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

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

3. Introduction: LPT for Cotton Mixing
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. Is Cotton Cost a big factor? Around 60 % of total production cost
LPT for Cotton Mixing
Is Cotton Cost a big factor?
Around 60 % of total production cost

6. Properties of Raw Materials that affect the final product:
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. Formulation of LPT model:
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. Objective Function: S.T. Constraints LPT for Cotton Mixing
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. Example: Aim: Required properties for the raw material:
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. Maturity Coefficient (%)
LPT for Cotton Mixing
Properties of Cottons available and their Costs:
Properties
Cottons
Norms 1 2 3
Length (mm)
Strength (gpt)
Maturity Coefficient (%)
Micronaire 33 24 83
3.5 31
20.5
80.2
3.85 30 19
79.8
3.9 32
21.5 82
3.7
Cost per lb (US $)
2.05
1.70
1.66
The values shown above are examples and do not represent any cottons as such.

11. Non-Negativity Constraints: P1, P2, P3  0
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*P *P2 + 19*P3  21.5
0.83*P *P *P3  0.82
3.5*P *P *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. Percentage to be Mixed (%)
LPT for Cotton Mixing
Results:
Objective Function Value: Min Z = 1.925
Cotton
Percentage to be Mixed (%) 1
64.3 2
35.7 3
Conclusion:
LPT can be efficiently used in cotton mixing
LPT eliminates wastage of raw materials and hence reduces the total Production Cost.