A Firm of Six Departments Has the Following Trip Matrix

question 164

Essay

A firm of six departments has the following trip matrix and current block plan of all departments:
$$\begin{array} { | c | c | c | c | c | c | c | } \hline \begin{array} { c } \text { Dept. } \\\text { Name }\end{array} & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } \\\hline \mathrm { A } & - - & 7 & 8 & 9 & 0 & 2 \\\hline \mathrm { B } & & - - & 6 & 3 & 0 & 10 \\\hline \mathrm { C } & & & - - & 2 & 12 & 0 \\\hline \mathrm { D } & & & & - & 3 & 0 \\\hline \mathrm { E } & & & & & - & 6 \\\hline \mathrm { F } & & & & & & - \\\hline\end{array}$$
$$\begin{array} { | l | l | l | } \hline \mathrm { A } & \mathrm { B } & \mathrm { C } \\\hline \mathrm { D } & \mathrm { E } & \mathrm { F } \\\hline\end{array}$$
a.What is the load-distance score for the current layout? (Assume rectilinear distance and that the distance between departments A and B is one unit of distance.)
b.What would be the load-distance score for the following layout?
$$\begin{array} { | l | l | l | } \hline \mathrm { A } & \mathrm { C } & \mathrm { E } \\\hline \mathrm { D } & \mathrm { B } & \mathrm { F } \\\hline\end{array}$$

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Definitions:

Pyridine

A basic heterocyclic organic compound with the formula C5H5N, featuring a ring structure similar to benzene but with one methine group (\(CH\)) replaced by a nitrogen atom.

Aromatic

Compounds that contain a planar ring of atoms that are stabilized by a delocalization of pi electrons according to Huckel's rule.

Antiaromatic

Antiaromatic compounds are cyclic, planar molecules that possess 4n π electrons (where n is an integer) and are destabilized due to their electronic structure, contradicting the stability seen in aromatic compounds.

Aromatic

Pertains to organic compounds that contain one or more planar rings of atoms with a degree of stability and special electronic structures.