Problem 5-01 The hospital administrators at General Hospital, University Hospital, County Hospital, and State Hospital have been meeting to discuss ways in which they can help one another to improve the performance at each of their hospitals. A consultant suggested that they consider using DEA to measure the performance of each hospital relative to the performance of all four hospitals. In discussing how this evaluation could be done, the following three input measures and four output measures were identified: ANNUAL RESOURSES CONSUMED (INPUTS) BY THE FOUR HOSPITALS Hospital Input measure General University Country Full-time equivalent nonphysicians 285.20 162.30 275.70 Supply expence ($1000s) 123.80 128.70 3 48.50 Bed-days available ($1000s) 106.72 64.21 104.10 State 210.40 154,10 104.04 ANNUAL SERVICES PROVIDED (OUTPUTS) BY THE FOUR HOSPITALS Hospital Output measure General University Country Medicare patient days (1000s) 48.14 34.62 36.72 Non-Medicare patient days (1000s) 43.10 27.11 45.98 Nurses trained 148 175 Interns trained 23 State 33.16 56.46 160 253 41 27 84 a. Use these data to develop a linear programming model that could be used to evaluate the performance of General Hospital. Round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. If your answer is zero, enter "0". If the constant is '1' it must be entered in the box. Let E = the fraction of General Hospital's input available to the composite hospital wg - weight applied to inputs and outputs for General Hospital wu = weight applied to inputs and outputs for University Hospital WC = weight applied to inputs and outputs for County Hospital Ws = weight applied to inputs and outputs for State Hospital + WS 33.16 ws + [ + 34.62 wu + Wu + 148 wu + wu + 160 wg + wg + 43.10 wg + wg + 41 wg + 285.20 wg + wg + 106.72 wg + + + 275.70 WC + E -123.80 E+ LE+ WC + 154.10 128.70 wu + Wu + 104.10 WC + wg, wu, wc, ws b. The following solution is optimal. Objective Function Value = 1.000 Variable Value Reduced Cost 1.000 0.000 WG 1.000 0.000 WU 0.000 0.000 WC 0.000 0.331 0.000 0.215 Does the solution indicate that General Hospital is relatively inefficient? No C. Which hospital or hospitals make up the composite unit used to evaluate General Hospital? General Hospital Explain why? The input in the box below will not be graded, but may be reviewed and considered by your instructor Problem 5-01 The hospital administrators at General Hospital, University Hospital, County Hospital, and State Hospital have been meeting to discuss ways in which they can help one another to improve the performance at each of their hospitals. A consultant suggested that they consider using DEA to measure the performance of each hospital relative to the performance of all four hospitals. In discussing how this evaluation could be done, the following three input measures and four output measures were identified: ANNUAL RESOURSES CONSUMED (INPUTS) BY THE FOUR HOSPITALS Hospital Input measure General University Country Full-time equivalent nonphysicians 285.20 162.30 275.70 Supply expence ($1000s) 123.80 128.70 3 48.50 Bed-days available ($1000s) 106.72 64.21 104.10 State 210.40 154,10 104.04 ANNUAL SERVICES PROVIDED (OUTPUTS) BY THE FOUR HOSPITALS Hospital Output measure General University Country Medicare patient days (1000s) 48.14 34.62 36.72 Non-Medicare patient days (1000s) 43.10 27.11 45.98 Nurses trained 148 175 Interns trained 23 State 33.16 56.46 160 253 41 27 84 a. Use these data to develop a linear programming model that could be used to evaluate the performance of General Hospital. Round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. If your answer is zero, enter "0". If the constant is '1' it must be entered in the box. Let E = the fraction of General Hospital's input available to the composite hospital wg - weight applied to inputs and outputs for General Hospital wu = weight applied to inputs and outputs for University Hospital WC = weight applied to inputs and outputs for County Hospital Ws = weight applied to inputs and outputs for State Hospital + WS 33.16 ws + [ + 34.62 wu + Wu + 148 wu + wu + 160 wg + wg + 43.10 wg + wg + 41 wg + 285.20 wg + wg + 106.72 wg + + + 275.70 WC + E -123.80 E+ LE+ WC + 154.10 128.70 wu + Wu + 104.10 WC + wg, wu, wc, ws b. The following solution is optimal. Objective Function Value = 1.000 Variable Value Reduced Cost 1.000 0.000 WG 1.000 0.000 WU 0.000 0.000 WC 0.000 0.331 0.000 0.215 Does the solution indicate that General Hospital is relatively inefficient? No C. Which hospital or hospitals make up the composite unit used to evaluate General Hospital? General Hospital Explain why? The input in the box below will not be graded, but may be reviewed and considered by your instructor