{
  "abstract": "We provide a uniform guarantee for a continuous-review lost-sales inventory system with unit Poisson demand, deterministic lead time, and fixed ordering costs: a simple algorithm computes an $(r,Q)$ policy and chooses between that policy and no replenishment, with cost at most $(\\sqrt2+\\sqrt6)/2<1.932$ times the unrestricted nonanticipative optimum. The algorithm starts by generating an optimal integer base-stock policy, which at zero setup cost achieves the tight worst-case factor $\\sqrt2$ relative to the optimal system cost. For positive setup costs, it uses the reorder point of this integer base-stock policy and an integer lot at the economic order quantity scale. The inclusion of ordinary base stock in the continuous-review capped base-stock family also improves that family's earlier asymptotic $1.79$ upper guarantee to a uniform $\\sqrt2$ guarantee valid at every finite parameter vector. To establish these guarantees, we construct a computable lower bound on the zero-setup optimal cost by tracking units already on hand or committed for delivery. We then combine it with a bound on holding and setup costs required by batching to obtain the general-setup guarantee and instance-specific performance bounds for any admissible replenishment policy. In our numerical study, the largest estimated policy-cost-to-lower-bound ratios are about $1.59$ for our heuristic $(r, Q)$ policy and $1.47$ after joint optimization of $r$ and $Q$. The heuristic also performs well against the optimized policy: over the sampled instances, its median extra cost ranges from $2.33\\%$ to $3.91\\%$, depending on the setup cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34576",
  "author_total": 1,
  "authors": [
    {
      "name": "Ming Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpf0h2q01n09g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34576",
  "fulltext_url": null,
  "id": "fpf0h2q01n09g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34576",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.34576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fpf0h2q01n09g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34576"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A 1.932 Guarantee for (r,Q) Policies in Continuous-Review Lost-Sales Inventory Systems",
  "title_text": "A 1.932 Guarantee for (r,Q) Policies in Continuous-Review Lost-Sales Inventory Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fpf0h2q01n09g",
  "venue": "arXiv",
  "versions": []
}