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Automated Design of Inventory Policy with Large Language Models: An Exploratory Study

Fenghua Yang, Preet Baxi, Yi Zhang, Stefanus Jasin, Yanzhe Lei, Mo Liu, Parshan Pakiman

arXiv:2609.08071v1cs.AI

TL;DR

Inventory policy design lacks a systematic way to search beyond researcher-specified policy classes. The paper integrates data, optimization, and LLMs in an evolutionary framework, finding policies that outperform optimized base-stock benchmarks and exceed 21% mean cost reductions across more than 10,000 new instances.

  • Problem

    The paper asks whether data, optimization, and LLMs can be integrated to systematically search beyond inventory policy classes specified by researchers in advance.

    Source: §1 · p. 2

  • Method

    AIPS combines an LLM's generation of parameterized policy classes with external numerical optimization in an evolutionary search.

    Source: §8 · p. 38

  • Results

    More than 10,000 target instances show mean cost reductions exceeding 21% versus the optimized base-stock benchmark for the capped, discounted-pipeline, and hybrid classes.

    Source: §8 · p. 39

  • Takeaways & Limitations

    Optimization-guided LLM search can identify high-performing inventory policies beyond prespecified classes while retaining interpretable structural motifs.

    Source: §8 · p. 39

    The framework could be extended with richer mechanisms for representing and recombining structural motifs.

    Source: §8 · p. 39

Abstract

from arXiv · show

Firms making inventory decisions have access to operational data, optimization tools, and large language models (LLMs). Typically, data characterize the operating environment, optimization selects parameters within a prespecified inventory policy class, and LLMs support coding and decision analysis. We develop an integrated framework that combines these resources to automate inventory policy design. Given demand data, the framework iteratively uses an LLM to generate parameterized policy classes and an external solver to optimize its parameters within each class. Across 30 lost-sales inventory instances, the mean cost reduction relative to optimized base-stock benchmarks increases from 17.5% after one generation to 30.0% after ten generations. Parameter optimization is central to this performance: an LLM-only variant performs substantially worse, whereas optimization-guided feedback improves policy quality, accelerates search, and directs the LLM toward better policy classes rather than merely better parameter values within a fixed class. The strongest discovered policies are also interpretable: they combine recognizable inventory-control motifs, including capped orders, discounted or weighted pipeline inventory, and threshold-based replenishment logic. The search thereby produces new policy-class functional forms that, to our knowledge, have not previously been studied in the lost-sales inventory literature. These functional forms are not specified ex ante but emerge from the search process. Moreover, after their parameters are re-optimized, three discovered policy classes achieve average cost reductions of 21.75% to 22.60% across 10,064 new inventory instances. Overall, the results show that data-driven parameter optimization can guide LLM-based search over a broad space of inventory policy classes and identify high-performing, interpretable, and transferable decision rules.

1. Introduction

The introduction presents AIPS as an optimization-guided LLM framework for searching over parameterized inventory policy classes and parameters beyond prespecified heuristics. It focuses on offline, stationary lost-sales systems and evaluates executable, interpretable, and transferable policies across heterogeneous settings and LLM backbones.

1. Introduction

  • AIPS addresses the unresolved problem of systematically discovering inventory policy classes beyond researcher-specified functional forms.Data and parameter optimization can improve policies within a class, but neither determines which class should be used; LLMs provide a mechanism for expanding the policy-design space.Source: §1 · p. 2
  • The framework is designed for offline policy-class design in stationary lost-sales inventory systems with positive lead times, rather than period-by-period LLM ordering decisions.Its method uses off-the-shelf LLMs to generate parameterized classes, external optimization to select parameters, and simulation to evaluate resulting policies.Source: §1 · pp. 3–4
  • AIPS alternates LLM-generated policy-class search with numerical parameter optimization and simulation-based evaluation, feeding optimized policies and performance back into subsequent search.The framework maps on-hand and pipeline inventory to orders, optimizes each generated class against a simulation-based empirical cost objective, and returns class code, parameters, and performance summaries to the LLM.Source: §1 · p. 3
  • The planned empirical evaluation covers benchmark comparisons, optimization ablations, structural motif analysis, generalization across environments, and cross-model sensitivity.These experiments assess both the quality of discovered policies and whether optimization-guided feedback improves search over policy classes.Source: §1 · p. 4

