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Article

A MATHEMATICAL METHOD FOR OPTIMAL INVENTORY POLICIES WITH BACKLOG SALES

DOI: 10.7708/ijtte.2021.11(2).11


11 / 2 / 323-340 Pages

Author(s)

Md Abu Helal - Southern Arkansas University – Magnolia, Arkansas, USA -

Alain Bensoussan - The University of Texas at Dallas – Richardson, Texas, USA -

Viswanath Ramakrishna - The University of Texas at Dallas – Richardson, Texas, USA -

Suresh P. Sethi - The University of Texas at Dallas – Richardson, Texas, USA -


Abstract

This article is concerned with stochastic inventory control problems with backlog sales in stock-out situations. We examine an infinite horizon model for piecewise linear concave ordering costs. Unlike finite horizons, however, infinite horizons lead to a functional equation for the value function. Such functional equations are solved numerically. Here we give a rigorous theory which explicitly solves this functional equation. We consider both the scenario in which an optimal selection can be made among two suppliers, as well as the scenario in which inventory can be purchased with incremental quantity discounts from a single supplier. We provide conditions that guarantee the optimality of standard (s,S) policy. Moreover, when these conditions fail to hold, we show that an extended four parameter policy is optimal.


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