Constrained optimal impulse control and inventory model

TL;DR

This paper develops a mathematical framework for impulsive control in inventory systems, reformulating the problem as a Markov decision process and analyzing the duality and solvability of associated optimization programs.

Contribution

It introduces a novel approach to impulsive control problems with constraints by formulating them as convex programs in occupation measure space, with applications to inventory models.

Findings

Reformulation of impulsive control as a Markov decision process

Development of primal and dual linear programs in occupation measure space

Application to an inventory model demonstrating the theory

Abstract

In this article, we consider the deterministic impulsively controlled system with infinite horizon and several discounted objective functionals. The constructed optimal control problem with functional constraints is reformulated as a Markov decision process, leading to (primal) convex and linear programs in the space of so-called occupation measures. We construct the dual programs and investigate the solvability of all the programs. Example of an inventory model illustrates the developed theory.