{"id":"70f1fb90-405d-4795-ae30-55d785109f42","arxiv_id":"2412.14052","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"An attention module that aggregates sampled processing-time scenarios gives learned schedulers a consistent edge on stochastic flexible job shop problems.","lead":"The paper introduces a scenario processing module (SPM) that lets neural schedulers for flexible job shops account for random processing times by watching many sampled scenarios at once. The resulting method, SPM-DAN, reportedly beats existing learning and non-learning solvers on most tested stochastic scheduling instances.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix CP-stoch VaR objective selects the minimum scenario makespan, not the 95th percentile, invalidating a key non-learning baseline if code matches.","rationale":"The reader's conditional verdict is reasonable. In good faith, the SPM-DAN contribution is supported by extensive experiments, t-tests, and a modular architecture. I examined the reader's weakest assumption: the lower-bound reward. This assumption is actually protected by the telescoping identity sum_t r_t = f(C_0) - f(C_T), where C_T is the terminal makespan vector of the reward scenarios; intermediate lower bounds act as a potential function and do not change the optimal policy for the terminal objective. So I do not regard that as the load-bearing weakness. The load-bearing weakness I found is in the CP-stoch baseline in Appendix B. The VaR95 constraint selects a scenario whose lower-bound count equals round(0.95 n); this is the minimum, not the 95th percentile, and for n=10 it is unsatisfiable. If the implementation matches the appendix, the CP-stoch numbers in Tables 1, 3, 4, and 5 are not for VaR95; if it does not match, the code and paper disagree. This does not by itself overturn SPM-DAN's other wins over CP-SAT and PDRs, but it does require a corrected formulation and re-reported comparisons before the claim of outperforming non-learning stochastic baselines can be accepted. Thus I recommend keeping the CONDITIONAL verdict.","tokens_in":22168,"tokens_out":20279,"duration_ms":195691,"concrete_test":"Clone the linked repository, locate the CP-stoch VaR implementation, and run a small instance (e.g., 3 jobs x 2 machines) with n=25 scenarios. Sort the 25 scenario makespans of the returned schedule and identify which rank the solver's is_obj_l picked; if the solver minimizes the smallest makespan instead of the 24th order statistic, CP-stoch is invalid. Independently, re-derive the constraint from Algorithm 2 with n=10 to confirm that no scenario satisfies round(0.95n)=10, which would make the published CP-stoch figures impossible under the appendix.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing weakness is in Appendix B, Algorithm 2, the CP-stoch VaR baseline used in Tables 1, 3, 4, and 5. In the VaR95 branch, for each scenario l a Boolean is_obj_l is enforced by Sum_{l' != l} [c_l <= c_l'] = round(0.95 n). But Sum_{l' != l} [c_l <= c_l'] counts the number of other scenarios whose makespan is at least c_l. For n=25, round(0.95n)=24, and this equality is satisfied by the smallest makespan, not the 95th percentile, which has about one other scenario at least as large. For n=10, round(0.95n)=10 exceeds n-1=9, so no scenario satisfies the condition and the XOR constraint makes the model infeasible or degenerate. If the released code matches the appendix, CP-stoch optimizes the wrong stochastic objective and all CP-stoch comparisons are invalid; if the code does not match the appendix, the manuscript is not reproducible. The reader's highlighted lower-bound reward is not the core problem: because r_t = f(C_t) - f(C_{t+1}) telescopes to f(C_0) - f(C_T) with C_T the true terminal makespan vector, the training objective is an exact potential-based shaping of the terminal objective.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes SPM-DAN, a neural scheduler for stochastic flexible job shop scheduling (FJSP) with random processing times. It extends the deterministic dual attention network (DAN) with a scenario processing module (SPM) that attends over sampled processing-time scenarios and feeds the resulting embeddings into the base network. The training procedure uses a scenario-based reward that can optimize either expected makespan or Value-at-Risk (VaR95%). Experiments on synthetic instances, larger out-of-distribution sizes, public benchmarks (mk, rdata, edata, vdata), different processing-time distributions, and an alternative base network (L2D) aim to show that SPM-DAN outperforms dispatching rules, deterministic CP-SAT, a stochastic CP-SAT extension (CP-stoch), and DAN-based learning baselines. The manuscript includes code, ablations, t-tests in the appendix, and a sensitivity analysis of the number of scenarios.","tokens_in":22436,"tokens_out":3484,"duration_ms":30079,"significance":"If the results hold, the paper makes a useful contribution by showing how an attention-based scenario module can extend neural combinatorial optimization to stochastic scheduling with different objectives, and it provides a thorough experimental study with public benchmarks, generalization tests, and transferability to another network architecture. The availability of code and the inclusion of statistical significance tests are strengths. However, the central comparison