The Output Shows the Solution to a DEA Model Where

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
0S+0F+0L+0D+1E
S.T.
1) 1S+1F+1L+1D=1
2) 5S+22F+36L+15D-36E<0
3) 400S+1500F+3150L+1060D-3150E<0
4) 24S+13F+32L+17D-32E<0
5) 800S+2900F+1860L+1700D+0E>1860
6) 95S+92F+83L+94D+0E>83
7) 83S+85F+90L+91D+0E>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:

Capital Balances

The amount of equity each partner or shareholder has in an enterprise, often represented as their ownership stake.