Stability of equilibrium points of demand-inventory model with stock-dependent demand

Abstract

A model of demand and inventory of a product in one echelon of supply chain is considered. The model is formulated as a system of difference equations, in which every equilibrium point is nonhyperbolic. A positive invariant set of the system is constructed. An analysis of properties of equilibrium points of the system is based on the Lyapunov method or reducing it to the family of systems of difference equations with hyperbolic equilibrium points.

Keywords:

• Demand-inventory model
• system of difference equations
• stability
• Lyapunov method

AMS Subject Classifications:

• 39A30
• 39A60

Acknowledgements

The authors are very grateful to the anonymous referee who has made many constructive comments that have helped to improve the results of the paper. We are also grateful to Bogdan Przeradzki for his helpful discussions.

Notes

No potential conflict of interest was reported by the authors.