Stock-based threshold policies, which set prices only by remaining inventory, achieve computable multi-unit prophet-inequality guarantees (e.g., 0.6269 for K=2 and 0.6816 for K=3) in continuous time with nonhomogeneous Poisson arrivals.
We introduce the auxiliary states ˙a(t) =c(t),˙g 3(t) =D(t)· sX k=1 xk t +c(t)·H(t),˙g 4(t) =D(t)· sX k=1 xk t +H(t), with zero initial values
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Competitive Analysis of Stock-based Thresholds via Prophet Inequalities in Continuous Time
Stock-based threshold policies, which set prices only by remaining inventory, achieve computable multi-unit prophet-inequality guarantees (e.g., 0.6269 for K=2 and 0.6816 for K=3) in continuous time with nonhomogeneous Poisson arrivals.