9/9/01 Inventory Theory Inventory Theory.S1 Inventory Models This chapter will consider several model types. Supplement 2 describes deterministic models. Even though many features of an inventory system involve uncertainty of some kind, it is common to assume much simpler deterministic models for which solutions are found using calculus. Deterministic models also provide a base on which to inco...

This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers’ inventories, and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation i...

In this paper we consider a stochastic multi item inventory problem. A retailer sells multiple products with stochastic demand and is replenished periodically from a supplier with ample stock. At each order instant it is decided which product to order and how much to order. For the delivery of the products trucks with a finite capacity are available. The dispatched trucks arrive at the retailer...

The practical experiences reveal that the Supply Chain Management (SCM) is under uncertain and variable conditions. One of the most important parts of SCM is inventory system management which is inherently in non-deterministic situation. The many departments of organization such as warehouse, marketing, sale, purchasing, financial, planning, production, maintenance and etc. are relevance to the...

We consider a production-inventory system where the production and demand follow Poisson processes whose rates are modulated by an external stochastic environment process. We study two such systems: with and without an external supplier, and show an interesting stochastic decomposition relationship between the steady state distribution of inventory levels in these two systems. We consider the o...

In this paper, we consider a dynamic stochastic inventory model with fixed inventory holding and shortage costs in addition to a fixed ordering cost. WE discuss a sufficient and necessary condition for an (s,S) policy to be optimal in the class of such stochastic inventory models. Furthermore, we explore how such a sufficient and necessary condition can be rewritten when the demand distribution...

In this project, we formulate a Stochastic optimization framework to manage the risk from input uncertainty in inventory management. In the classical inventory management, the stochastic programming is used to find an optimal policy that optimizes the risk-neutral expected cost over a certain planning horizon [3], or the risk from the randomness of the demand [7]. However, to the best of our kn...

Abstract: It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control pro...

Copyright: © 2016 INFORMS Abstract. We propose and analyze robust optimization models of an inventory management problem, where cumulative purchase, inventory, and shortage costs over n periods are minimized for correlated nonidentically distributed demand. We assume that the means and covariance matrix of stochastic demand are known; the distributions are not needed. We derive closed-form orde...