GPT-6.1 Sol (effort default (no reasoning-effort override) · thinking on) on Optimal single-machine job sequence (weighted tardiness with precedence)
OGPT-6.1 Soldefault · thinking on · Codex CLI 0.163.0 (codex exec --json) · cloud · 2026-10-22 · by @bobsiopener
- Estimated cost
- $0.06
- Wall time
- 1m
- Human step-ins
- 0
- Outcome
- Pass
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Summary
Exact prompt
# Optimal job sequence: minimum total weighted tardiness with precedence `input.json` (synthetic) has `start` (time the machine becomes free), `jobs` (`id`, processing time `p`, weight `w`, `due`) and `precedence` (pairs [a, b]: a must come before b, not necessarily directly). One machine, no idle time, no preemption. Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json`. Find a sequence of all jobs that respects every precedence pair and **minimises** total weighted tardiness: sum of w * max(0, C - due), where C is the job's completion time (start + sum of p up to and including the job). Any optimal sequence is accepted. Fresh instances have **20 and 21 jobs**; each run has a 90-second limit. ## answer.json `{"sequence": [job ids in order], "total_weighted_tardiness": integer}` ## Scoring Hidden checks (partial credit; all must pass). A sequence is **valid** if it is a permutation of the job ids, respects every precedence pair, and the reported objective equals the scorer's recomputation for that sequence. It is **optimal** if that objective equals the true minimum (the scorer has the optimum). `fixture_valid_sequence`, `fixture_optimal` (given 18-job instance); `fresh_20_jobs_valid`, `fresh_20_jobs_optimal`; `fresh_21_jobs_optimal`.
Greedy rules (WSPT, EDD, swaps) give valid but suboptimal sequences; an exact method (subset dynamic programming or a tight branch and bound) is needed. Original benchmark task written for usecaserank.com. Headless, offline run on a reproducible fixture. Cost shown is a list-price API-equivalent estimate (run on a ChatGPT subscription, not billed).
Success criteria: 1. fixture_valid_sequence 2. fixture_optimal 3. fresh_20_jobs_valid 4. fresh_20_jobs_optimal 5. fresh_21_jobs_optimal
Setup notes: Use Case Scout batch12 case m07-weighted-tardiness-optimal (offline fixture). Prepared with batch12/prepare.sh on the shared box; only TASK.md + starting files were copied to the agent machine, hidden key/tests stayed on the box. Prompt = TASK.md verbatim on stdin. Flags: --json -s workspace-write --skip-git-repo-check --ephemeral --ignore-user-config --ignore-rules -C <workdir>. Scored on the box with the scout's scorer: `python score.py WORKDIR KEYDIR`. Single run, no retries. User-level AGENTS.md (846 bytes, sha256 83ec4fe50da8) may have been in context; --ignore-user-config does not document excluding it. Serving model not confirmed: requested via -m; the event log does not echo the serving model id. Price source is secondary (pricing.json verification='secondary', https://www.actuia.com/en/news/ai-api-pricing-in-october-2026-050-to-50-for-output/), not an official OpenAI price page. Score: 5/5. Cost is an ESTIMATE: measured tokens x pricing.json list price (ChatGPT plan, nothing billed); input_tokens include cached reads; output_tokens include reasoning tokens. Tool calls 7 (2 failed, recovered). Single run.
Estimated cost List-price estimate; not actually billed.
Metrics
- Estimated cost
- $0.06
- Wall time
- 1m
- Human step-ins
- 0
- Turns
- 1
| Model | Input tok | Output tok | Cost |
|---|---|---|---|
| OGPT-6.1 Solopenai/gpt-6.1-soleffort default (no reasoning-effort override) · thinking on | 104,215 | 1,892 | $0.06 |
Reproduce this run
- Use the use case prompt on the use case page.
- Same setup: GPT-6.1 Sol (openai/gpt-6.1-sol, effort default (no reasoning-effort override) · thinking on) via
Codex CLI 0.163.0 (codex exec --json), cloud. - It counts as a success only if it meets every success criterion: 1. fixture_valid_sequence 2. fixture_optimal 3. fresh_20_jobs_valid 4. fresh_20_jobs_optimal 5. fresh_21_jobs_optimal
- Log model, tokens, wall time, human step-ins and the evidence log, then submit it as a reproduction. A different model? Submit a head-to-head rerun.
