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Data Envelopment Analysis

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.

Input Measures
Hospital Full-Time Supply Bed-Days
Equivalent Expense Available
Nonphysicians (1000s) (1000s)
A 310.0 134.60 116.00
B 278.5 114.30 106.80
C 165.6 131.30 65.52
D 250.0 316.00 94.40
E 206.4 151.20 102.10
F 384.0 217.00 153.70
G 530.1 770.80 215.00

Output Measures
Hospital Patient-Days Patient-Days Nurses Interns
(65 or older) (Under 65) Trained Trained
(1000s) (1000s)
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 55.30 157 82
F 48.78 81.92 285 92
G 58.41 119.70 111 89

a.Formulate a linear programming model so that data envelopment analysis can be used to evaluate the performance of hospital D.
b.Solve the model.
c.Is hospital D relatively inefficient? What is the interpretation of the value of the objective function?
d.How much patient-days of each type are produced by the composite hospital?
e.Which hospitals would you recommend hospital D consider emulating to improve the efficiency of its operation?

(See attached file for full problem description)


Solution Preview

Please see attached files.

For theory: have a look at the reference website

a. Let Ei be the efficiency of hospital I, we have:

where wj the weight of output j
mj the value of output measure j
wk the weight of input k
mk the value of input measure k

We want to maximize the weighted output of hospital D, which is:
Subject to the following constraints:

The first two constraints require the weighing factor to be positive. The third constraint requires the weighted input of hospital D to be 1. This is required because we want to normalize and linearise the program (see reference for more details).

There is also another constraint which ...

Solution Summary

The solution provides detailed explanations and discussions in 4 pages of Word and Excel document.