
163A Schedule-Based Formulation fortheCyclic Inventory Routing Problem
T
B
d
T
B
i
i
i
≥
Totaldemandover
.EOF
These bounds can be extended to nonconstant demand and the condi-
tion B
i
≤ H can also be relaxed. To nd the bound on the minimum num-
ber of replenishments needed for any customer i, we rst need to construct
an inventory ow network G
i
(N
i
, E
i
) for each customer i ∈ M as shown in
Figure6.1.
Each node n ∈ N
i
is indexed by two more parameters t ∈ T and p, where
0 ≤ p ≤ B
i
and p is integer. Dene the set of nodes indexed by t as N
it
. There
are two types of arcs in the inventory ow network: consumption arcs and
replenish arc ...