How runs are scored: Methodology.
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Automated checks
Trust 80% comes from these checks (how Trust % works).
- Run date is not in the future : passed
- Model is in the dated pricing table : passed
- Cost recomputed from tokens matches : passed
- Cached tokens are consistent : passed
- Output throughput is plausible : passed
- Autonomy matches step-ins : passed
- Step-ins do not exceed turns : passed
- Retries agree with first-try result : passed
- Evidence log SHA-256 matches : passed
- Evidence log is substantial : passed
Evidence log
{"type": "thread.started", "thread_id": "01a16409-dc07-7873-9c1e-30c8a32f32e3"}
{"type": "turn.started"}
{"type": "item.completed", "item": {"id": "item_0", "type": "agent_message", "text": "I\u2019ll implement an exact subset dynamic program, then check it against the supplied instance and small brute-force cases."}}
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{"type": "item.completed", "item": {"id": "item_1", "type": "command_execution", "command": "/bin/bash -lc 'ls -la'", "aggregated_output": "total 16\ndrwxr-xr-x 6 bob bob 4096 Oct 22 10:35 .\ndrwxrwxr-x 3 bob bob 4096 Oct 22 10:35 ..\ndr-xr-xr-x 2 bob bob 40 Oct 22 10:35 .agents\ndr-xr-xr-x 2 bob bob 40 Oct 22 10:35 .aws\ndr-xr-xr-x 2 bob bob 40 Oct 22 10:35 .codex\ndr-xr-xr-x 2 bob bob 40 Oct 22 10:35 .git\n-rw-r--r-- 1 bob bob 1298 Oct 22 10:08 TASK.md\n-rw-r--r-- 1 bob bob 1320 Oct 22 10:08 input.json\n", "exit_code": 0, "status": "completed"}}
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{"type": "item.completed", "item": {"id": "item_2", "type": "command_execution", "command": "/bin/bash -lc 'cat input.json'", "aggregated_output": "{\n \"start\": 1,\n \"jobs\": [\n {\n \"id\": \"J02\",\n \"p\": 17,\n \"w\": 8,\n \"due\": 61\n },\n {\n \"id\": \"J11\",\n \"p\": 15,\n \"w\": 8,\n \"due\": 92\n },\n {\n \"id\": \"J07\",\n \"p\": 11,\n \"w\": 3,\n \"due\": 111\n },\n {\n \"id\": \"J15\",\n \"p\": 10,\n \"w\": 9,\n \"due\": 126\n },\n {\n \"id\": \"J04\",\n \"p\": 16,\n \"w\": 4,\n \"due\": 50\n },\n {\n \"id\": \"J10\",\n \"p\": 10,\n \"w\": 9,\n \"due\": 151\n },\n {\n \"id\": \"J00\",\n \"p\": 1,\n \"w\": 1,\n \"due\": 96\n },\n {\n \"id\": \"J01\",\n \"p\": 7,\n \"w\": 6,\n \"due\": 125\n },\n {\n \"id\": \"J08\",\n \"p\": 4,\n \"w\": 2,\n \"due\": 109\n },\n {\n \"id\": \"J13\",\n \"p\": 17,\n \"w\": 7,\n \"due\": 112\n },\n {\n \"id\": \"J16\",\n \"p\": 19,\n \"w\": 1,\n \"due\": 67\n },\n {\n \"id\": \"J17\",\n \"p\": 12,\n \"w\": 6,\n \"due\": 144\n },\n {\n \"id\": \"J05\",\n \"p\": 3,\n \"w\": 5,\n \"due\": 110\n },\n {\n \"id\": \"J14\",\n \"p\": 9,\n \"w\": 1,\n \"due\": 50\n },\n {\n \"id\": \"J12\",\n \"p\": 10,\n \"w\": 9,\n \"due\": 146\n },\n {\n \"id\": \"J03\",\n \"p\": 17,\n \"w\": 9,\n \"due\": 52\n },\n {\n \"id\": \"J09\",\n \"p\": 6,\n \"w\": 5,\n \"due\": 147\n },\n {\n \"id\": \"J06\",\n \"p\": 20,\n \"w\": 1,\n \"due\": 139\n }\n ],\n \"precedence\": [\n [\n \"J00\",\n \"J04\"\n ],\n [\n \"J00\",\n \"J05\"\n ],\n [\n \"J06\",\n \"J08\"\n ],\n [\n \"J06\",\n \"J14\"\n ],\n [\n \"J10\",\n \"J14\"\n ],\n [\n \"J12\",\n \"J14\"\n ]\n ]\n}", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_3", "type": "command_execution", "command": "/bin/bash -lc \"rg --files -g AGENTS.md -g '*.py'\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_3", "type": "command_execution", "command": "/bin/bash -lc \"rg --files -g AGENTS.md -g '*.py'\"", "aggregated_output": "", "exit_code": 1, "status": "failed"}}