1.1. Contributions and Related Literature

  • The paper positions its contribution at the intersection of lost-sales inventory control, data-driven inventory decision making, LLM-based automatic heuristic design, and approximate policy search.It develops an automated policy-search framework intended to expand inventory policy design beyond a prespecified menu of standard heuristics.Source: §1.1 · p. 4
  • The study tests when LLM-generated classes outperform optimized base-stock benchmarks, quantifies optimization and feedback effects, examines structural motifs and transfer across environments, and measures sensitivity to six LLM backbones.The experiments vary lead times, cost ratios, demand distributions, search features, and the use of numerical parameter optimization.Source: §1.1 · p. 5
  • AIPS uses numerical optimization to evaluate optimized representatives of LLM-generated policy classes, producing more informative feedback that directs the search toward increasingly effective classes.This extends evaluator-guided heuristic design by assessing each class after parameter optimization rather than using its initial parameterization.Source: §1.1 · p. 5
  • AIPS discovers interpretable policy classes that recombine order caps, discounted or weighted pipeline inventory, and threshold-based replenishment logic without requiring these motifs to be specified ex ante.The framework therefore expands the set of effective and transferable policy classes available for optimization and evaluation.Source: §1.1 · p. 6
  • Discovered classes are evaluated for transfer across lead times, cost ratios, and demand distributions with parameters reoptimized in each new environment, extending robustness analysis beyond new realizations from a fixed environment.Model choice affects economic performance, while numerical optimization reduces but does not eliminate this variation.Source: §1.1 · p. 6

1.2. Organization

  • The paper introduces a lost-sales inventory model and benchmark policies, presents AIPS with policy generation, numerical optimization, simulation evaluation, and feedback, reports experiments, and studies transferability across operational settings.Section 4 reports benchmark and ablation results and analyzes structural motifs in discovered policies; Section 5 studies transferability across lead times, cost ratios, and demand distributions.Source: §1.2 · p. 7

2. Model and Optimization Objective

The paper models finite-horizon lost-sales inventory control with deterministic lead times and optimizes stationary replenishment policies using empirical demand data and parameterized policy classes. This formulation separates policy-class design from within-class parameter optimization while addressing unknown demand and an intractable unrestricted policy space.

Model and Optimization Objective

  • The system is a single-item, periodic-review lost-sales model with finite horizon T, deterministic lead time L, and i.i.d. demand.Orders enter the pipeline and arrive after L periods; unmet demand is lost.Source: §2 · p. 7
  • Period costs combine holding and lost-sales penalties, with zero variable ordering cost: c(I_t,D_t) = h(Ī_t − D_t)^+ + p(D_t − Ī_t)^+.The holding term charges leftover inventory, while the lost-sales term penalizes unmet demand.Source: §2 · p. 8
  • The objective minimizes expected total cost over feasible stationary Markov replenishment policies mapping inventory states to bounded order quantities.Stationarity removes explicit period dependence, while the Markov property makes the current inventory state sufficient for decisions.Source: §2 · p. 8
  • Two obstacles motivate the framework: unknown demand prevents direct expectation evaluation, while unrestricted policy optimization is infinite-dimensional and suffers state-dimensionality growth with lead time.The inventory state includes on-hand inventory and the full pipeline, making direct optimization generally intractable.Source: §2 · p. 8
  • Sample-average approximation evaluates policies on shared demand trajectories, while parameterized classes restrict policy search and distinguish functional-form design from parameter optimization.A class Π_Θ specifies a functional form and feasible parameter space; θ then selects a fully specified policy within that class.Source: §2 · pp. 8–9

3. LLM-Guided Inventory Policy Search

This section describes AIPS, an evolutionary search that combines LLM-generated inventory policy structures with external parameter optimization. It explains how optimized policies are evaluated, propagated, and validated for executability and reproducibility across generations.

