Year: 2025
Type: preprint
Abstract: This study considers a continuous-review inventory model for a single item with two replenishment modes. Replenishments may occur continuously at any time with a higher unit cost, or at discrete times governed by Poisson arrivals with a lower cost. From a practical standpoint, the model represents an inventory system with random deal offerings. Demand is modeled by a spectrally positive Lévy process (i.e., a Lévy process with only positive jumps), which greatly generalizes existing studies. Replenishment quantities are continuous and backorders are allowed, while lead times, perishability, and lost sales are excluded. Using fluctuation theory for spectrally one-sided Lévy processes, the optimality of a hybrid barrier policy incorporating both kinds of replenishments is established, and a semi-explicit expression for the associated value function is computed. Numerical analysis is provided to support the optimality result.
Source: arXiv (Cornell University)
Authors: Pérez, José Luis, Yamazaki, Kazutoshi, Zhang, Qingyuan
Institution: The University of Queensland
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: green
Funder: Arizona State University
OpenAlex ID: W7103144176
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