Optimal Inventory Management in a Fluctuating Market

In the highly competitive environment in which companies operate today, it is crucial that the supporting processes such as inventory management are as efficient as possible. In particular, a trade-off between inventory costs and service levels needs to be assessed. In this paper, we determine an optimal batch ordering policy accounting for both demand and market price fluctuations such that the long-term discounted cost is minimised. This means that future costs are reduced by a constant factor as we need to take inflation and other factors into account. To this end, the inventory system is modelled as a Markovian queueing system with finite capacity in a random environment. Assuming phase-type distributed lead times, Markovian demand and price fluctuations, the optimal ordering strategy is determined by a Markov decision process (MDP) approach. To illustrate our results, we analyse the ordering policy under several price fluctuation scenarios by some numerical examples.

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