{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DNPZKSYFLFJJAKDEEV722CWQW4","short_pith_number":"pith:DNPZKSYF","schema_version":"1.0","canonical_sha256":"1b5f954b055952902864257fad0ad0b715476076f09658e413918d7d9b8fa9be","source":{"kind":"arxiv","id":"1611.08775","version":1},"attestation_state":"computed","paper":{"title":"Chance-Constrained Two-Stage Unit Commitment under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Zeng, Jianxue Wang, Yao Zhang, Zechun Hu","submitted_at":"2016-11-27T03:31:41Z","abstract_excerpt":"In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using McCormick linearization method. Then, we develop a bilinear variant of Benders decomposition method, wh"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.08775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-27T03:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"2ab4eef96b6d5c169f6bc80833fe39d86ed6a7a6f5d46ccdff6230d296ba6a8d","abstract_canon_sha256":"bc6d5d7fa5ab8b47a6dd0b570af29a30ee264b2113f28be2d226c9c6a0f935e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:36.813726Z","signature_b64":"kGQwjIuCovPJJ4kpmGH6KF6B/xbgJu6vZEiDyDxDj7/tXJBt8ldSaj2HVJuJpOfOX5/Wf7E8kw/yFRRCaAnTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b5f954b055952902864257fad0ad0b715476076f09658e413918d7d9b8fa9be","last_reissued_at":"2026-05-18T00:56:36.813119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:36.813119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chance-Constrained Two-Stage Unit Commitment under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Zeng, Jianxue Wang, Yao Zhang, Zechun Hu","submitted_at":"2016-11-27T03:31:41Z","abstract_excerpt":"In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using McCormick linearization method. Then, we develop a bilinear variant of Benders decomposition method, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08775","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.08775","created_at":"2026-05-18T00:56:36.813194+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08775v1","created_at":"2026-05-18T00:56:36.813194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08775","created_at":"2026-05-18T00:56:36.813194+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNPZKSYFLFJJ","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNPZKSYFLFJJAKDE","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNPZKSYF","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4","json":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4.json","graph_json":"https://pith.science/api/pith-number/DNPZKSYFLFJJAKDEEV722CWQW4/graph.json","events_json":"https://pith.science/api/pith-number/DNPZKSYFLFJJAKDEEV722CWQW4/events.json","paper":"https://pith.science/paper/DNPZKSYF"},"agent_actions":{"view_html":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4","download_json":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4.json","view_paper":"https://pith.science/paper/DNPZKSYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08775&json=true","fetch_graph":"https://pith.science/api/pith-number/DNPZKSYFLFJJAKDEEV722CWQW4/graph.json","fetch_events":"https://pith.science/api/pith-number/DNPZKSYFLFJJAKDEEV722CWQW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4/action/storage_attestation","attest_author":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4/action/author_attestation","sign_citation":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4/action/citation_signature","submit_replication":"https://pith.science/pith/DNPZKSYFLFJJAKDEEV722CWQW4/action/replication_record"}},"created_at":"2026-05-18T00:56:36.813194+00:00","updated_at":"2026-05-18T00:56:36.813194+00:00"}