Download A Software for Facility Layout with Queueing

ρt=λtE(St)/mt. In order to account for this difference, expected flow time through the materialhandling system is calculated as follows:
 Ca 2 + C s 2
t
E ( Ft ) =  t

2

 (m ρ )mt P0 ρ
t t
 t t
 mt !(1 − ρ t )2

1 M M
 + ∑∑ pij (t depot ,i ( X ) + t ij ( X ) ).
λ
 t i =1 j =1
(74)
The two parameters, tije and tijf, are given by:
t ij = t depot ,i + t j ,depot
e
(75)
and,
t ij = t ij .
f
(76)
9.6 Layout Design Formulation
The previous performance measures can now be used to reformulate the layout design
problem so that operational performance measures other than the simple material handling cost
measure of the quadratic assignment problem (QAP) formulation are used.
Let us first restate the QAP formulation in terms of our notation. Given a layout
configuration X={xij}, the QAP can be formulated as follows:
Minimize
M
M
L
L
i
j
k
l
∑∑∑∑ x
ik
x jk λij d kl
(77a)
Subject to:
L
∑x
ik
= 1 i = 1,.., M
(77b)
= 1 k = 1,.., L
(77c)
k =1
M
∑x
ik
i
xik = 0,1 i = 1,.., M k = 1,.., L
(77d)
The objective function (73a) minimizes material handling cost by minimizing average distance
traveled by an arbitrary unit load of material. Since our model deals with discrete materialhandling devices, this QAP formulation also minimizes the average distance traveled by the
devices when they are full – i.e., while carrying a load. Constraints (73b) and (73c) ensure,
respectively, that each department is assigned one location and each location is assigned at most
one department. Since the QAP formulation ignores empty travel, a QAP-optimal layout is not
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