{
  "abstract": "Single-machine asymmetric weighted earliness--tardiness (AWET) scheduling asks how to sequence jobs around a common synchronization date when early and late completion incur unrelated job-dependent penalties. At the boundary nonrestrictive date $d=\\sum_jp_j$, a compact V-shaped schedule reduces the continuous-time problem to a quadratic choice of a nonempty early set. We establish four complementary results for this model. First, the positive-integer problem is strongly NP-complete by a unary-polynomial reduction from Restricted Exact Cover by 3-Sets. Second, unrestricted AWET admits a polynomial-time $(3+2\\sqrt2+\\varepsilon)$-approximation based on an anchored semidefinite relaxation and deterministic marginal thresholding. Third, when the earliness and tardiness ratio orders are strict reversals, the problem is weakly NP-complete but has an exact two-resource pseudopolynomial dynamic program. Fourth, for fixed total refinements whose ratio permutation is separable, an exact separating-tree recurrence and coordinated geometric trimming yield an FPTAS. The proofs use different manifestations of the same canonical objective: scale-separated prefix penalties, positive-semidefinite minimum-kernel covariance, a dominant completed load square, and a bounded four-coordinate decomposition interface. Together, the results show that the decisive issue is not merely whether the two ratio orders agree, but whether their interaction can be controlled by a global certificate or compressed into a bounded constructive interface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16046",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicholas G. Hall"
    },
    {
      "name": "Hans Kellerer"
    },
    {
      "name": "Miao Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cyrszqp5s6bk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16046",
  "fulltext_url": null,
  "id": "1cyrszqp5s6bk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16046",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2209|Scheduling and Optimization Algorithms"
    ]
  ],
  "openalex": "W7213392643",
  "pdf_url": "https://arxiv.org/pdf/2609.16046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cyrszqp5s6bk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Asymmetric Weighted Earliness-Tardiness: Scheduling with a Nonrestrictive Common Due Date",
  "title_text": "Asymmetric Weighted Earliness-Tardiness: Scheduling with a Nonrestrictive Common Due Date",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/1cyrszqp5s6bk",
  "venue": "arXiv",
  "versions": []
}