Example $5$: Machine Layout Problem $($Week $11)$

Four equal$-$sized $(1616)$ machines are grouped into a manufacturing cell in a linear single$-$row layout.

Assume the clearance between each pair of machines is $6.$ The material handling device is a two$-$way

shuttle cart system. The pickup and delivery location for each machine is at the midpoint along the

edge of the machine parallel to the aisle. The material flow information is given in the below from$-$to

a$)$ Determine the sequence of machines that will minimize the cost of loaded travel distance.

b$)$ What is the minimum cost?