W to begin? I became involved with inventory theory in 1955, but the proper starting point for this memoir is some years earlier, in the fall of 1951, when I began my graduate training in the Department of Mathematics at Princeton University. I had lived at home during my undergraduate years at Temple University and was totally unprepared for the remarkable features of life at Princeton in the ...

Abstract: In today’s world the financial decisions of any business/retail enterprise are very crucial, as from the financial standpoint, an inventory i.e., stock on display represents a capital investment and must compete with other assets for a firm’s limited capital funds. Moreover, rising inflation rate directly affects the financial situation of an organization. On the contrary, the today’s...

This paper deals with the question of optimal inventory sizes in a compétitive environment in which the demand for a product at a vendor dépends on the inventory level of the product at that vendor relative to the inventories of the same product held by other competing vendors. The total demand for the product at all vendors is assumed to be fixed. This question is examined for two different re...

Consider a multiple booking class airline-seat inventory control problem that relates to either a single flight leg or to multiple flight legs. During the time before the flight, the airline may face the problems of (1) what are the suitable prices for the opened booking classes, and (2) when to close those opened booking classes. This work deals with these two problems by only using the pricin...

We consider the joint pricing and inventory control problem for a single product with a finite horizon and periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show t...

Solving Robust Inventory Problems In this work we consider setting the optimal inventory control policies for a single buffer when demand is uncertain, in a robust framework. Unlike traditional inventory models we do not assume that the demand is random with a known distribution. Instead, demand can take values from a given uncertainty set. Our objective is to find the policy that minimize the ...

This paper considers inventory models with advance demand information and flexible delivery. Customers place their orders in advance, and delivery is flexible in the sense that early shipment is allowed. Specifically, an order placed at time t by a customer with demand leadtime T should be fulfilled by period t+T ; failure to fulfill it within the time window [t, t+T ] is penalized. We consider...

The common belief is that using Reinforcement Learning methods (RL) with bootstrapping gives better results than without. However, inclusion of bootstrapping increases the complexity of the RL implementation and requires significant effort. This study investigates whether inclusion of bootstrapping is worth the effort when applying RL to inventory problems. Specifically, we investigate bootstra...

We consider the periodic review inventory control problem in which the purchasing cost of the product changes, in a Markovian fashion, from one period to the next. After establishing (with and without the non-speculation assumption) that an order upto policy is optimal, we develop an efficient recursive solution procedure to compute the optimal levels. In addition, we propose a measure for the ...