against CP-stoch, a key non-learning stochastic baseline, is undermined by an error in the VaR formulation in Appendix B, so the claim of outperforming non-learning stochastic methods is not currently established.","major_comments":[{"comment":"The VaR95% objective in Algorithm 2 enforces Sum_{l' != l} [c_l <= c_l'] = round(0.95 n) to set is_obj_l. This counts the number of other scenarios whose makespan is at least c_l, so for n=25 the constraint is satisfied by the minimum makespan (for which all 24 other scenarios are >=), not by the 95th percentile, which has about one other scenario at least as large. For n=10, round(0.95*10)=10 exceeds the maximum possible count n-1=9, making the constraint infeasible or degenerate. Because this CP-stoch baseline is used in Tables 1, 3, 4, and 5, the reported CP-stoch results do not actually optimize the VaR95% objective as claimed.","section":"Appendix B, Algorithm 2 (CP-stoch VaR95% branch)"},{"comment":"The abstract's claim that the approach 'outperforms existing learning and non-learning methods' relies in part on the CP-stoch baseline, which is not correctly formulated as a VaR95% optimizer (see preceding comment). The comparisons against CP-SAT and the learning baselines are unaffected, but the CP-stoch comparison must be corrected by re-implementing the VaR95% constraint (for instance, using an order-statistic or auxiliary-variable formulation) and re-running the experiments, or the claim must be narrowed to exclude CP-stoch.","section":"Abstract and Section 'Synthetic Datasets Results' (Tables 1, 3, 4, 5)"}],"minor_comments":[{"comment":"The reward uses lower-bound completion-time estimates for unscheduled operations; the authors should state explicitly that because the sum of rewards telescopes to f(C_0) - f(C_T) with C_T the exact terminal scenario makespans, the lower-bound approximation does not bias the terminal objective, which would preempt a common concern about reward shaping.","section":"Section 'Reward' (paragraph on stochastic reward)"},{"comment":"The main tables report mean objective values and gaps without standard deviations; although t-tests are provided in Appendix D, reporting standard deviations in the tables would allow readers to assess the dispersion of the results more easily.","section":"Tables 1-6"},{"comment":"The transferability results for SPM-L2D are reported without statistical significance tests or run-to-run variation; a brief note on the number of seeds or instances would strengthen this preliminary evidence.","section":"Appendix A, Table 7"}],"recommendation":"major_revision","confidential_remarks":"The CP-stoch baseline issue is the main obstacle to acceptance. If the authors correct the VaR95% formulation and confirm that the released code matches the corrected algorithm, the paper's central contribution regarding SPM-DAN is likely to remain valid, but this needs to be verified. The reported comparisons to CP-SAT and to learning baselines are not affected by this issue. I did not inspect the code repository; the appendix and the public code must be consistent after the revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. The scenario processing module (SPM) is a genuinely useful addition to the neural combinatorial optimization toolkit, and the experimental study is unusually thorough. But there is a real problem with the CP-stoch baseline: as written in Appendix B, the VaR95 constraint forces the selected makespan to be at most every other scenario makespan, i.e., the minimum, not the 95th percentile. For n=10 the constraint is infeasible because round(0.95n)=10 exceeds n-1=9. That invalidates the CP-stoch numbers in Tables 1, 3, 4, and 5 unless the released code does something different from the appendix. If the code matches the appendix, those comparisons should be discarded or redone; if it doesn't, the manuscript is not reproducible as written.\n\nWhat is genuinely new here is the SPM itself: a Set-Transformer-style cross-attention module with inducing points that compresses nscn sampled scenarios into an embedding, concatenated with the deterministic DAN features. It is modular, transfers to L2D on the JSP, and works with both expected makespan and VaR objectives. The training reward telescopes to the terminal objective, so the lower-bound estimate is a legitimate potential-based shaping of the final makespan; the reader's concern about that is unfounded. The evaluation is broad: t-tests, generalization to larger instances, public benchmarks, sensitivity to nscn, and different distributions. That is solid work.\n\nThe CP-stoch flaw is the main soft spot. It is load-bearing for the claim of outperforming a scenario-based CP method, though not fatal to the overall story: SPM-DAN also beats deterministic CP-SAT and the DRL baselines on most larger instances. The abstract's \"outperforms existing non-learning methods\" is too strong if the strongest non-learning baseline is broken. Missing standard deviations in the main tables is a minor complaint; the t-tests partially compensate. The mk dataset overclaim is actually acknowledged in the text. The code is public but without a commit hash or data snapshot, which is a reproducibility nit.