Using Data Envelopment Analysis

1. How many decision variables are there in the model?
2. Formulate a maximization model to evaluate the relative efficiency of County hospital.
3. Are the results from the minimization method and the maximization method reciprocal of each other? Why not?

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 improve the performance. 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: Input measures 1. The number of full-time equivalent (FTE) nonphysician personnel Output measures 1. Patient-days of service under Medicare 2. Patient-days of service not under Medicare 1 3. Number of nurses trained. 2. The amount spent on supplies 3. The number of bed-days available. 4. Number of interns trained. Summaries of the input and output measures for a one-year period at each of the four hospitals are shown in Tables 1 and 2. Formulate a LP model to determine the relative efficiency of County hospital. 3. Number of nurses trained. 2. The amount spent on supplies 3. The number of bed-days available. 4. Number of interns trained. Summaries of the input and output measures for a one-year period at each of the four hospitals are shown in Tables 1 and 2. Formulate a LP model to determine the relative efficiency of County hospital. Table 1: Annual resources consumed (inputs) by the four hospitals Hospital Input measure General University County State Full-time equivalent nonphysicans 285.20 162.30 275.70 210.40 Supply expense ($1000s) 123.80 128.70 348.50 154.10 Bed-days available (1000) 106.72 64.21 104.10 104.04 Table 2: Annual services provided (outputs) by the four hospitals Hospital Output measure General University County Medicare patient-days (1000s) 48.14 34.62 36.72 Non-Medicare patient-days (1000s) 43.10 27.11 45.98 Nurses trained 253 148 175 Interns trained 41 27 23 State 33.16 56.46 160 84