Problem 2. A Data Envelopment Analysis evaluating the relative efficiency of hospitals
(DEA) is an application of linear programming used to measure the relative efficiency of operating units with the same goals and objectives. As explained in the course, DEA can measure the relative efficiency of a group of hospitals. The data seen below involving seven teaching hospitals include three input measures and four output measures.
Input Measures
Hospital
Full-Time Equivalent Nonphysicians
Supply
Expense ($1000s)
Bed-Days Available
(1000s)
A
310
134.6
116
B
278.5
114.3
106.8
C
165.6
131.3
65.52
D
250
316
94.4
E
206.4
151.2
102.1
F
384
217
153.7
G
530.1
770.8
215
Output Measures
Hospital
Patient-Days (65 or older)
(1000s)
Patient-Days (under 65)
($1000s)
Nurses Trained
Interns Trained
A
55.31
49.52
291
47
B
37.64
55.63
156
3
C
32.91
25.77
141
26
D
33.53
41.99
160
21
E
32.48
55.3
157
82
F
48.78
81.9
285
92
G
58.41
119.7
111
89
Formulate a linear programming model based on DEA approach to evaluate the performance of hospital D.
Solve the problem formulated in (a), and show all of the Excel or QM templates you use in your
Is hospital D relatively inefficient? What is your interpretation of the value of the objective function?
How many patient-days of each type are produced by the composite hospital?
Which hospital would you recommend hospital D consider emulating to improve the efficiency of its operation?