The Output Shows the Solution to a DEA Model Where $0 \mathrm {~S} + 0 \mathrm {~F} + 0 \mathrm {~L} + 0 \mathrm { D } + 1 \mathrm { E }$

question 31

Essay

The output shows the solution to a DEA model where facilities in Seaview (S),Farmington (F),Lewiston (L),and San Domingo (D)are compared.The inputs,in order,are number of machines,size of work force,and goodness of location.The outputs,in order,are production,quality rating,and on-time completion percentage.The model examines the efficiency of Lewiston.
Min $0 \mathrm {~S} + 0 \mathrm {~F} + 0 \mathrm {~L} + 0 \mathrm { D } + 1 \mathrm { E }$
S.T. 1) $1 \mathrm {~S} + 1 \mathrm {~F} + 1 \mathrm {~L} + 1 \mathrm { D } = 1$
2) $5 \mathrm {~S} + 22 \mathrm {~F} + 36 \mathrm {~L} + 15 \mathrm { D } - 36 \mathrm { E } < 0$
3) $400 \mathrm {~S} + 1500 \mathrm {~F} + 3150 \mathrm {~L} + 1060 \mathrm { D } - 3150 \mathrm { E } < 0$
4) $24 \mathrm {~S} + 13 \mathrm {~F} + 32 \mathrm {~L} + 17 \mathrm { D } - 32 \mathrm { E } < 0$
5) $800 \mathrm {~S} + 2900 \mathrm {~F} + 1860 \mathrm {~L} + 1700 \mathrm { D } + 0 \mathrm { E } > 1860$
6) $95 \mathrm {~S} + 92 \mathrm {~F} + 83 \mathrm {~L} + 94 \mathrm { D } + 0 \mathrm { E } > 83$
7) $83 \mathrm {~S} + 85 \mathrm {~F} + 90 \mathrm {~L} + 91 \mathrm { D } + 0 \mathrm { E } > 90$
OPTIMAL SOLUTION
Objective Function Value = 0.510 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { S } & 0.000 & 0.385 \\\text { F } & 0.167 & 0.000 \\\text { L } & 0.000 & 0.490 \\\text { D } & 0.833 & 0.000 \\\text { E } & 0.510 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 1.365 \\2 & 2.208 & 0.000 \\3 & 474.479 & 0.000 \\4 & 0.000 & 0.031 \\5 & 40.000 & 0.000 \\6 & 10.667 & 0.000 \\7 & 0.000 & - 0.021\end{array}$$
a.Is the Lewiston plant efficient? Why or why not? If not, which plants should it emulate in order to improve?
b.How much more production does the composite facility provide than the Lewiston site?
c.What is the quality rating for the composite facility?

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Definitions:

Numbness of Extremities

A lack of sensation or feeling in the limbs, such as the hands or feet, often indicative of nerve damage or circulation issues.

Fainting

A sudden, temporary loss of consciousness, often due to a decrease in blood flow to the brain.

Limited Function

Refers to a condition or situation where the capabilities or actions of a system, organ, or individual are restricted.

Fetus Size

A measurement that refers to the dimensions or growth development of a fetus during pregnancy, typically assessed via ultrasound.