Inventory Control with Modulated Demand and a Partially Observed Modulation Process

Abstract

We consider a periodic review inventory control problem having an underlying modulation process that affects demand and that is partially observed by the uncensored demand process and a novel additional observation data (AOD) process. Letting K be the reorder cost, we present a condition, A1, which is a generalization of the Veinott attainability assumption, that guarantees the existence of an optimal myopic base stock policy if K = 0 and the existence of an optimal (s, S) policy if K > 0, where both policies depend on the belief function of the modulation process. Assuming A1 holds, we show that (i) when K = 0, the value of the optimal base stock level is constant within regions of the belief space and that these regions can be described by a finite set of linear inequalities and (ii) when K > 0, the values of s and S and upper and lower bounds on these values are constant within regions of the belief space and that these regions can be described by a finite set of linear inequalities. Computational procedures for K ≥ 0 are outlined, and results for the K = 0 case are presented when A1 does not hold. Special cases of this inventory control problem include problems considered in the Markov-modulated demand and Bayesian updating literatures.

Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information

“…They characterize the optimal policy structure in both cases of backlogging and lost sales. Malladi et al (2019) consider discrete-time inventory systems with finite demand, full backlogging, zero lead time, fixed and linear variable ordering costs. The demand state is partially revealed via an observation process that contains the past demand data.…”

“…Only a few researchers have considered Markovmodulated demand under partial information about the demand state. These researchers have focused only on finite-horizon total-cost and infinite-horizon discounted-cost inventory systems with bounded or Poisson demand (Bayraktar and Ludkovski 2010, Malladi et al 2019, Treharne and Sox 2002. To our knowledge, in the literature dealing with Markovmodulated demand and partial information, no one has studied the infinite-horizon average-cost inventory systems.…”