\n\nThis paper deserves a serious referee. The core contribution is sound and the evaluation is more careful than most in this area; the CP-stoch issue is fixable by rerunning with a correct VaR formulation or dropping those columns. I would send it to peer review with a clear request to address that baseline before acceptance.","headline":"Useful SPM-DAN extension for stochastic FJSP, but the CP-stoch baseline in Appendix B optimizes the minimum scenario makespan rather than VaR95, so those non-learning comparisons need rework.","tokens_in":22964,"tokens_out":2749,"would_cite":true,"duration_ms":25202,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that an attention-based scenario processing module, SPM-DAN, learns flexible job shop schedules under stochastic processing times that beat both learning and non-learning baselines by feeding sampled scenarios into the…","keywords":["stochastic flexible job shop scheduling","neural combinatorial optimization","scenario processing module","deep reinforcement learning","attention mechanism","Value-at-Risk","makespan","processing time uncertainty"],"falsifier":"Train the same SPM-DAN architecture twice on an instance family with high processing-time variance: once with the paper's lower-bound reward and once with a reward computed from full Monte Carlo makespan simulations, then compare VaR95 on 1000 fresh scenarios. If the lower-bound-trained policy is worse, the lower-bound approximation is the component that limits the method.","tokens_in":21974,"feed_emoji":"🏭","tokens_out":7042,"duration_ms":55150,"temperature":0.7,"pith_summary":"The paper's central claim is that a neural combinatorial optimization scheduler can be made effective for the flexible job shop scheduling problem with stochastic processing times by explicitly feeding it what the uncertainty looks like, not just training it on noisy rewards. To do this, the authors add a scenario processing module (SPM) to an existing dual attention network, forming SPM-DAN. The module takes several independently sampled processing-time scenarios, compresses them with attention into a single embedding, and concatenates that embedding with the deterministic instance features at every scheduling step. The same training loop is adapted so that rewards are computed from sampled scenarios under either the expected-makespan or the Value-at-Risk objective. Across synthetic and benchmark instances, SPM-DAN improves on dispatch rules, the deterministic base network, a stochastic-reward variant without the module, and the CP-SAT solver, which matters because real factories must commit to schedules before processing times are known.","feed_headline":"Neural scheduler reads scenarios, beats CP-SAT on stochastic shops","feed_subtitle":"An attention module feeds sampled scenarios into a learned scheduler, improving makespan and Value-at-Risk.","key_machinery":"The central object is the scenario processing module (SPM), an attention block that maps a set of $n_{\\mathrm{scn}}$ scenario state embeddings to a single stochastic embedding. It uses a trainable set of inducing points $I\\in\\mathbb{R}^{m\\times d}$ so that the attention complexity stays linear in the number of scenarios: $\\mathrm{SPM}(H)=\\mathrm{Avg}(\\mathrm{MHAB}(H,\\mathrm{MHAB}(I,H)))$. The module is permutation invariant, so it treats the sampled scenarios as an unordered approximation of the underlying processing-time distribution. It is plugged into a base dual attention network as an additional input source for operation, machine, and operation-machine features, converting a deterministic scheduler into a stochastic one without restructuring the base network.","core_discovery":"The discovery is that stochasticity can be incorporated into a learned scheduler as a state feature rather than only as reward noise. At each decision step, the SPM summarizes a set of sampled scenarios into an embedding via multi-head cross-attention with learnable inducing points, followed by permutation-invariant mean aggregation. This embedding is concatenated with the deterministic operation, machine, and operation-machine features before the base network scores actions. The reward is a scenario-level objective difference $f(C_t)-f(C_{t+1})$ computed from makespan lower bounds under the recursion $C(O_{ij},s_t)=C(O_{i(j-1)},s_t)+\\min_k p^k_{ij}$, with $f$ equal to the expected makespan or $\\mathrm{VaR}_{95\\%}$. The paper argues, and its experiments show, that this arrangement lets the policy distinguish states that look identical deterministically but differ in their sampled processing-time distributions, and that the resulting schedules outperform both learning and non-learning baselines on a variety of instances.","pith_inferences":["A connection not explored in the paper is applying the same scenario-embedding idea to other stochastic combinatorial optimization problems with known distributions, such as stochastic vehicle routing or project scheduling, where sample approximations are already standard.","The paper does not analyze whether the attending embeddings capture higher-order moments such as skew or tail thickness or only mean shifts; a testable extension is to vary the tail thickness while holding the mean fixed and see whether SPM-DAN's improvement persists.","Because the module is permutation invariant over scenarios, it could in principle be trained to produce distributionally robust schedules by treating the set of scenarios as a synthetic ambiguity set, though the authors do not investigate