Sonin’s inventory model with a long-run average cost functional

Abstract

We present an inventory model where a manufacturer (firm) uses for “production” a “commodity” (resource), which is consumed with the unit intensity. The price of the commodity follows a stochastic process, modelled by a continuous-time Markov chain with a finite number of states and known transition rates. The firm can buy this commodity at the current price or use a “stored” one. The storage cost is proportional to the storage level. The goal of the firm is to minimize the long-run average cost functional.

We prove the existence of a canonical triplet with an optimal threshold strategy, present an algorithm for constructing optimal thresholds and the optimal value of the functional, and discuss issues of uniqueness.