functionality of theMATLAB algorithm as well as LP model against somedocumented cutting stock problem, a case from the reference[15] has been taken whose solution is already known,. Then,solution from all approaches are obtained using the referenceinput values of the stock sheet and the items to be cut, asgiven in TABLE 6. The reference optimal cutting plan will bea baseline against which the optimal cutting plans from themethods of this paper will be compared and evaluated.Thus, if the results of the approaches match with those fromthe reference paper, their validity will be established and viceversa.A. Comparison of ResultsFigure 10 shows the pictorial view of the optimal cuttingplan from the reference paper [15] for the said case whilst theoptimal cutting plan from MATLAB algorithm is shown inthe Figure 11 and Figure 12. Moreover, cutting plan and theirresults screen shots of all LP model approaches are shown inFigure 13 and Figure 14 whilst Figure 15 shows the screenshot of the result obtained through the Cutting OptimizationSoftware: ITEMIZER9.For the sake of a quick and better comparison of the resultsfrom all approaches, the output values are tabulated inTABLE VI including those from the original paper. It isevident from the results that all approaches are in compliancewith each other and lead to the same results. Hence it can beinferred that the MATLAB algorithm as well as LP model foroptimal cutting plan developed in this work are valid andconsistent with each other.B. Graphical Representation of ResultsResults from the original paper and those from theapproaches of this paper are shown below.TABLE VI: COMPARISON RESULTS FROM ALL APPROACHES WITH THE REFERENCE CASEStock Size (cm) 180x150 Item Size (cm) 90x56Optimal Cutting Solution No. of Items Objective Value PercentageWasteApproach UsedCut(Yield)YieldFractionReference Case[15]5 25200 93.33% 0.067MATLAB Algorithm – Cut Across Then AlongFibre (Sheet Rotated)5 25200 93.33% 0.067ArcherTool LP Model –No Direction Constraint5 25200 93.33% 0.067LINGO8.0 LP Model –No Direction Constraint5 25200 93.33% 0.067ITEMIZER9 Graphic Solution –CSP Optimization5 25200 93.33% 0.067488
International Journal of Innovation, Management and Technology, Vol. 1, No. 5, December 2010ISSN: 2010-0248Figure 10: Optimal Cutting Plan from the Reference [15]Figure 11: Sequence of MATLAB Algorithm (Sheet Rotated 90°)150135120105Cutting along fibre180162144126Cutting across fibreWidth - Across Fibre (cm) →9075604530150Length - Along Fibre (cm) →108907254361800 18 36 54 72 90 108 126 144 162 1800 15 30 45 60 75 90 105 120 135 150Length - Along Fibre (cm) →Width - Across Fibre (cm) →Figure 12: All Possible Cutting Plans from MATLAB Algorithm (Sheet Rotated 90°)489
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