Presentation on theme: "Linear Programming Technique for Cotton Mixing"— Presentation transcript:
1 Linear Programming Technique for Cotton Mixing PavaniHarshaMB 30 - Quantitative Methods in DecisionsProf.Jaideep Naidu
2 Acknowledgements Prof. Jaideep Naidu, Philadelphia University LPT for Cotton MixingAcknowledgementsProf. Jaideep Naidu, Philadelphia UniversityMr. Thavasi Vijayakumar, Spinning Manager, Pt. Gokak, Indonesia
3 Introduction: LPT for Cotton Mixing Quantitative methods used in Textile industry:Linear programming technique - Cotton mixing- SchedulingForecasting in apparel industry - Seasonal ForecastingInventory control – Various production stagesCPM/ PERT - two or more simultaneous projects on timeTransportation technique – Raw materials & finished goods
4 LPT for Cotton Mixing: LPT for Cotton Mixing Why is cotton mixed? Balancing Cost and QualityAchieve best quality yarn at lowest production CostWhy cotton quality varies?Natural fiberUneven and non-uniformHow are Cost & Quality related?As Quality increases cost increases
5 Is Cotton Cost a big factor? Around 60 % of total production cost LPT for Cotton MixingIs Cotton Cost a big factor?Around 60 % of total production cost
6 Properties of Raw Materials that affect the final product: LPT for Cotton MixingProperties of Raw Materials that affect the final product:LengthStrengthMaturity CoefficientFineness – MicronaireWhy is LPT used?Minimize Total costMaximize quality
7 Formulation of LPT model: LPT for Cotton MixingFormulation of LPT model:LetC1, C2, C3,….Cn be the costs of ‘n’ cottonsP1, P2, P3,…..Pn be the Percentages of each cotton to be mixedL1, L2, L3,….Ln be the lengths of each cottonS1, S2, S3,….Sn be the strengths of each cottonM1, M2, M3,….Mn be the maturity coefficients of each cottonF1, F2, F3,….Fn be the micronaire value of each cotton
8 Objective Function: S.T. Constraints LPT for Cotton Mixing Min Z = (C1*P1) + (C2*P2) + (C3*P3) + … + (Cn*Pn)S.T. ConstraintsL1*P1 + L2*P2 + L3*P3 + … + Ln*Pn LrS1*P1 + S2*P2 + S3*P3 + … + Sn*Pn SrM1*P1 + M2*P2 + M3*P3 + … + Mn*Pn MrF1*P1 + F2*P2 + F3*P3 + … + Fn*Pn FrP1 + P2 + P3 + … + Pn = 1P1, P2, P3,….. Pn 0Right Hand Side values are obtained from given set of Norms
9 Example: Aim: Required properties for the raw material: LPT for Cotton MixingExample:Aim:To manufacture 10 Tex cotton yarnRequired properties for the raw material:Length: 31.5mm – 34mmStrength: 20gpt – 23gptMaturity Coefficient: 80% - 83%Micronaire Value: 3.6 – 3.9The values shown above are examples and do not represent any cottons as such.
10 Maturity Coefficient (%) LPT for Cotton MixingProperties of Cottons available and their Costs:PropertiesCottonsNorms123Length (mm)Strength (gpt)Maturity Coefficient (%)Micronaire3324833.53120.580.23.85301979.83.93221.5823.7Cost per lb (US $)2.051.701.66The values shown above are examples and do not represent any cottons as such.
11 Non-Negativity Constraints: P1, P2, P3 0 LPT for Cotton MixingObjective Function:Min Z = (2.05*P1) + (1.70*P2) + (1.66*P3)S.T. Constraints:33*P1 + 31*P2 + 30*P3 3224*P *P2 + 19*P3 21.50.83*P *P *P3 0.823.5*P *P *P3 3.7P1 + P2 + P3 = 1Non-Negativity Constraints: P1, P2, P3 0P1, P2, P3 values are obtained by solving this LP Model using SIMPLEX method (Microsoft Excel can be used)
12 Percentage to be Mixed (%) LPT for Cotton MixingResults:Objective Function Value: Min Z = 1.925CottonPercentage to be Mixed (%)164.3235.73Conclusion:LPT can be efficiently used in cotton mixingLPT eliminates wastage of raw materials and hence reduces the total Production Cost.