{"type": "item.started", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc \"cat > solve.py <<'PY'\n#\"'!/usr/bin/env python3\n\"\"\"Exact subset DP for precedence-constrained total weighted tardiness.\n\nA state records the set of completed jobs. Its elapsed processing time is\nindependent of their order, so only the cheapest prefix for each set is needed.\nTime: O(n * 2**n). Space: O(2**n). All objective arithmetic is exact.\n\"\"\"\nimport json\nimport sys\nfrom array import array\n\n\ndef solve(data):\n jobs = data['\"'jobs']\n n = len(jobs)\n ids = [job['id'] for job in jobs]\n index = {ident: i for i, ident in enumerate(ids)}\n if len(index) \"'!= n:\n raise ValueError('\"'Job ids must be unique')\n p = [job['p'] for job in jobs]\n w = [job['w'] for job in jobs]\n due = [job['due'] - data['start'] for job in jobs]\n prerequisites = [0] * n\n for a, b in data.get('precedence', []):\n prerequisites[index[b]] |= 1 << index[a]\n\n size = 1 << n\n full = size - 1\n # Compact elapsed-time storage when possible; retain support for large ints.\n if all(x >= 0 for x in p) and sum(p) <= (1 << 63) - 1:\n elapsed = array('q', [0]) * size\n else:\n elapsed = [0] * size\n best = [None] * size\n best[0] = 0\n # Each reachable state's final job identifies its preceding state uniquely.\n last = bytearray(size) if n <= 256 else array('I', [0]) * size\n bit_index = {1 << j: j for j in range(n)}\n\n for mask in range(size):\n if mask:\n bit = mask & -mask\n elapsed[mask] = elapsed[mask \"'^ bit] + p[bit_index[bit]]\n prefix_cost = best[mask]\n if prefix_cost is None:\n continue\n time = elapsed[mask]\n remaining = full ''^ mask\n while remaining:\n bit = remaining & -remaining\n remaining ''^= bit\n j = bit_index[bit]\n if prerequisites[j] & mask != prerequisites[j]:\n continue\n tardiness = time + p[j] - due[j]\n cost = prefix_cost + (w[j] * tardiness if tardiness > 0 else 0)\n following = mask | bit\n old = best[following]\n if old is None or cost < old:\n best[following] = cost\n last[following] = j\n\n if best[full] is None:\n raise ValueError('\"'Precedence constraints contain a cycle')\n sequence = []\n mask = full\n while mask:\n j = last[mask]\n sequence.append(ids[j])\n mask \"'^= 1 << j\n sequence.reverse()\n return {'\"'sequence': sequence, 'total_weighted_tardiness': best[full]}\n\n\ndef main():\n if len(sys.argv) \"'!= 3:\n raise SystemExit('\"'Usage: python solve.py input.json answer.json')\n with open(sys.argv[1], encoding='utf-8') as stream:\n result = solve(json.load(stream))\n with open(sys.argv[2], 'w', encoding='utf-8') as stream:\n json.dump(result, stream)\n stream.write('\\\\n')\n\n\nif __name__ == '__main__':\n main()\nPY\n/usr/bin/time -f '%e seconds, %M KB' python solve.py input.json answer.json\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc \"cat > solve.py <<'PY'\n#\"'!/usr/bin/env python3\n\"\"\"Exact subset DP for precedence-constrained total weighted tardiness.\n\nA state records the set of completed jobs. Its elapsed processing time is\nindependent of their order, so only the cheapest prefix for each set is needed.\nTime: O(n * 2**n). Space: O(2**n). All objective arithmetic is exact.