A Risk-Averse Inventory Model with Markovian Purchasing Costs

Abstract

We study a few dynamic risk-averse inventory models using additive utility functions. We add Markovian behavior of purchasing costs in our models. Such Markovian purchasing costs can reflect a market situation in a global supply chain such as fluctuations at exchange rates or the existence of product spot markets. We provide our problem formulations with finite and infinite MDP (Markovian Decision Process) problems. For finite time models, we first prove (joint) concavity of the model for each state and obtain a (modified) base-stock optimal policy. Then, we conduct comparative static analysis for model parameters and derive monotone properties to the optimal solutions. For infinite time models, we show the existence of stationary base-stock optimal policies and the inheritance of the monotone properties proven at our finite time models.