Managing supply delays with advance orders and contingent expediting in a single-period inventory model

Abstract

We study a single-period newsvendor with an advance order from a low-cost supplier with random lead time and a contingent backup order from a reliable, costlier source placed at time τ < T if needed. The resulting two-stage problem is concave and admits simple critical-fractile/threshold policies driven by conditional delivery probabilities. We characterize when to use only the reliable source, only the unreliable source, or both. We further analyze the effect of the backup-order timing, giving monotonicity conditions and identifying when the initial and backup orders can be non-monotone, with numerical examples for illustration.