\n\"\"\"\nimport json\nimport sys\nfrom array import array\n\n\ndef solve(data):\n jobs = data['\"'jobs']\n n = len(jobs)\n ids = [job['id'] for job in jobs]\n index = {ident: i for i, ident in enumerate(ids)}\n if len(index) \"'!= n:\n raise ValueError('\"'Job ids must be unique')\n p = [job['p'] for job in jobs]\n w = [job['w'] for job in jobs]\n due = [job['due'] - data['start'] for job in jobs]\n prerequisites = [0] * n\n for a, b in data.get('precedence', []):\n prerequisites[index[b]] |= 1 << index[a]\n\n size = 1 << n\n full = size - 1\n # Compact elapsed-time storage when possible; retain support for large ints.\n if all(x >= 0 for x in p) and sum(p) <= (1 << 63) - 1:\n elapsed = array('q', [0]) * size\n else:\n elapsed = [0] * size\n best = [None] * size\n best[0] = 0\n # Each reachable state's final job identifies its preceding state uniquely.\n last = bytearray(size) if n <= 256 else array('I', [0]) * size\n bit_index = {1 << j: j for j in range(n)}\n\n for mask in range(size):\n if mask:\n bit = mask & -mask\n elapsed[mask] = elapsed[mask \"'^ bit] + p[bit_index[bit]]\n prefix_cost = best[mask]\n if prefix_cost is None:\n continue\n time = elapsed[mask]\n remaining = full ''^ mask\n while remaining:\n bit = remaining & -remaining\n remaining ''^= bit\n j = bit_index[bit]\n if prerequisites[j] & mask != prerequisites[j]:\n continue\n tardiness = time + p[j] - due[j]\n cost = prefix_cost + (w[j] * tardiness if tardiness > 0 else 0)\n following = mask | bit\n old = best[following]\n if old is None or cost < old:\n best[following] = cost\n last[following] = j\n\n if best[full] is None:\n raise ValueError('\"'Precedence constraints contain a cycle')\n sequence = []\n mask = full\n while mask:\n j = last[mask]\n sequence.append(ids[j])\n mask \"'^= 1 << j\n sequence.reverse()\n return {'\"'sequence': sequence, 'total_weighted_tardiness': best[full]}\n\n\ndef main():\n if len(sys.argv) \"'!= 3:\n raise SystemExit('\"'Usage: python solve.py input.json answer.json')\n with open(sys.argv[1], encoding='utf-8') as stream:\n result = solve(json.load(stream))\n with open(sys.argv[2], 'w', encoding='utf-8') as stream:\n json.dump(result, stream)\n stream.write('\\\\n')\n\n\nif __name__ == '__main__':\n main()\nPY\n/usr/bin/time -f '%e seconds, %M KB' python solve.py input.json answer.json\"", "aggregated_output": "/usr/bin/time: cannot run python: No such file or directory\nCommand exited with non-zero status 127\n0.00 seconds, 1068 KB\n", "exit_code": 127, "status": "failed"}}
{"type": "item.started", "item": {"id": "item_5", "type": "command_execution", "command": "/bin/bash -lc \"/usr/bin/time -f '%e seconds, %M KB' python3 solve.py input.json answer.json\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_5", "type": "command_execution", "command": "/bin/bash -lc \"/usr/bin/time -f '%e seconds, %M KB' python3 solve.py input.json answer.json\"", "aggregated_output": "0.17 seconds, 16152 KB\n", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_6", "type": "command_execution", "command": "/bin/bash -lc \"python3 - <<'PY'\nimport itertools, random, time\nfrom solve import solve\nrng = random.Random(7)\nfor case in range(40):\n n = rng.randrange(1, 8)\n jobs = [dict(id=i,p=rng.randrange(1,10),w=rng.randrange(1,7),due=rng.randrange(0,40)) for i in