Applying Integer Linear Programming to the Fleet Assignment Problem ABARA American Airlines Decision Ti’chnohi^ics PO Box 619616 Dallasll’ort Worth Airport‚ Texas 75261-9616 We formulated and solved the fleet assignment problem as an integer linear programming model‚ permitting assignment of two or more fleets to a flight schedule simultaneously. The objective function can take a variety of forms including profit maximization‚ cost minimization‚ and the optimal utilization of a particular
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Briefly 1 explain the techniques and tools of Operations Research. Operations Research Methodology Techniques and tools of Operations Research 2 5 10 5 a. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming. b. Alpha Limited produces & sells two different products under the brand names black & white. The profit per unit on these products in Rs. 50 & Rs. 40 respectively. Both the products employ the same
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1 DEFINITION OF LINEAR PROGRAMMING (LP) Linear programming (LP) is a mathematical technique used in finding the best possible allocation of resources to achieve the best outcome‚ which is maximising profit or minimising cost. However‚ it is only applicable where there is a linear relationship between the variables. For example‚ the linear relationships between hours of labour and output in a textiles factory means an increase or decrease in labour force has a direct impact on production‚ which
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|BUAD – 555 Decision Science |October 3rd. | | |2012 | |Mini Exam # 2 | | |Students’ Version
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problem is identified properly because this problem statement will indicate the following three major aspects: Q2. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming. (Steps involved in LPP-4‚ Example-3 Advantages of LPP-3) 10 marks Answer. Steps of formulating Linear Programming Problem (LPP) The following steps are involved to formulate LPP : Step 1 : Identify the decision variables of the problem. Q3. a. What
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blend. It did so based on the properties of available stocks and blend proportions suggested by the blender. Then‚ by the 60’s computers advanced quit a bit. Linear programming models were being solved by linear programming introduced by the refiner engineers. A process optimization program for nonlinear optimization that solved nonlinear programming problems was developed by IBM‚ called POP II. Then‚ immediately after‚ the GOP blending optimization system was developed that used the POP II system.
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basis. 3. 3 surplus variables‚ 3 artificials‚ and 4 variables in the basis. 4. 2 surplus variables‚ 2 artificials‚ and 3 variables in the basis. 5. - 16. For obtaining the solution of dual of the following Linear Programming Problem‚ how many slack and/or surplus‚ and artificial variables are required? Maximize profit = $50X1 + $120X2 subject to 2X1 + 4X2 ≤ 80 3X1 + 1X2 ≤ 60 1. Two slack variables 3 2. Two surplus variables 3. Two surplus
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Graphical and Simplex Methods of Linear Programming The graphical method is the more popular method to use because they are easy to use and understand. Working with only a few variables at a time they allow operations managers to compare projected demand to existing capacity. The graphical method is a trial and error approach that can be easily done by a manager or even a clerical staff. Since it is trial and error though‚ it does not necessarily generate the optimal plan. One downside of this
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Mathematical optimization . . . . . . 1.2 Least-squares and linear programming 1.3 Convex optimization . . . . . . . . . . 1.4 Nonlinear optimization . . . . . . . . 1.5 Outline . . . . . . . .
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characteristics. [ 5 marks] b. Explain the nature of Operations Research and its limitations.[ 5 marks] 2. a. What are the essential characteristics of a linear programming model?[ 5 marks] b. Explain the graphical method of solving a LPP involving two variables.[ 5 marks] 3. a. Explain the simplex procedure to solve a linear programming problem. [ 5 marks] b. Explain the use of artificial variables in L.P [ 5 marks] 4. a. Explain the economic interpretation of dual variables. [ 5 marks]
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