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Unformatted text preview: Chapter 5 Advanced Linear Programming Applications Learning Objectives 1. Learn about applications of linear programming that are solved in practice. 2. Develop an appreciation for the diversity of problems that can be modeled as linear programs. 3. Obtain practice and experience in formulating realistic linear programming models. 4. Understand linear programming applications such as: data envelopment analysis revenue management portfolio selection game theory 5. Know what is meant by a twoperson, zerosum game. 6. Be able to identify a pure strategy for a twoperson, zerosum game. 7. Be able to use linear programming to identify a mixed strategy and compute optimal probabilities for the mixed strategy games. 8. Understand the following terms: game theory twoperson, zerosum game saddle point pure strategy mixed strategy Note to Instructor The application problems of Chapter 5 are designed to give the student an understanding and appreciation of the broad range of problems that can be approached by linear programming. While the problems are indicative of the many linear programming applications, they have been kept relatively small in order to ease the student's formulation and solution effort. Each problem will give the student an opportunity to practice formulating a linear programming model. However, the solution and the interpretation of the solution will require the use of a software package such as The Management Scientist , Microsoft Excel 's Solver or LINGO. 5  1 Chapter 5 Solutions: 1. a. Min E s.t. wg + wu + wc + ws = 1 48.14 wg + 34.62 wu + 36.72 wc + 33.16 ws ≥ 48.14 43.10 wg + 27.11 wu + 45.98 wc + 56.46 ws ≥ 43.10 253 wg + 148 wu + 175 wc + 160 ws ≥ 253 41 wg + 27 wu + 23 wc + 84 ws ≥ 41 285.2 E + 285.2 w g + 162.3 wu + 275.7 wc + 210.4 ws ≤ 0 123.80 E + 1123.80 w g + 128.70 wu + 348.50 wc + 154.10 ws ≤ 0 106.72 E + 106.72 w g + 64.21 wu + 104.10 wc + 104.04 w s ≤ 0 wg , wu , wc , ws ≥ b. Since wg = 1.0, the solution does not indicate General Hospital is relatively inefficient. c. The composite hospital is General Hospital. For any hospital that is not relatively inefficient, the composite hospital will be that hospital because the model is unable to find a weighted average of the other hospitals that is better. 2. a. Min E s.t. wa + wb + wc + wd + we + wf + wg = 1 55.31 wa + 37.64 wb + 32.91 wc + 33.53 wd + 32.48 we + 48.78 wf + 58.41 wg ≥ 33.53 49.52 wa + 55.63 wb + 25.77 wc + 41.99 wd + 55.30 we + 81.92 wf + 119.70 w g ≥ 41.99 281 wa + 156 wb + 141 wc + 160 wd + 157 we + 285 wf + 111 wg ≥ 160 47 wa + 3 wb + 26 wc + 21 wd + 82 we + 92 wf + 89 wg ≥ 21250 E +310 wa + 278.5 wb + 165.6 wc + 250 wd + 206.4 we + 384 wf + 530.1 wg ≤316 E +134.6 wa + 114.3 wb + 131.3 wc + 316 wd + 151.2 we + 217 wf + 770.8 wg ≤94.4 E +116 wa + 106.8 wb + 65.52 wc + 94.4 wd + 102.1 we + 153.7 wf + 215 wg ≤ wa , wb , wc , wd , we , wf , wg ≥ b. E = 0.924 wa = 0.074 wc = 0.436 we = 0.489 All other weights are zero....
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 Spring '10
 DR.JENASHAFAI
 Linear Programming, Optimization, Game Theory, Linear Programming Applications, Management Scientist

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