this direction.","The reliance on lower-bound rewards suggests that a curriculum that starts with loose bounds and tightens them as training progresses might separate the module's contribution from the reward approximation's contribution; this is not explored in the paper."],"forward_implications":["On synthetic instances, greedy SPM-DAN schedules beat the CP-SAT solver on the largest tested sizes (20x10 and above), while sampling-based SPM-DAN beats CP-SAT on nearly all reported instance sets.","Policies trained on one objective (VaR95) and one distribution transfer to the expected-makespan objective and to beta, gamma, and mixed distributions without retraining.","The same scenario module can be attached to a different base network and problem: a preliminary SPM-L2D experiment improves over L2D on stochastic JSP.","Training with fewer scenarios (50 or 100) costs little performance, and inference can trade runtime for solution quality by increasing the number of inference scenarios.","The stochastic-aware module adds roughly 20% greedy-inference runtime and about three times sampling runtime compared with the deterministic base, while improving objective values."],"supporting_citations":[{"why":"Supplies the dual attention network (DAN) used as the base architecture into which the scenario processing module is inserted.","marker":"(Wang et al. 2023)"},{"why":"Establishes the end-to-end deep reinforcement learning approach for FJSP that the training paradigm follows.","marker":"(Song et al. 2022)"},{"why":"Provides the L2D scheduling method with the lower-bound completion-time recursion and reward formulation that the stochastic reward generalizes.","marker":"(Zhang et al. 2020)"},{"why":"Provides the inducing-point cross-attention construction that the scenario processing module adapts to summarize scenario embeddings.","marker":"(Lee et al. 2019)"},{"why":"Supplies the proximal policy optimization algorithm used for training the extended network.","marker":"(Schulman et al. 2017)"},{"why":"Provides the CP-SAT solver used as the main non-learning baseline that SPM-DAN is compared against.","marker":"(Perron, Didier, and Gay 2023)"},{"why":"Formulates the closest learning-based stochastic job shop baseline, which the paper contrasts with its scenario-embedding approach.","marker":"(Infantes et al. 2024)"},{"why":"Supplies the benchmark environment and CP-SAT implementation used for the non-learning baseline comparisons.","marker":"(Reijnen et al. 2023)"}],"fun_headline_variants":["Scenario attention boosts neural scheduler for stochastic job shops","Neural policy uses scenario embeddings to outperform baselines on stochastic shops","Attention to scenario samples improves neural job shop scheduling","Stochastic JSP tackled by neural scheduler with scenario cross-attention","Neural scheduler leverages scenario attention to handle stochastic processing times"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the makespan lower bound used as a reward signal approximates the true stochastic objective closely enough for the learned policy to stay aligned with that objective.","fun_headline_variants_meta":{"raw":{"variants":["Scenario attention boosts neural scheduler for stochastic job shops","Neural policy uses scenario embeddings to outperform baselines on stochastic shops","Attention to scenario samples improves neural job shop scheduling","Stochastic JSP tackled by neural scheduler with scenario cross-attention","Neural scheduler leverages scenario attention to handle stochastic processing times"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000419,"raw_usage":{"total_tokens":2147,"prompt_tokens":922,"completion_tokens":1225,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":1144}},"tokens_in":538,"tokens_out":1225,"duration_ms":11771,"temperature":1.0,"reasoning_tokens":1144,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:31:01.272112+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same SPM-DAN architecture twice on an instance family with high processing-time variance: once with the paper's lower-bound reward and once with a reward computed from full Monte Carlo makespan simulations, then compare VaR95 on 1000 fresh scenarios. If the lower-bound-trained policy is worse, the lower-bound approximation is the component that limits the method.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the dual attention network (DAN) used as the base architecture into which the scenario processing module is inserted."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the end-to-end deep reinforcement learning approach for FJSP that the training paradigm follows."},{"cited_title":"S.; and Chi, X","cited_arxiv_id":null,"evidence_quote":"Provides the L2D scheduling method with the lower-bound completion-time recursion and reward formulation that the stochastic reward generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the inducing-point cross-attention construction that the scenario processing module adapts to summarize scenario embeddings."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the CP-SAT solver used as the main non-learning baseline that SPM-DAN is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Formulates the closest learning-based stochastic job shop baseline, which the paper contrasts with its scenario-embedding approach."}],"review_version":1}