3. LLM-Guided Inventory Policy Search

  • AIPS embeds LLM proposals and numerical optimization in an evolutionary loop where high-performing policies guide subsequent policy-class generation.The procedure combines operational data, optimization, and LLMs under a finite search budget.Source: §3 · p. 9

3.1. Policy-Class Design via an LLM

  • The LLM iteratively generates parameterized policy classes using parent policies’ functional forms, optimized parameters, and empirical costs as structural feedback.It outputs one new class, an initial parameter vector, and a feasible parameter domain; the supplied initialization is subsequently optimized externally.Source: §3.1 · p. 10

3.2. Within-Class Parameter Optimization

  • The external optimizer holds each generated policy’s functional form fixed and searches its feasible parameter domain, without changing state transformations, operations, or branching logic.Because computation is finite, the routine retains the lowest-cost successfully evaluated parameter vector rather than assuming local or global optimality.Source: §3.2 · p. 12

3.3. Algorithm

  • The evolutionary algorithm initializes with an optimized base-stock policy, generates optimized offspring from selected low-cost parents, and retains the K lowest-cost policies across generations.Its search is governed by K, M, m, and G, respectively controlling pool size, proposals per generation, parent count, and generations.Source: §3.3 · p. 13
  • After optimizing M proposals, AIPS combines offspring with incumbents, retains the min{K,|eP(g)|} lowest-cost policies, and returns the lowest-cost final survivor.Surviving policies become candidates for parent selection, giving better-performing structures greater influence over later proposals.Source: §3.3 · p. 14
  • The external optimizer calibrates each LLM-proposed policy class, while optimized empirical costs determine which structures survive and guide subsequent LLM proposals.This lets the LLM focus on searching policy structures while numerical optimization searches parameter values within each structure.Source: §3.3 · p. 14

3.4. Validation and Numerical Implementation Details

  • Generated proposals undergo static validation requiring parseable code, consistent parameters, valid domains, and deterministic stationary policies using only current inventory state.Invalid proposals are discarded before numerical search; the policy must return a scalar order quantity without dependence on period, trajectory, prior calls, or hidden state.Source: §3.4 · p. 15
  • Runtime checks reject parameter vectors causing training-trajectory timeouts, execution errors, or nonfinite orders, while L-BFGS-B performs a bounded 15-iteration search without optimality guarantees.The implementation retains the valid evaluated vector with the lowest empirical training cost despite nonsmooth simulation objectives.Source: §3.4 · p. 15

4. Performance and Structure of Discovered Policies

This section examines the performance and structure of AIPS-discovered policies across heterogeneous lost-sales inventory settings. It characterizes their cost reductions relative to optimized base-stock policies and analyzes the interpretable inventory-control motifs and evolving pipeline representations underlying their replenishment responses.

4.1. Problem Instances and Performance Metrics

  • The benchmark comprises 30 instances spanning lead times L ∈{2,4,6}, cost settings (h,p) ∈{(1,2),(1,5)}, and five demand specifications.Each instance uses 10 generations, 10 offspring per generation, and 10 independent repeats; performance is measured against the optimized base-stock policy.Source: §4.1 · p. 16

