lpt

Linear Programming Technique for Cotton Mixing: 

Linear Programming Technique for Cotton Mixing Pavani Harsha MB 30 - Quantitative Methods in Decisions Prof.Jaideep Naidu

Acknowledgements: 

Acknowledgements Prof. Jaideep Naidu, Philadelphia University Mr. Thavasi Vijayakumar, Spinning Manager, Pt. Gokak, Indonesia LPT for Cotton Mixing

LPT for Cotton Mixing: 

LPT for Cotton Mixing Introduction: Quantitative methods used in Textile industry: Linear programming technique - Cotton mixing - Scheduling Forecasting in apparel industry - Seasonal Forecasting Inventory control – Various production stages CPM/ PERT - two or more simultaneous projects on time Transportation technique – Raw materials & finished goods

LPT for Cotton Mixing:: 

LPT for Cotton Mixing: Why is cotton mixed? Balancing Cost and Quality Achieve best quality yarn at lowest production Cost Why cotton quality varies? Natural fiber Uneven and non-uniform How are Cost & Quality related? As Quality increases cost increases LPT for Cotton Mixing

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Is Cotton Cost a big factor? Around 60 % of total production cost http://www.cottoninc.com/EFSConference/homepage.cfm?page=1099 LPT for Cotton Mixing

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Properties of Raw Materials that affect the final product: Length Strength Maturity Coefficient Fineness – Micronaire Why is LPT used? Minimize Total cost Maximize quality LPT for Cotton Mixing

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Formulation of LPT model: Let C1, C2, C3,….Cn be the costs of ‘n’ cottons P1, P2, P3,…..Pn be the Percentages of each cotton to be mixed L1, L2, L3,….Ln be the lengths of each cotton S1, S2, S3,….Sn be the strengths of each cotton M1, M2, M3,….Mn be the maturity coefficients of each cotton F1, F2, F3,….Fn be the micronaire value of each cotton LPT for Cotton Mixing

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Objective Function: Min Z = (C1*P1) + (C2*P2) + (C3*P3) + … + (Cn*Pn) S.T. Constraints L1*P1 + L2*P2 + L3*P3 + … + Ln*Pn  Lr S1*P1 + S2*P2 + S3*P3 + … + Sn*Pn  Sr M1*P1 + M2*P2 + M3*P3 + … + Mn*Pn  Mr F1*P1 + F2*P2 + F3*P3 + … + Fn*Pn  Fr P1 + P2 + P3 + … + Pn = 1 P1, P2, P3,….. Pn  0 Right Hand Side values are obtained from given set of Norms LPT for Cotton Mixing

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Example: Aim: To manufacture 10 Tex cotton yarn Required properties for the raw material: Length: 31.5mm – 34mm Strength: 20gpt – 23gpt Maturity Coefficient: 80% - 83% Micronaire Value: 3.6 – 3.9 LPT for Cotton Mixing The values shown above are examples and do not represent any cottons as such.

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Properties of Cottons available and their Costs: LPT for Cotton Mixing The values shown above are examples and do not represent any cottons as such.

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Objective Function: Min Z = (2.05*P1) + (1.70*P2) + (1.66*P3) S.T. Constraints: 33*P1 + 31*P2 + 30*P3  32 24*P1 + 20.5*P2 + 19*P3  21.5 0.83*P1 + 0.802*P2 + 0.798*P3  0.82 3.5*P1 + 3.85*P2 + 3.9*P3  3.7 P1 + P2 + P3 = 1 Non-Negativity Constraints: P1, P2, P3  0 P1, P2, P3 values are obtained by solving this LP Model using SIMPLEX method (Microsoft Excel can be used) LPT for Cotton Mixing

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Results: Objective Function Value: Min Z = 1.925 Conclusion: LPT can be efficiently used in cotton mixing LPT eliminates wastage of raw materials and hence reduces the total Production Cost. LPT for Cotton Mixing