Managing Inventories of
Perishables: The Effect of Substitution
by
Itir Z. Karaesmen-Aydin
University of Maryland
In this talk, we will introduce a discrete-time model for a supplier managing
inventories of perishable goods. Inventory control of perishables remains a
well-studied problem; earlier results date back to 1960s. The novel features of
our model are that (i) there are separate demand streams for items of different
ages and (ii) goods of different ages may be substitutable. We study the
supplier's problem for replenishing the goods and fulfilling the demand. We
propose
two practical replenishment policies: replenishing inventory according to
order-up-to level policies based on either (i) total inventory in system or (ii)
new itemsin stock. We concentrate on four different ways of fulfilling demand: (1) demand
for an item can only be satisfied by an item of that age (No-Substitution);
(2) demand for new items can only be satisfied by new ones, but excess demand
for old items can be satisfied by new (Downward-Substitution); (3) demand
for old items can only be satisfied by old, but excess demand for new items can
be satisfied by old (Upward-Substitution); (4) both downward and upward
substitution are employed (Full-Substitution). The main research question here
is not which form of substitution is best for the supplier, but whether a
supplier
that can practice one or more forms of substitution would indeed benefit from
that. To answer this, we compare the four substitution options analytically in
terms of the infinite horizon expected costs and provide conditions on cost
parameters that determine when (if at all) one substitution option is more
profitable
than the others. We also prove that inventory is "fresher" whenever downward
substitution is employed. Our results are based on sample-path analysis, and
as such we make no assumptions on demand. We complement our results with
numerical experiments exploring the effect of problem parameters on performance.
(joint work with Borga Deniz and Alan Scheller-Wolf of Carnegie Mellon
University)