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Linear Programming. Applications. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry. Linear Programming. Applications. Guideline for Model Formulation. 1. Understand the problem thoroughly.

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  1. Linear Programming Applications ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  2. Linear Programming Applications Guideline for Model Formulation 1. Understand the problem thoroughly. 2. Write a verbal statement of the objective function and eachconstraint. 3. Define the decision variables. 4. Write the objective function in terms of the decision variables. 5. Write the constraints in terms of the decision variables. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  3. Linear Programming Applications • Production Process Models • Blending Problems • Marketing Research • Portfolio Selection Problem • Cutting Stock Problem • Transportation Problem • Assignment Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  4. Linear Programming Blending Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  5. Inputs(Ingredients) Output(Final blend) Linear Programming Applications Blending Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  6. Inputs Output • chemicals Quality Quantity RestrictionsRequirements • metal alloys • crude oils • livestock feeds • foodstuffs Cost Objective Linear Programming Applications Blending Problem Decision variables: amount of ingredients used in final blend ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  7. Linear Programming Applications Blending Problem Example – Feed • Design the optimal composition of nutritive mix that • will contain at least 100 units of proteins • will contain at least 300 units of starch • will weigh at least 200 kg • Objective: minimize total cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  8. Linear Programming Applications Blending Problem Example – Feed • Contents of proteins and starch in 1kg of each nutritive feed and prices for 1 kg of feed ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  9. Linear Programming Applications Blending Problem Example – Feed Decision variables ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  10. Linear Programming Applications Blending Problem Example – Feed Optimal solution ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  11. Linear Programming Marketing Research ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  12. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. • Evaluating consumer’s reaction to new products and services • MQ‘s client introduces a new type of washing powder • Prepare a campaign with door-to-door personal interviews about households’ opinion • Households: with childrenwithout children • Time of interview: daytime evening ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  13. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. • Plan: to conduct 1000 interviews • At least 300 households with children should be interviewed • At least 400 households without children should be interviewed • Number of evening interviews  number of daytime interviews • At least 35% of the interviews for households with children should be conducted during evening • At least 65% of the interviews for households without children should be conducted during evening ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  14. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. • Cost • Objective: minimize total cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  15. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. Decision variables ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  16. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. 1)Plan: to conduct 1000 interviews 2)   At least 300 households with children should be interviewed 3)   At least 400 households without children should be interviewed 4)Number of evening interviews  number of daytime interviews 5)   At least 35% of the interviews for households with children should be conducted during evening 6)   At least 65% of the interviews for households without children should be conducted during evening ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  17. Linear Programming Applications Marketing Research Example – MarketQuest, Inc. Optimal solution ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  18. Linear Programming Portfolio Selection Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  19. Alternative investments (shares, bonds, etc.) Mutual funds, credit unions, banks, insurance companies Maximization of expected return Minimization of risk Linear Programming Applications Portfolio Selection Problem ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  20. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. • Investing money in stocks of companies producing drinks • Plan to invest to 4 shares and 1 government bond ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  21. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. • Plan: to invest 2 000 000 CZK • No more than 200 000 CZK might be invested in Bohemian Milk shares • Government bonds should cover at least 20% of all investments • Because of diversification of portfolio neither alcohol-drink company should receive more than 800 000 CZK • Risk index of the final portfolio should be maximally 0.05 • Objective: maximize annual return of the portfolio ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  22. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. Decision variables ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  23. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  24. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. 1)Plan: to invest 2 000 000 CZK 2)   No more than 200 000 CZK might be invested in Bohemian Milk shares 3)   Government bonds should cover at least 20% of all investments 4)   Because of diversification of portfolio neither alcohol-drink company should receive more than 800 000 CZK 5)   Risk index of the final portfolio should be maximally 0.05 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

  25. Linear Programming Applications Portfolio Selection Problem Example – Drink Invest, Inc. Optimal solution ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

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