On the Optimal Inventory Equation

Richard Bellman · Irving Glicksberg · Oliver Gross

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Supply Chain and Inventory Management Management and Optimization Techniques Optimization and Search Problems

Abstract

The purpose of this paper is to discuss a number of functional equations which arise in the “optimal inventory” problem. This is a particular case of the general problem of ordering in the face of an uncertain future demand. Actually, an important aspect of the problem is that of determining a suitable criterion of cost, one which is both realistic and analytically malleable.

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1958The Theory of Inventory Management

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2008Inventory Models for Substitutable Products: Optimal Policies and Heuristics 1965The Optimal Inventory Policy for Batch Ordering 1981Myopic Solutions of Markov Decision Processes and Stochastic Games 2005Integrating direct and indirect sales channels under decentralized decision-making 2016Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times 1969Bounds on the Solution of the Lagged Optimal Inventory Equation with No Demand Backlogging and Proportional Costs 1965An Empirical Study of Exactly and Approximately Optimal Inventory Policies 1977Optimal Inventories for an (S − 1, S) System with No Backorders

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