4.2. Performance Results

  • By generation 10, mean cost reduction increases with lead time, from 15.1% at L = 2 to 30.7% at L = 4 and 44.1% at L = 6; across cost settings, corresponding means are 33.6% and 26.3%.Source: §4.2 · p. 17
  • 17.5% to 30.0%: mean cost reduction rises from generation 1 to generation 10, with all reductions positive and 84.8% of improvement realized by generation 5.By generation 10, reductions range from 5.2% to 72.7%, and AIPS outperforms the optimized base-stock benchmark across the heterogeneous instances.Source: §4.2 · p. 17
  • Figure 4 shows that longer-lead-time improvements shift entire cost-reduction distributions rightward, rather than reflecting only a few extreme outcomes.The corresponding means are 15.1%, 30.7%, and 44.1% for L = 2, 4, and 6, respectively.Source: Figure 4 · p. 18, §4.2 · p. 18
  • 48% versus 12%: generation-10 mean reductions range from approximately 48% under Poisson demand to 12% under Exponential demand.Within the Normal family, gains decline monotonically with variability: approximately 45% at σ = 10, 27% at σ = 30, and 18% at σ = 50.Source: Figure 5 · p. 19, §4.2 · p. 19
  • AIPS policies achieve substantially lower empirical cost than optimized base-stock policies across settings, with performance varying across lead times and cost settings.Source: §4.3 · p. 19, §4.2 · p. 19

4.3. Structural Analysis of Discovered Policies

  • The policies modify target-gap responses using partial adjustment, state-dependent targets, clipping, thresholding, smoothing, or baseline replenishment.Partial adjustment can reduce overshooting by closing inventory gaps gradually, while the other motifs alter the target or the order-response mechanism.Source: §4.3 · pp. 20, 22
  • AIPS searches over interpretable structural building blocks and their combinations, while numerical optimization calibrates their parameters instead of requiring experts to prespecify the relevant bases.Most discovered policies combine several motifs, which are treated as recurring replenishment logic rather than literal code patterns.Source: §4.3 · pp. 21–22
  • Discovered policies often retain inventory position while modifying how pipeline inventory is represented through weighted, nonlinear, or state-dependent summaries.These representations allow ordering decisions to distinguish among different pipeline configurations rather than assigning equal weight to all outstanding orders.Source: §4.3 · pp. 21–23
  • The discovered policies combine informative state summaries, richer representations of pipeline inventory, and moderated replenishment responses, with inventory-position logic and pipeline weighting appearing in 77.0% and 49.0%.Partial adjustment appears in 33.0% of the full sample.Source: §4.3 · p. 23
  • 3.31 motifs per sampled policy on average, with only 3 of 100 policies containing one motif, shows that discovered rules are combinations of interpretable building blocks.The median policy contains three motifs, so the policies are not merely minor variations of one benchmark rule.Source: §4.3 · p. 23

4.4. Representative Evolutionary Trajectory

  • 745.56 training cost, a 56.9% reduction versus the optimized base-stock benchmark, is achieved by Policy 5, which remains best through generation 10.The representative run improves from 1,727.92 at generation 0 through successive incumbents to 745.56, with no better policy after generation 8.Source: Figure 6 · p. 24, §4.4 · pp. 24–25
  • The representative search changes both pipeline-state summaries and response aggressiveness, moving among weighting, partial adjustment, thresholding, and clipping instead of monotonically adding complexity.Successive policies include timing-sensitive or discounted pipeline signals, partial adjustment, and one- or two-sided order clipping; Policy 1 also uses a threshold and cap.Source: §4.4 · p. 25

5. Cross-Environment Generalization

This section examines how AIPS transfers discovered policy classes across environments by retaining their functional forms and re-optimizing parameters for each target instance. It evaluates their performance across diverse target instances and operating regimes, including lead times, cost ratios, and demand environments.

