168 Supply Chain Management and Logistics
x
jm
jM
o
=
∈
1 (6.34)
xx
ij
jM
ji
jM∈∈
−=∀∈
(6.35)
bHBx
ij
jM
∈
∈
min{ ,} , (6.36)
i
iM
≤
(6.37)
x
ij
∈ {0,1}, b
i
≥ 0 ∀i, j ∈ M. (6.38)
Here, we assume α
ot
= β
ot
= 0 for the consistency. The objective function in
Equation 6.32 minimizes the reduced cost of the schedule. The constraints
in Equations 6.33 through 6.35 are the ow balance constraints for the route.
The constraints in Equation 6.36 ensure the delivered inventory b
i
can be
positive only if customer i is visited. The constraints in Equation 6.37 are
the capacity constraints. Although the objective function in Equation 6.32 is
quadratic, it can be linearized as follows:
min( )
,
cx b
ij it ij it it i
iMij M
−− +
∈∈
γ
(6.39)
Here, we p ...