Lingo 做线性规划 - DEA

Reference: <An Introduction to Management Science Quantitative Approaches to Decision Making, Revised 13th Edition>

Evaluating the Performance of Hospitals
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 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:
Input Measures
1. The number of full-time equivalent (FTE) nonphysician personnel
2. The amount spent on supplies
3. The number of bed-days available
Output Measures
1. Patient-days of service under Medicare
2. Patient-days of service not under Medicare
3. Number of nurses trained
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 5.1 and 5.2. Let us show how DEA can use these data to identify relatively inefficient hospitals.

Build Model as below:

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

We first note that the value of the objective function shows that the efficiency score for County Hospital is 0.905. This score tells us that the composite hospital can obtain at least the level of each output that County Hospital obtains by having available no more than 90.5% of the input resources required by County Hospital.