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)