Aero Maintenance is a small aircraft engine maintenance facility located in Wichita, Kansas. Its new administrator, Ann Daniel, decides to improve material flow in the facility, using the process layout method she studied at Wichita State University. The current layout of Aero Maintenance's eight departments is shown in Figure $9\mathrm{.}14.$ The only physical restriction perceived by Daniel is the need to keep the entrance in its current location. All other departments can be moved to a different work area $($each $10$ feet square$)$ if layout analysis indicates a move would be beneficial. First, Daniel analyzes records to determine the number of material movements among departments in an average month. These data are shown in Figure $9\mathrm{.}15.$ Her objective, Daniel decides, is to lay out the departments so as to minimise the total movement $($distance traveled$)$ of material in the facility. She writes her objective as: Minimize material movement $=$

i$=1$

$8$

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j$=1$

$8$

$$

X

tg

$$

C

ij

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where X

ij

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$=$ number of material movements per month $($loads or trips$)$ moving from department i to department j C

ij

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$=$ distance in feet between departments i and j $($which$,$ in this case, is the equivalent of cost per load to move between departments$)$ Note that this is only a slight modification of the cost$-$objective equation shown earlier in the chapter. Daniel assumes that adjacent departments, such as entrance $($now in work area A$)$ and receiving $($now in work area B$),$ have a walking distance of $10$ feet. Diagonal departments are also considered adjacent and assigned a distance of $10$ feet. Nonadjacent departments, such as the entrance and parts $($now in area C

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$)$ or the entrance and inspection $($area G$)$ are $20$ feet apart, and nonadjacent rooms, such as entrance and metallurgy $($area D$),$ are $30$ feet apart. $($Hence$,10$ feet is considered $10$ units of cost$,20$ feet is $20$ units of cost$,$ and $30$ feet is $30$ units of cost$.)$ Given the above information, redesign Aero Maintenance's Figure $9\mathrm{.}15$ Number of Material Movernents $($Loads$)$ Between Departments in $1$ Month