22 Human Factors of a Global Society
PO
min
XYZQ
ij ijk
j
i
k
,,
===
001
(2.12)
ijk
k
K
i
n
=∀=
==
∑∑
10
(2.13)
ijk jik
i
n
i
n
==
∑∑
0
00
(2.14)
x
ojk
i
n
≤
=
∑
1
1
(2.15)
yy
ji ij j
i
n
i
n
−=∀≠
==
∑∑
10
0 (2.16)
zz
ij ji j
i
n
i
n
−=∀≠
==
∑∑
10
0 (2.17)
yzca
ij ij ijk
k
K
+≤
=
∑
1
(2.18)
ts
e
iik
a
i
(2.19)
tTMx t
ik
a
iij ijk jk
a
++−−≤τ
1 (2.20)
cx L
ij ijk
j
n
i
n
≤
==
∑∑
00
(2.21)
x
ijk
∈ {0,1}; y
ij
≥ 0; z
ij
≥ 0 (2.22)
where constraints 2.13 and 2.14 ensure customer visit specications, Equation 2.15 gives the limited
number of vehicles, Equations 2.16 and 2.17 are the ow conservation equations for pickup and
delivery demands, Equation 2.18 shows that demands will be transported using arcs included in the
solution, Equations 2.19 and 2.20 are the time-window constra