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Introduction
Distribution systems often contain a set of regional
warehouses, each of which stores a variety of items supplied by multiple
manufacturers in order to serve a regional population of customers. Effectively
managing the inventory of multiple items under limited warehouse storage
capacity is critical to ensure good customer service without incurring excessive
inventory holding costs. Each regional ware-house manager thus faces the
challenge of coordinating the inventory levels and deliveries of multiple items
in order to meet desired service levels while obeying warehouse
capacity limits. Suppliers to such regional warehouses must efficiently manage
the tradeoffs they face between inventory and transportation costs, which often
leads different suppliers to prefer different warehouse replenishment
frequencies. For example, manufacturers who supply items with a high
value-to-weight ratio typically find it more economic to send relatively
frequent shipments in small quantities, whereas those who supply items with a
low value-to-weight ratio often prefer to deliver large quantities less
frequently (Ballou, 1999). These different replenishment frequency preferences,
combined with varying degrees of demand uncertainty, further compound the
challenges the warehouse manager faces in effectively utilizing limited
warehouse capacity. To address the challenges faced by the warehouse manager,
this paper discusses new stochastic multi-item inventory models that account for
warehouse-capacity constraints and varying replenishment frequencies. We present
a set of effective heuristic methods to minimize warehouse inventory-related
costs under these warehouse capacity and replenishment frequency restrictions.
We assume throughout that the warehouse suppliers dictate delivery schedules
(and therefore replenishment intervals) to the warehousing firm. The warehouse
inventory manager does not therefore have the flexibility to alter suppliers'
delivery schedules, as would be the case when suppliers either possess a high
degree of relative channel power, or when suppliers face operational constraints
that prohibit changing replenishment schedules (e.g., when production cycles
must obey a particular minimum or maximum frequency and replenishment
frequencies are constrained by production-cycle frequencies).
Stochastic inventory models involving (production)
capacity-constrained periodic-review policies have attracted the attention of
many researchers. Evans (1967) was the first to consider this issue by modeling
periodic-review production and inventory systems with multiple products, random
demands and a finite planning horizon. He develops the form of the optimal
policy for multi-product control for such a system. Since then, much of the
literature has studied periodic-review, single-product systems with
production-capacity constraints. Florian and Klein (1971) and De Kok et al.
(1984) characterize the structure of the optimal solution to a multi-period,
single-item production model with a capacity constraint. Federgruen and Zipkin
(1986a, 1986b) show that a modified base-stock policy is optimal under both
discounted and average cost criteria and an infinite planning horizon. The
modified base-stock policy requires that, when initial stock is below a certain
critical number, we produce enough to bring the total stock up to that number,
or as close to it as possible, given the limited capacity; otherwise, we do not
produce. They also characterize the optimal policy by deriving expressions for
the expected costs of modified base-stock policies. Kapuscinski and Tayur (1998)
provide a simpler proof of optimality than Federgruen and Zipkin (1986a) for the
infinite-horizon discounted cost case, based on results from Bertsekas (1988).
Ciarallo et al. (1994) and Wang and Gerchak (1996a) analyze a production model
with variable capacity in a similar environment as Federgruen and Zipkin
(1986a). Wang and Gerchak (1996b) also incorporate variable capacity explicitly
into continuous-review models. |
