{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BXTF7IFKJEHUCDPPREEHUOP7GN","short_pith_number":"pith:BXTF7IFK","schema_version":"1.0","canonical_sha256":"0de65fa0aa490f410def89087a39ff3340d1642ab01645f7def5237af7ed2903","source":{"kind":"arxiv","id":"1110.6572","version":1},"attestation_state":"computed","paper":{"title":"Optimal Control of Brownian Inventory Models with Convex Inventory Cost: Discounted Cost Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Dacheng Yao, Jim Dai","submitted_at":"2011-10-30T01:45:50Z","abstract_excerpt":"We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a th"},"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":"1110.6572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-30T01:45:50Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"53701ac1b8b0944c0e87c202b376741fb790578f7d843c67ded11ba83b1b64d6","abstract_canon_sha256":"066dd41f37c53895e9859dffe68878d4b9d08d87a371f56ef0b889b34bf1a2e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:54.692888Z","signature_b64":"efw7tvQTwEbfUkFfre0dZ6+EX/hLMLD9s/JGQ/2EEt/CNBtiaaPpcHGHGV9XAcqCDn8oK13YW+iPqV3FPzzGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de65fa0aa490f410def89087a39ff3340d1642ab01645f7def5237af7ed2903","last_reissued_at":"2026-05-18T03:01:54.692489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:54.692489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Control of Brownian Inventory Models with Convex Inventory Cost: Discounted Cost Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Dacheng Yao, Jim Dai","submitted_at":"2011-10-30T01:45:50Z","abstract_excerpt":"We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6572","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":"1110.6572","created_at":"2026-05-18T03:01:54.692551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6572v1","created_at":"2026-05-18T03:01:54.692551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6572","created_at":"2026-05-18T03:01:54.692551+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXTF7IFKJEHU","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXTF7IFKJEHUCDPP","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXTF7IFK","created_at":"2026-05-18T12:26:24.575870+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/BXTF7IFKJEHUCDPPREEHUOP7GN","json":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN.json","graph_json":"https://pith.science/api/pith-number/BXTF7IFKJEHUCDPPREEHUOP7GN/graph.json","events_json":"https://pith.science/api/pith-number/BXTF7IFKJEHUCDPPREEHUOP7GN/events.json","paper":"https://pith.science/paper/BXTF7IFK"},"agent_actions":{"view_html":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN","download_json":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN.json","view_paper":"https://pith.science/paper/BXTF7IFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6572&json=true","fetch_graph":"https://pith.science/api/pith-number/BXTF7IFKJEHUCDPPREEHUOP7GN/graph.json","fetch_events":"https://pith.science/api/pith-number/BXTF7IFKJEHUCDPPREEHUOP7GN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN/action/storage_attestation","attest_author":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN/action/author_attestation","sign_citation":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN/action/citation_signature","submit_replication":"https://pith.science/pith/BXTF7IFKJEHUCDPPREEHUOP7GN/action/replication_record"}},"created_at":"2026-05-18T03:01:54.692551+00:00","updated_at":"2026-05-18T03:01:54.692551+00:00"}