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
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 triple with an optimal
threshold strategy, present an algorithm for constructing optimal thresholds and the optimal value
of the functional, and discuss issues of uniqueness.
Keywords and phrases:inventory model, Markov chain, optimality equation, canonical triplet.
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