5. Cross-Environment Generalization

  • AIPS transfers policy classes—not fixed parameter values—by retaining each functional form and feasible parameter set, then re-optimizing parameters for changed demand, costs, or lead times.Performance is evaluated against the optimized base-stock policy for the same target instance, measuring structural generalization.Source: §5 · pp. 25–26

5.1. Discovered Inventory Policy Classes

  • The three discovered classes are capped, discounted-pipeline, and hybrid, recombining order-clipping, pipeline-weighting, partial-adjustment, thresholding, and constant-order motifs.The capped class changes replenishment through order clipping, while the discounted-pipeline and hybrid classes also modify pipeline representation.Source: §5.1 · pp. 26–27

5.2. Target Instances and Performance Metrics

  • 10,064 target instances span 13 demand families, 629 demand specifications, four lead times, and four lost-sales-penalty-to-holding-cost ratios.Each transferred class and the base-stock policy is re-optimized per target; performance uses percentage cost reduction and within-instance policy rank.Source: §5.2 · pp. 27–28

5.3. Results

  • 22.60%, 21.75%, and 22.10% mean cost reductions are achieved by the capped, discounted-pipeline, and hybrid classes, respectively, versus optimized base-stock.Their mean policy ranks are 1.93, 2.17, and 2.01, compared with 3.89 for base-stock; the capped class performs best on average.Source: §5.3 · p. 28
  • 34.94%: hybrid mean cost reduction at L = 8, compared with 9.20% at L = 2 for the capped class, while all discovered classes substantially outperform optimized base-stock policies across lead times.Mean reductions for the capped class are 9.20%, 18.86%, 27.43%, and 34.90% at L = 2,4,6,8; discounted-pipeline reductions are 7.47%, 17.84%, 27.00%, and 34.70%; hybrid reductions are 7.80%, 18.32%, 27.32%, and 34.94%.Source: Figure 7 · p. 29, §5.3 · p. 29
  • 26.95% to 17.63%: hybrid mean cost reduction as R increases from 2 to 10, with all discovered classes remaining substantially better than optimized base-stock policies.The advantage is largest when lost sales are relatively inexpensive and narrows as lost sales become more expensive; the base-stock benchmark remains near rank 4 while discovered classes remain near rank 2.Source: Table 4 · p. 30, §5.3 · p. 30
  • Cost reductions are largest under bounded discrete demand, substantial under bounded continuous and light- to moderate-tailed demand, and markedly smaller under heavy-tailed or highly skewed demand.The heavy-tailed or highly skewed group includes observations near or below zero, making performance gains less uniform across target instances.Source: §5.3 · p. 30, Figure 8 · p. 31
  • Policy-class rankings vary by regime: the capped class performs best under low variability and short lead times, whereas discounted-pipeline and hybrid classes become more competitive as variability and lead time increase.The capped class has median rank 1 under low variability at short lead times, while the hybrid class strengthens particularly under moderate variability as lead time increases.Source: Figure 9 · p. 31, §5.3 · p. 31
  • No single transferred class is uniformly best: capped policies suit stable demand and limited corrective orders, while richer pipeline treatment is more valuable with greater variability or longer lead times.These patterns indicate that different structural-motif combinations are useful in different operating regimes.Source: §5.3 · p. 32

6. Value of Optimization

External optimization improves AIPS through parameter calibration, faster convergence, and guidance of policy-class search. Final-step calibration recovers only a small share of the advantage, showing that optimization changes the evolutionary path itself.

Experimental comparison

  • Even with twice the generation budget, the no-optimizer search does not compensate for removing numerical optimization.The optimizer-throughout variant optimizes every proposed class before evaluation, selection, and feedback; the no-optimizer variant evaluates LLM-supplied initialization directly.Source: §6 · pp. 32–33, Figure 10 · p. 33

Convergence speed

  • Optimization accelerates convergence: median time falls from 15.0 to 7.5 generations, mean time from 11.6 to 6.8, and interquartile range from [4,18] to [5,9].The convergence target is each variant’s own final performance within 1%.Source: Table 5 · p. 33, §6 · pp. 33–34

Separating parameter calibration from search guidance

  • Final-step optimization recovers only 1.1 of 72.9 percentage points for Poisson, none of 16.1 for Exponential, and 3.1 of 43.8 for Normal demand.Thus, most of optimizer-throughout’s advantage remains after calibrating the final no-optimizer class.Source: Table 6 · p. 35, §6 · p. 35
  • Optimization improves within-class calibration, accelerates convergence, and most importantly supplies feedback that guides policy-class search toward better structural forms.Calibrated evaluation can preserve promising classes with poor initial parameters, whereas final-step optimization cannot recover classes discarded earlier.Source: §6 · p. 35

7. LLM Backbone Ablation

LLM backbone choice materially affects AIPS search quality and speed, while external optimization improves performance across all six backbones. Stronger models identify high-performing policy classes earlier, but lower-cost models can also perform well with optimization.

