On the inventory model with continuous and discrete lead time, backorders and lost sales

A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time

We consider a perishable inventory system that operates under stochastic demand, constant lifetime and a constant lead time. The system employs a continuous review ðr;Q Þ inventory control policy where unfilled demands are lost. We investigate the properties of the cost function and present an approximation procedure to find the parameters r and Q that minimize the total cost. We then conduct a...

Optimal Control of a Production-Inventory System with both Backorders and Lost Sales

We consider the optimal control of a production inventory-system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether...

Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales

An Inventory Allocation System with Backorders and Sales Rejection

We consider a variant of the periodic review system with a virtual warehouse that is due to Eppen and Schrage (1981). Depending on the realized pattern of demand during the delivery leadtime, this inventory is dynamically allocated or rationed to each of the retailers. While Eppen and Schrage (1981) assume that all unfilled demand is backordered, we allow some demand to be rejected to keep inve...

Supply interruptions in a lost-sales inventory system with random lead time

This paper presents an analytical model for computing the stationary distribution of the on-hand inventory in a continuous-review inventory system with compound Poisson demand, Erlang distributed lead time, and lost sales, where the supplier can assume one of the two “available” and “unavailable” states at any point in time according to a continuous-time Markov chain. Exact analytical expressio...