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Linear Programming Technique for Cotton Mixing

Linear Programming Technique for Cotton Mixing. Pavani Harsha. MB 30 - Quantitative Methods in Decisions Prof.Jaideep Naidu. LPT for Cotton Mixing. Acknowledgements. Prof. Jaideep Naidu, Philadelphia University Mr. Thavasi Vijayakumar, Spinning Manager, Pt. Gokak, Indonesia.

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Linear Programming Technique for Cotton Mixing

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

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

  3. 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

  4. 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

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

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

  7. LPT for Cotton Mixing 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

  8. LPT for Cotton Mixing • 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

  9. LPT for Cotton Mixing 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 The values shown above are examples and do not represent any cottons as such.

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

  11. LPT for Cotton Mixing 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)

  12. LPT for Cotton Mixing 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.

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