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1. Linear Programming Cutting Stock Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

2. Rawproduct Linear Programming Applications Cutting Stock Problem Finalproduct Loss ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

3. 2 finalproducts Rawproduct Cutting patterns Linear Programming Applications Cutting Stock Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

4. Linear Programming Applications Cutting Stock Problem • Raw products - pipes- roles of paper or textile- bars- wooden sticks or bars - steel plates • Objective  minimization of total loss or number of cut raw products maximization of number of assembled products ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

5. Linear Programming Applications Cutting Stock Problem • Decision variables ~ patterns The value of the variable determines the number of the raw products being cut/sliced according to corresponding pattern • Finding of all possible cutting patterns ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

6. Linear Programming Applications Cutting Stock Problem Example – John Starling & Sons • 2 products: bird table bird box • Inputs: wooden boards screws time • Special collection for the exhibition (with possible sales) in 20 days Objective: maximize total revenue (all production will be sold) ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

7. Linear Programming Applications Cutting Stock Problem Example – John Starling & Sons ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

8. Linear Programming Applications Cutting Stock Problem Example – John Starling & Sons Cutting patterns & Decision variables ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

9. Linear Programming Applications Cutting Stock Problem Example – John Starling & Sons Optimal solution ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

10. Linear Programming Applications • Production Process Models • Blending Problems • Marketing Research Distribution Problems • Portfolio Selection Problem • Cutting Stock Problem • Transportation Problem • Assignment Problem ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

11. Linear Programming Transportation Problem ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

12. Linear Programming Applications Transportation Problem Shipments Sources Destinations ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

13. Sources Destinations  supply= demand Balanced  supply= demand Unbalanced Linear Programming Applications Transportation Problem ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

14. Sources Destinations  supply> demand Dummy destination  supply< demand Dummy source Linear Programming Applications Transportation Problem ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

15. Benešov Humpolec Tábor Jihlava Pelhřimov Linear Programming Applications Transportation Problem Example – Star Chips, Inc. WarehousesHumpolecPelhřimov SubsidiariesBenešovJihlavaTábor ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

16. Supply of potatoes Requirements Linear Programming Applications Transportation Problem Example – Star Chips, Inc. WarehousesHumpolecPelhřimov SubsidiariesBenešovJihlavaTábor Objective: satisfy requirements with minimal total shippingcost ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

17. 150 140 Linear Programming Applications Transportation Problem Example – Star Chips, Inc. Supply, demand, unit shipping cost ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

18. 150 Linear Programming Applications Transportation Problem Example – Star Chips, Inc. Dummy destination ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

19. Linear Programming Applications Transportation Problem Example – Star Chips, Inc. Decision variables ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry

20. Linear Programming Applications Transportation Problem Example – Star Chips, Inc. Optimal solution ___________________________________________________________________________ QuantitativeMethodsof Management Jan Fábry