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

question 54

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.
OPTIMAL SOLUTION
Objective Function Value = 0.510
$$\text { Min } 0 \mathrm {~S} + 0 \mathrm {~F} + 0 \mathrm {~L} + 0 \mathrm { D } + 1 \mathrm { E }$$
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) $83 \mathrm {~S} + 85 \mathrm {~F} + 90 \mathrm {~L} + 91 \mathrm { D } + 0 \mathrm { E } > 90$ $$\begin{array} { l l l } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { S } & 0.000 & 0.385 \\\text { F } & 0.167 & 0.000 \\\text { L } & 0.000 & 0.490 \\\text { D } & 0.833 & 0.000 \\\text { E } & 0.510 & 0.000\end{array}$$ $$\begin{array} { l l l } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 1.365 \\2 & 2.208 & 0.000 \\3 & 474.479 & 0.000 \\4 & 0.000 & 0.031 \\5 & 40.000 & 0.000 \\6 & 10.667 & 0.000 \\7 & 0.000 & - 0.021\end{array}$$
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:

Direct Labor Cost

The total expense that a company incurs for the labor directly involved in the manufacture of a product.

Work in Process

Goods partially completed during the manufacturing process; they are not yet finished products.

Manufacturing Overhead

Indirect costs related to manufacturing that are not directly tied to a specific product, including costs like factory rent, utilities, and maintenance.

Direct Labor Costs

Expenses associated with the labor directly involved in producing a product or delivering a service.