The Hospital Administrators at New Hope, County General, and City $\quad$

question 66

Essay

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months.
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Hospital }$
$\begin{array}{lccc}&\text { New Hope } & \text { Countv General } & \text { City East }\\\hline \text { Input Measures } & & & \\\text { Bed days unused (1000s) } & 83.0 & 105.0 & 104.1 \\\text { Supply expense }(\$ 1000 \mathrm{~s}) & 123.8 & 162.3 & 154.0 \\\text { Full-time staff } & 225.0 & 200.0 & 231.0 \\\text { Output Measures } & & & \\\text { Patient-days (1000s) } & 105.0 & 71.0 & 82.7 \\\text { Nurses qualified } & 253.0 & 92.0 & 175.0 \\\text { Assistants on staff } & 125.0 & 45.0 & 65.0 \\\text { satiefartion } & 98.0 & 88.0 & 83.0\end{array}$


What are the key formulas for this Excel spreadsheet implementation of the following formulation?
Let $\quad w _ { i } =$ werght as5igned to dutput $j , j = 1 , \ldots , 4$
$\mathbf { v } _ { i } =$ waight as5igned to ingut $i , i = 1 , \ldots , 3$
MAX: $0 0. \quad 82.7 w _ { 1 } + 175 .0 w _ {2 } + 65.0 w _ { 3 } + 83 .0 w _ { 4 }$
Subject ta:
$105.1 w _ { 1 } + 253.0 w _ { 2} + 125.0 w _ { 3 } + 98.0 w _ { 4 } - 83.0 v _ { 1 } - 123.8 v _ { 2 } - 225.0 v _ { 3 } \leq 0$
$71.0 w _ { 1 } + 92.0 w _ { 2 } + 45.0 w _ { 3 } + 88.0 w _ { 4 } - 105.0 v _ { 1 } - 162.3 v _ { 2 } - 200 v _ { 3 } \leq 0$
$82.7 w _ { 1 } + 175.0 w _ { 2} + 65.0 w _ { 3 } + 83.0 w _ { 4 } - 104.1 v _ { 1 } - 154.0 v _ { 2 } - 231.0 v _ { 3 } \leq0$
$104.1 \mathbf { v } _ { 1 } + 154.0 \mathbf { v } _ { \mathbf { 2 } } + 231.0 \mathbf { v } _ { \mathbf { 3 } } = 1$
$w _ { 1 , } w _ { 2 } w _ { 3 , } w _ { 4 } , \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \geq0$

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Definitions:

Continuity

The consistent operation or development of something over a period of time without interruption.

Transtheoretical Model

A psychological framework that outlines stages of change individuals go through when modifying behavior, providing insight into the process of change.

Anger Issues

A pattern of emotional responses characterized by inappropriate or excessive feelings of irritability, rage, or frustration.

Precontemplation

The stage in the process of change where the individual is not yet considering change or is unaware of the need for change.