HW5 CCE 6100

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Western Michigan University *

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6100

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Civil Engineering

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Apr 3, 2024

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WESTERN MICHIGAN UNIVERSITY CCE-6100-100 - Civil Systems Analysis HW.5 Done by: Aws Tarawneh
1. Data envelopment analysis can measure the relative efficiency of a group of hospitals. The following data from a particular study involving seven teaching hospitals include three input measures and four output measures: a. Formulate a linear programming model so that data envelopment analysis can be used to evaluate the performance of hospital D. E= efficiency of hospital D HA= hospital A HB= hospital B HC= hospital C HD= hospital D HE= hospital E HF= hospital F HG= hospital G Min E s.t. HA+HB+HC+HD+HE+HF+HG=1 310HA+278.5HB+165.6HC+250HD+206.4HE+384HF+530HG-250E<=0 134HA+114.3HB+131.3HC+316HD+151.2HE+217HF+770.8HG-316E<=0 116HA+106.8HB+65.52HC+94.4HD+102.1HE+153.7HF+215HG-94.4E<=0 55.31HA+37.64HB+32.91HC+33.53HD+32.48HE+48.78HF+58.41HG>=33.53 49.52HA+55.63HB+25.77HC+41.99HD+55.3HE+81.92HF+119.7HG>=41.99 291HA+156HB+141HC+160HD+157HE+285HF+111HG>=160 47HA+3HB+26HC+21HD+82HE+92HF+89HG>=21 b. Solve the model. Global optimal solution found. Objective value: 0.9235235 Infeasibilities: 0.000000 Total solver iterations: 6 Model Class: LP Total variables: 8 Nonlinear variables: 0 Integer variables: 0 Total constraints: 9 Nonlinear constraints: 0 Total nonzeros: 60 Nonlinear nonzeros: 0 Variable Value Reduced Cost
E 0.9235235 0.000000 HA 0.7446598E-01 0.000000 HB 0.000000 0.4737552E-01 HC 0.4361526 0.000000 HD 0.000000 0.7647654E-01 HE 0.4893814 0.000000 HF 0.000000 0.1252398E-01 HG 0.000000 0.4825028 Row Slack or Surplus Dual Price 1 0.9235235 -1.000000 2 0.000000 -0.1492373 3 34.82291 0.000000 4 150.5937 0.000000 5 0.000000 0.1059322E-01 6 0.8376040 0.000000 7 0.000000 -0.1224079E-01 8 0.000000 -0.1626847E-02 9 33.96914 0.000000 E=0. 9235235 HA=0.0744 HC=0.4361 HE=0.4893 c. Is hospital D relatively inefficient? What is the interpretation of the value of the objective function? Hospital F is relatively inefficient Composite requires 92.4 of D’s resources d. How many patient-days of each type are produced by the composite hospital? 33.53 patient days (65 or older) 41.99 patient days (under 65) e. Which hospitals would you recommend hospital D consider emulating to improve the efficiency of its operation? Hospitals A, C and E.
2. With the data in Problem 1 a. Formulate a linear programming model that can be used to perform data envelopment analysis for hospital E. Min E s.t. HA+HB+HC+HD+HE+HF+HG=1 310HA+278HB+165HC+250HD+206.4HE+384HF+530HG-206.4E<=0 134HA+114.3HB+131.3HC+316HD+151.2HE+217HF+770.8HG-151.2E<=0 116HA+106.8HB+65.52HC+94.4HD+102.1HE+153.7HF+215HG-102.1E<=0 55.31HA+37.64HB+32.91HC+33.53HD+32.48HE+48.78HF+58.41HG>=32.48 49.52HA+55.63HB+25.77HC+41.99HD+55.3HE+81.92HF+119.7HG>=55.3 291HA+156HB+141HC+160HD+157HE+285HF+111HG>=157 47HA+3HB+26HC+21HD+82HE+92HF+89HG>=82 b. Solve the model. Global optimal solution found. Objective value: 1.000000 Infeasibilities: 0.000000 Total solver iterations: 1 Model Class: LP Total variables: 8 Nonlinear variables: 0 Integer variables: 0 Total constraints: 9 Nonlinear constraints: 0 Total nonzeros: 60 Nonlinear nonzeros: 0 Variable Value Reduced Cost E 1.000000 0.000000 HA 0.000000 0.9287673 HB 0.000000 1.310314 HC 0.000000 0.4823454 HD 0.000000 0.9551427 HE 1.000000 0.000000 HF 0.000000 0.7385139 HG 0.000000 1.482464 Row Slack or Surplus Dual Price 1 1.000000 -1.000000 2 0.000000 0.000000 3 0.000000 0.4844961E-02 4 0.000000 0.000000 5 0.000000 0.000000 6 0.000000 0.000000 7 0.000000 0.000000 8 0.000000 0.000000 9 0.000000 -0.1219512E-01
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