Impact of the LLM backbone

  • Across generations, Gemini 3 Flash achieves about 45% mean cost reduction in generation 1 and remains around 46%, while GPT-5 Mini approaches 46% by generation 10.DeepSeek V3 rises from about 34% in generation 1 to approximately 45% by generation 10.Source: §7 · p. 36

8. Conclusion

AIPS combines LLM-generated policy classes, numerical optimization, and data-driven feedback to automate inventory-policy design. It discovers interpretable, transferable policies that outperform optimized base-stock benchmarks, while optimization materially improves search and realized performance.

  • AIPS combines LLM-generated parameterized replenishment classes, numerical optimization, and performance feedback to evolve inventory-policy structures.The framework uses optimized policies and empirical results to guide subsequent generations of structural search in lost-sales systems with positive lead times.Source: §8 · pp. 38–39
  • The discovered policies substantially outperform optimized base-stock benchmarks while remaining interpretable through recurring inventory-control motifs.These motifs include richer pipeline-inventory representations, partial adjustment, clipping, thresholding, and state-dependent replenishment.Source: §8 · p. 39
  • AIPS’s capped, discounted-pipeline, and hybrid policy classes achieve mean cost reductions exceeding 21% across more than 10,000 new target instances.Their parameters are reoptimized while retaining the discovered functional forms and feasible parameter spaces.Source: §8 · p. 39
  • Relative policy performance varies systematically across operating regimes, indicating that different motif combinations suit different demand, lead-time, and cost conditions.The transfer evaluation spans different demand distributions, lead times, and cost ratios.Source: §8 · p. 39
  • Ablations show numerical optimization calibrates parameters, accelerates convergence, and improves policy-class feedback, whereas post-search optimization recovers only a small portion of lost performance.Across six LLM backbones, structural-search quality depends on the LLM, but optimization improves realized performance for all backbones.Source: §8 · p. 39
  • AIPS can start from expert-designed policies and extend them by adding, combining, and refining structural motifs; future work targets richer recombination and broader inventory settings.Proposed extensions include nonstationary demand, stochastic lead times, capacity constraints, multi-item systems, and multi-echelon networks.Source: §8 · p. 39

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EC.1. Prompt Template

The AIPS prompt supplies instance-specific demand, parent-policy, optimized-parameter, and cost information to generate a strictly stationary Python inventory policy. It explicitly models lead-time pipeline initialization through zero-demand planning periods before evaluating holding and lost-sales costs during the selling horizon.

Prompt Inputs

  • The prompt inserts training demand trajectories, selected parent-policy code, optimized parameter values, and empirical cost statistics, repeating the parent block when multiple parents are provided.These substitutions guide generation of a modified policy intended to reduce average historical cost.Source: EC.1. Prompt Template · pp. 44, 46

Time Indexing

  • The simulation prepends L zero-demand, zero-cost planning periods to initialize the pipeline, followed by T cost-incurring selling periods corresponding to the paper’s horizon.Orders placed during planning arrive during the first L selling periods, making pre-horizon pipeline initialization explicit.Source: EC.1. Prompt Template · p. 44

Inventory Model

  • The inventory model tracks on-hand inventory and an L-period FIFO pipeline, places orders before demand realization, and charges holding and lost-sales costs only during the selling phase.The stationary policy maps (I_t, Q_t) to order quantity a_t, while inventory and pipeline states update after demand is realized.Source: EC.1. Prompt Template · pp. 44–45

