4.5 Flexible Bay Structure
71
Fig. 4.7 Facility layout with
flexible bays: the width of
each bay (column) depends
on the assigned departments
1
2
3
4
5
6
7
8
9
11
advantages in practice. In particular, the bay boundaries form the basis of an aisle
structure that facilitates the transfer of the layout solution to an actual facility design.
We let the continuous variables x i , y i represent the location of department i, and
we define h ik to be the height of department i in bay k. Let K be the (given) set of
bays. The binary variables are defined as follows:
z ik =
1, if department i is assigned to bay k
0, otherwise;
α ij =
1, if department i is above department j in the same bay
0, otherwise;
δ k =
1, if bay k is occupied
0, otherwise.
A MILO model to optimize the flexible bay layout is as follows:
minimize
1≤i c ij (d
x
ij + d
y
ij )
s.t. d
x
ij ≥ x i − x j , d
x
ij ≥ x j − x i , 1 ≤ i < j ≤ n,
d
y
ij ≥ y i − y j , d
y
ij ≥ y j − y i , 1 ≤ i < j ≤ n,
k∈K
z ik = 1, 1 ≤ i ≤ n,
(4.35)
w k =
1
h F
n
i=1
z ik A i , k ∈ K,
(4.36)
w
min
i z ik ≤ w k ≤ w
max
i
+ w F (1 − z ik ), 1 ≤ i ≤ n, k ∈ K
(4.37)
x i ≥
j ≤k w j −
1
2 w k − (w F − w min
i )(1 − z ik ), 1 ≤ i ≤ n, k ∈ K,
x i ≤
j ≤k w j −
1
2 w k + (w F − w min
i )(1 − z ik ), 1 ≤ i ≤ n, k ∈ K,
(4.38)