Abstract
We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α|a), where \(\sum_{\alpha=0}^{a}P(\alpha|a)=1\). Let z=d−x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ ∗ is such that δ ∗(z)=0 for z≤0, δ ∗(z)≥z≥0, and δ ∗(z)−z is monotonically non-decreasing for z≥0. Such a “staircase” structure has a simple parametric description, which can help to accelerate value iteration and policy iteration.
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Cheong, T., White, C.C. Inventory replenishment control under supply uncertainty. Ann Oper Res 208, 581–592 (2013). https://doi.org/10.1007/s10479-011-0929-9
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DOI: https://doi.org/10.1007/s10479-011-0929-9