The combination of inventory management and vehicle routing decisions yields a difficult combinatorial optimization problem called the Inventory-Routing Problem (IRP). This problem arises when both types of decisions must be taken jointly, which is the case in vendor-managed inventory systems. The IRP has received significant attention in recent years. Several heuristic and exact algorithms are...

Generally ordering policies are done by two methods, including fix order quantity (FOQ) and fix order period (FOP). These methods are static and either the quantity of ordering or the procedure of ordering is fixing in throughout time horizon. In real environments, demand is varying in any period and may be considered as uncertainty. When demand is variable in any period, the traditional and st...

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...

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...