The equilibrium equations for the lost sales (r,q) policy with inventory level dependent demand and multiple outstanding orders

2012/06/11 by Bryan Johnston, Johnston, Bryan
Business, Management and Accounting · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Supply Chain and Inventory Management #math.OC

paper · pdf · doi:10.48550/arxiv.1206.2291

openalex publication_date 2012/06/11 · arxiv created 2013/09/28 · arxiv updated 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the equilibrium equations for the a model generalizing the continuous review (r, q) lost-sales model with constant lead time, multiple outstanding orders and unit Poisson demand. Demand rate is allowed to depend on inventory level. The model is solved for the case r=2,q=2 as well as the general case q=1. An application is given for a system involving lateral transshipments.

Related

• Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes
• Fixed non-stockout-probability policies for the single-item lost-sales model
• Asymptotic Optimality of Projected Inventory Level Policies for Lost Sales Inventory Systems with Large Leadtime and Penalty Cost
• Bounds on performance measures for the (r, q) lost sales system with Poisson demand and constant lead time
• An Inventory System with Two Supply Modes and Lévy Demand