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-Hours

The total hours worked by employees directly involved in manufacturing a product, often used as a basis for allocating costs.

Traditional Costing

An accounting method that allocates overhead costs to products based on a predetermined overhead rate and the volume of goods produced.

Overhead Assigned

Refers to the allocation of indirect costs to products, services, or cost centers.

Product U4

Product U4 is a designated name for a specific product, possibly indicating its position or type within a wider range of products offered by a company or manufacturer.