{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IYXEHGMMKIBDATYAWOHTI4UJQW","short_pith_number":"pith:IYXEHGMM","canonical_record":{"source":{"id":"1205.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-28T18:31:20Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"30e848fca91be7dea71bfba5f05fa69cdc4611cee7c85c420d366e9ac755da1e","abstract_canon_sha256":"ed25724d67bedf7212456affd47878c046f8164dd29881195bf5cb9caeaee6f1"},"schema_version":"1.0"},"canonical_sha256":"462e43998c5202304f00b38f34728985ae0955a3507c7508a513a618b5898d80","source":{"kind":"arxiv","id":"1205.6179","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6179","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6179v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6179","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"IYXEHGMMKIBD","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYXEHGMMKIBDATYA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYXEHGMM","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IYXEHGMMKIBDATYAWOHTI4UJQW","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-28T18:31:20Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"30e848fca91be7dea71bfba5f05fa69cdc4611cee7c85c420d366e9ac755da1e","abstract_canon_sha256":"ed25724d67bedf7212456affd47878c046f8164dd29881195bf5cb9caeaee6f1"},"schema_version":"1.0"},"canonical_sha256":"462e43998c5202304f00b38f34728985ae0955a3507c7508a513a618b5898d80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.875999Z","signature_b64":"6G75R+QgS2u9kbNWcC52xwAZl14/g0C//+vkhfKnpBpk/j9kd9ufxjx1mhlCsa8FHgOYrCt22/NggPpK3h+BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"462e43998c5202304f00b38f34728985ae0955a3507c7508a513a618b5898d80","last_reissued_at":"2026-05-18T03:54:36.875219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.875219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6179","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ih688XRxnTzjT1LpNZAcwSI9up8lcrJTRv4+xjaEx8N8YX9s/Szrt5PA+kDE3AdEq4hM2MJeNcVwK3FZx2CfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:05:06.711991Z"},"content_sha256":"67f85dc8e79e9856c2a1590f926144a3dce11ed86e5d798fb26d4a0ebb870dc0","schema_version":"1.0","event_id":"sha256:67f85dc8e79e9856c2a1590f926144a3dce11ed86e5d798fb26d4a0ebb870dc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IYXEHGMMKIBDATYAWOHTI4UJQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Mixed Integer Programming Model Formulation for Solving the Lot-Sizing Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"math.OC","authors_text":"Maryam Mohammadi, Masine Md. Tap","submitted_at":"2012-05-28T18:31:20Z","abstract_excerpt":"This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6179","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p356T2T7KC4XRSCX+0xk5nAfsPBM6U4LTUOtMZwLdfm9WGi9FSKGVOjZq8wHUs6aRjH88i5l2Zp0SjSqk0b4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:05:06.712340Z"},"content_sha256":"06d5b3d20eb594abdb6dd5d0a9725d7420aa3196e2c86d3b1b56cffb4c9cd9d3","schema_version":"1.0","event_id":"sha256:06d5b3d20eb594abdb6dd5d0a9725d7420aa3196e2c86d3b1b56cffb4c9cd9d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/bundle.json","state_url":"https://pith.science/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T05:05:06Z","links":{"resolver":"https://pith.science/pith/IYXEHGMMKIBDATYAWOHTI4UJQW","bundle":"https://pith.science/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/bundle.json","state":"https://pith.science/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYXEHGMMKIBDATYAWOHTI4UJQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IYXEHGMMKIBDATYAWOHTI4UJQW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed25724d67bedf7212456affd47878c046f8164dd29881195bf5cb9caeaee6f1","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-28T18:31:20Z","title_canon_sha256":"30e848fca91be7dea71bfba5f05fa69cdc4611cee7c85c420d366e9ac755da1e"},"schema_version":"1.0","source":{"id":"1205.6179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6179","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6179v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6179","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"IYXEHGMMKIBD","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYXEHGMMKIBDATYA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYXEHGMM","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:06d5b3d20eb594abdb6dd5d0a9725d7420aa3196e2c86d3b1b56cffb4c9cd9d3","target":"graph","created_at":"2026-05-18T03:54:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.","authors_text":"Maryam Mohammadi, Masine Md. Tap","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-28T18:31:20Z","title":"A Mixed Integer Programming Model Formulation for Solving the Lot-Sizing Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6179","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:67f85dc8e79e9856c2a1590f926144a3dce11ed86e5d798fb26d4a0ebb870dc0","target":"record","created_at":"2026-05-18T03:54:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ed25724d67bedf7212456affd47878c046f8164dd29881195bf5cb9caeaee6f1","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-05-28T18:31:20Z","title_canon_sha256":"30e848fca91be7dea71bfba5f05fa69cdc4611cee7c85c420d366e9ac755da1e"},"schema_version":"1.0","source":{"id":"1205.6179","kind":"arxiv","version":1}},"canonical_sha256":"462e43998c5202304f00b38f34728985ae0955a3507c7508a513a618b5898d80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"462e43998c5202304f00b38f34728985ae0955a3507c7508a513a618b5898d80","first_computed_at":"2026-05-18T03:54:36.875219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:36.875219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6G75R+QgS2u9kbNWcC52xwAZl14/g0C//+vkhfKnpBpk/j9kd9ufxjx1mhlCsa8FHgOYrCt22/NggPpK3h+BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:36.875999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67f85dc8e79e9856c2a1590f926144a3dce11ed86e5d798fb26d4a0ebb870dc0","sha256:06d5b3d20eb594abdb6dd5d0a9725d7420aa3196e2c86d3b1b56cffb4c9cd9d3"],"state_sha256":"e0e43f04fc044e98d741fb22e06fa4ddfd688cb494d167c2a8b478f790558e6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMxdTGzGqpDw+r54CQNWfhCu4uvbMNOKU3LMPes0BzIXyBrKZjGSVbfS7V2G+bH7Dla5NhKsNoBciaN/TXswBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T05:05:06.714203Z","bundle_sha256":"13c0758d9acecc7dbdd0683ad32b9e30bb924a6a33ebba32db2b3f00485b754e"}}