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

TL;DR

This paper derives equilibrium equations for a generalized lost-sales inventory model with inventory-dependent demand, multiple outstanding orders, and specific (r,q) parameters, including an application to lateral transshipments.

Contribution

It extends the (r,q) lost-sales model to include inventory-dependent demand and multiple orders, providing solutions for specific cases and an application example.

Findings

Derived equilibrium equations for the generalized model.

Solved the case r=2, q=2 and q=1.

Applied the model to lateral transshipment systems.

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.