# 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)

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#### 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:

Maximise

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.