Generation Constraints

  • Generated policies must be Python functions of on-hand inventory and pipeline orders alone, return finite nonnegative integer orders, and expose at most 10 optimizable in-function parameters.The prompt prohibits time dependence, hidden memory, trajectory indices, and state stored across calls.Source: EC.1. Prompt Template · p. 46

Parent Policy Baseline

  • The historical parent policy has average total cost per period 14.76, with average holding cost 5.67 and lost-sales cost 9.10.Its per-trajectory total cost has mean 826.80, standard deviation 163.23, and range (494.00, 1584.00).Source: EC.1. Prompt Template · p. 47

EC.2. Additional Results for Section 4

Table EC.1 reports mean cost-reduction percentages and standard errors across problem instances and generations, with each instance represented by paired rows for the mean and its standard error.

Table EC.1

  • Table EC.1 reports mean cost-reduction percentages across problem instances and generations, alongside their standard errors.Each instance occupies two rows: the first gives the mean over ten repeats, and the parenthesized second row gives its standard error.Source: EC.2. Additional Results for Section 4 · p. 48
  • Instance labels encode demand distribution, lead time, cost ratio, and demand variability.Exp denotes Exponential demand; L2, L4, and L6 denote lead times; CR2 and CR5 denote p/h = 2 and p/h = 5; Normal10, Normal30, and Normal50 denote Normal demand with σ = 10, 30, and 50.Source: EC.2. Additional Results for Section 4 · p. 48
  • Mean cost reduction and standard error can also be reported for a subset of problem instances K ⊂[K].The table defines these statistics for selected subsets of the full instance set.Source: EC.2. Additional Results for Section 4 · p. 48

EC.3. Construction of the Robustness Demand Set

The robustness demand set spans 13 distribution families and diverse demand behaviors, with specifications converted into training and test trajectories across multiple inventory environments. Parameter-grid construction yields 629 demand specifications and 10,064 distinct inventory test environments.

EC.3. Construction of the Robustness Demand Set

EC.3.1. Trajectory Generation

  • Each demand specification generates integer-valued trajectories of length T = 50, with training trajectories used for parameter optimization and separate test trajectories reserved for out-of-sample evaluation.The environments vary four lead times, L ∈{2,4,6,8}, and four lost-sales penalties, p ∈{2,4,6,10}, while holding h = 1.Source: EC.3.1. Trajectory Generation · pp. 48–49
  • 10,064 distinct inventory test environments result from 629 demand specifications crossed with 16 combinations of lead times and lost-sales penalties.The construction uses 100 training trajectories and 1,000 separate test trajectories for each demand specification.Source: EC.3.1. Trajectory Generation · pp. 48–49

EC.3.2. Distribution Families and Parameter Grids

  • The parameter grids retain 123 distinct scaled-beta moment specifications after removing duplicate pairs, producing 629 demand specifications across all 13 families.Table EC.2 reports the complete parameter grid used for each demand family.Source: EC.3.2. Distribution Families and… · pp. 50–51

EC.4. Test-Set Performance for the Value of Optimization

Test-set performance closely matches the training-set performance, and incorporating an external optimizer significantly improves AIPS performance. The comparison evaluates no-optimizer results at generation 20 versus optimizer-assisted results at generation 10.

EC.5. LLM Backbone

External numerical optimization improves both the speed and level of LLM-based inventory-policy search across all six backbones. These gains persist on the test set, although Gemini 3 Flash remains strong without optimization.

Generation-by-generation performance

  • Optimization improves both performance level and search speed across all six backbones, with substantial heterogeneity across instances and repeats.Optimizer-enabled experiments terminate at generation 10, whereas no-optimizer experiments continue through generation 20.Source: EC.5. LLM Backbone · p. 51
  • At generation 10, optimization achieves mean cost reductions of 41.9%, 46.1%, 45.5%, 33.5%, 23.1%, and 46.3% across the six backbones.Source: EC.5. LLM Backbone · p. 51

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