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The squared coefficient of variation of inter-arrival time to the material-handling system,
Cat2, can be approximated as follows [3][4]:
M
λ  2
2
Ca t = ∑  it Cdit ,
i =1  λt 
(11)
where Cdit2 is the square coefficient of the inter-arrival time from department i to the materialhandling system and is given by:
Cdit =
2
λit
λ
2
C di + 1 − it
λi
λi
i = 1,.., M .
(12)
The squared coefficients of variation of inter-arrival time, Cai2, and external inter-arrival time,
Caout,i2, to department i can be obtained as follows:
λout ,iCaout ,i + λti Cati
2
Cai =
2
2
i = 1,.., M
λi
,
(13)
where
Caout ,i
2




D j R j1i  2

=∑ N
C

 j
j =1
 ∑ Dl Rl1i 
 l =1

N
i = 1,.., M .
(14)
The squared coefficients of variation of inter-departure time at department i and at the materialhandling system are approximated as follows [3][4]:
Cd t = 1 + (1 − ρt )(Ca t − 1) +
2
2
2
ρt
2
(Cst − 1) ,
mt
2
(15)
and
Cdi = 1 + (1 − ρ i )(Cai
2
2
ρ
2
− 1) + i (Csi − 1) i = 1,.., M .
mi
2
2
(16)
The squared coefficient of variation of inter-departure time from the material-handling system to
department i, Cati2, can be approximated as follows [3][4]:
Cati = pi Cdt + 1 − pi
2
2
where pi is given by:
30
i = 1,.., M ,
(17)