range(n)]\n edges = [(i,j) for i in range(n) for j in range(i+1,n) if rng.random()<.15]\n data = dict(start=rng.randrange(5),jobs=jobs,precedence=edges)\n def cost(seq):\n t=data['start']; total=0\n for i in seq:\n t+=jobs[i]['p']; total+=jobs[i]['w']*max(0,t-jobs[i]['due'])\n return total\n optimum=min(cost(s) for s in itertools.permutations(range(n)) if all(s.index(a)<s.index(b) for a,b in edges))\n result=solve(data)\n assert result['total_weighted_tardiness']==optimum\n assert cost(result['sequence'])==optimum\nprint('40 brute-force comparisons passed')\nn=21\ndata=dict(start=5,jobs=[dict(id=i,p=rng.randrange(1,20),w=rng.randrange(1,10),due=rng.randrange(30,200)) for i in range(n)],precedence=[])\nt=time.perf_counter(); result=solve(data)\nprint('21-job unconstrained benchmark:',round(time.perf_counter()-t,2),'seconds; objective',result['total_weighted_tardiness'])\nPY\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_6", "type": "command_execution", "command": "/bin/bash -lc \"python3 - <<'PY'\nimport itertools, random, time\nfrom solve import solve\nrng = random.Random(7)\nfor case in range(40):\n n = rng.randrange(1, 8)\n jobs = [dict(id=i,p=rng.randrange(1,10),w=rng.randrange(1,7),due=rng.randrange(0,40)) for i in range(n)]\n edges = [(i,j) for i in range(n) for j in range(i+1,n) if rng.random()<.15]\n data = dict(start=rng.randrange(5),jobs=jobs,precedence=edges)\n def cost(seq):\n t=data['start']; total=0\n for i in seq:\n t+=jobs[i]['p']; total+=jobs[i]['w']*max(0,t-jobs[i]['due'])\n return total\n optimum=min(cost(s) for s in itertools.permutations(range(n)) if all(s.index(a)<s.index(b) for a,b in edges))\n result=solve(data)\n assert result['total_weighted_tardiness']==optimum\n assert cost(result['sequence'])==optimum\nprint('40 brute-force comparisons passed')\nn=21\ndata=dict(start=5,jobs=[dict(id=i,p=rng.randrange(1,20),w=rng.randrange(1,10),due=rng.randrange(30,200)) for i in range(n)],precedence=[])\nt=time.perf_counter(); result=solve(data)\nprint('21-job unconstrained benchmark:',round(time.perf_counter()-t,2),'seconds; objective',result['total_weighted_tardiness'])\nPY\"", "aggregated_output": "40 brute-force comparisons passed\n21-job unconstrained benchmark: 4.58 seconds; objective 284\n", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_7", "type": "command_execution", "command": "/bin/bash -lc 'cat answer.json'", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_7", "type": "command_execution", "command": "/bin/bash -lc 'cat answer.json'", "aggregated_output": "{\"sequence\": [\"J02\", \"J00\", \"J04\", \"J03\", \"J11\", \"J07\", \"J15\", \"J13\", \"J05\", \"J01\", \"J17\", \"J12\", \"J09\", \"J10\", \"J06\", \"J08\", \"J14\", \"J16\"], \"total_weighted_tardiness\": 462}\n", "exit_code": 0, "status": "completed"}}
{"type": "item.completed", "item": {"id": "item_8", "type": "agent_message", "text": "Created [solve.py](solve.py) using exact subset dynamic programming, and generated [answer.json](answer.json) with objective **462**.\n\nVerified against 40 brute-force cases. A 21-job benchmark completed in **4.58 seconds**.\n\nRun: `python3 solve.py input.json answer.json`"}}
{"type": "turn.completed", "usage": {"input_tokens": 104215, "cached_input_tokens": 90496, "cache_write_input_tokens": 0, "output_tokens": 1892, "reasoning_output_tokens": 343}}