Question $1[12$ points$]$

a$.[5$ points$]$ Consider the following layout given below. It is assumed that each pair of

machines $($labeled by blue circle$)$ are adjacent if they are located on the same line segment

according to the following definition:

xij $=\{$

$1,$ if both i and j are located on the same line segment

$0,$ otherwise

If the flow system is balanced with a flow amount of $5$ units $($i$.$e$.,$ fij $=5,$i and $$j$)$

calculate the adjacency score for the layout.

b$.[2$ points$]$ What is the ideal layout for the machines arrangement given in part$($a$)?$

c$.[5$ points $]$Consider the following layout and the flow matrix assuming each small box in

the layout is of size $1$m x $1$m$.$ The thick lines indicates the boundary of the departments.

A B C D E F G H

A $030010503$

B $40310002\mathrm{.}5$

C $02050050$

D $00504200$

E $80300020$

F $04005010$

G $00630003$

H $02\mathrm{.}5000600$

The associated assumptions with the above layout are:

i$.$ Traveling from departments A to E $($or E to A$)$ is infeasible.

ii$.$ There is a directed flow $($one way only$)$ from department C to department G$.$

iii. The movement factor between departments D and F is $2.$

iv$.$ The movement factor between departments B and H is $3.$

If the cost of moving a unit load one distance unit among all the departments is equal to $1,$

calculate the total flow distance in terms of distance based criterion.