  We study problems that integrate depot location decisions along with the
inventory routing problem of serving clients from these depots over time
balancing the costs of routing vehicles from the depots with the holding costs
of demand delivered before they are due. Since the inventory routing problem is
already complex, we study the version that assumes that the daily vehicle
routes are direct connections from the depot thus forming stars as solutions,
and call this problem the Star Inventory Routing Problem with Facility Location
(SIRPFL). As a stepping stone to solving SIRPFL, we first study the Inventory
Access Problem (IAP), which is the single depot, single client special case of
IRP. The Uncapacitated IAP is known to have a polynomial time dynamic program.
We provide an NP-hardness reduction for Capacitated IAP where each demand
cannot be split among different trips. We give a $3$-approximation for the case
when demands can be split and a $6$-approximation for the unsplittable case.
For Uncapacitated SIRPFL, we provide a $12$-approximation by rounding an LP
relaxation. Combining the ideas from Capacitated IAP and Uncapacitated SIRPFL,
we obtain a $24$-approximation for Capacitated Splittable SIRPFL and a
$48$-approximation for the most general version, the Capacitated Unsplittable
SIRPFL.
