by QunevoAI Scheduler for Manufacturers

Apex in benchmarks

Apex and four established algorithms solve the same scheduling problems. We compare completion time and flow time.

See the resultsRead the study (opens in a new tab)
€3.29 millionResearch funding across three projects

The algorithmic core grew out of these research and development projects, in collaboration with partners in industry and research.

Participants included Miele & Cie. KG, AUNDE Group SE and Fraunhofer IOSB-INA.

Explore the research foundations

Shorter times on average

Apex achieves better average results for both completion time and flow time. The comparison value is the mean of four established algorithms.

69Production datasets compared

Total completion time

Time until the last order is finished

Apex algorithm: 1.72 %
Established algorithm: 22.22 %

Gap in % · lower is better

Flow time

Total time all orders spend in production

Apex algorithm: 3.33 %
Established algorithm: 25.34 %

Gap in % · lower is better

A shorter bar means a better result. The charts show the average gap to the best result found for each dataset.

How the comparison worksDatasets, methods and limits
Benchmark cases
These cases come from established scientific benchmarks, covering job shops with alternative machines and flow production. Every exported schedule was independently checked against the benchmark rules.
How results are aggregated
The charts show the best makespan and total flow time found by each method; these may come from different plans. For each dataset and method, we take the middle value of three repetitions, then average equally across datasets.
Production-time reduction
The homepage's 15% shorter production time is a rounded benchmark result for total order flow time. For each dataset, we compare Apex with the mean of the four classical methods, then average the percentage reductions equally across datasets. This is a benchmark result, not a forecast for an individual factory.
Compared algorithms
Apex shows the configuration with the best average joint quality on the shared comparison set, selected after the evaluation. The bar for established algorithms shows the equally weighted average of NSGA-II, SPEA2, MOEA/D and SMS-EMOA. The same Apex configuration is used for every dataset.
What the comparison can tell you
Results vary by shop floor: on the fully compared flow shops, the established-algorithm average leads in joint quality. All exported plans were independently checked. The comparison tests algorithm implementations, not commercial APS or MES products, and does not establish superiority on every production problem.
Research projects and publicationsProject funding, industrial context and scientific sources

Years of research behind the algorithm

From predictive scheduling and human-centred production planning to an adaptable planning core: three research and development projects underpin Apex.

Qunevo spin-off project (opens in a new tab)
Project period
2024–2026
Funding reference
EFRE 20800400

A general model for discrete production, an adaptive scheduling algorithm and language-based integration of company-specific planning rules.

Research partner
Hochschule Bielefeld

Project funding€234,000
SUPPORT research project (opens in a new tab)
Project period
2022–2025
Funding reference · it's OWL
005-2111-0026

AI-based planning that balances production efficiency and ergonomic workload. Digital twins of Miele production and a variant-rich Isringhausen assembly line supplied the industrial use cases.

Industry partners
Miele & Cie. KG; Isringhausen GmbH & Co. KG

Research partners
Hochschule Bielefeld; Fraunhofer IOSB-INA

Project funding€1,240,000
Human-Centred Smart Service Lab (opens in a new tab)
Project period
2019–2023
Funding reference
EFRE-0300180

Predictive Scheduling developed digital twins and measures of plan robustness under uncertainty. Smart Demand Forecasting explored AI-based demand forecasting for procurement and production.

Industry partners
Bio-Circle Surface Technology GmbH; MIT GmbH & Co. KG; PerFact Innovation GmbH & Co. KG

Research partner
Hochschule Bielefeld

Project funding€1,820,000
Total funding across the three projects€3,294,000

The amounts cover the respective projects as a whole, including their partners and other research activities.

Scientific foundations

The published Apex study is listed first, followed by publications from the underlying research.

  1. APEX: An Extensible Model for Agent-Assisted Production Scheduling (opens in a new tab)

    Felix J. Grumbach, Stefan Görlitz

    arXiv:2609.33430 · 2026

  2. Robust-stable scheduling in dynamic flow shops based on deep reinforcement learning (opens in a new tab)

    F. Grumbach, A. Müller, P. Reusch, S. Trojahn

    Journal of Intelligent Manufacturing · 2024

  3. A Memetic Algorithm With Reinforcement Learning for Sociotechnical Production Scheduling (opens in a new tab)

    F. Grumbach, N. E. A. Badr, P. Reusch, S. Trojahn

    IEEE Access · 2023

  4. Reinforcement Learning for Two-Stage Permutation Flow Shop Scheduling—A Real-World Application in Household Appliance Production (opens in a new tab)

    A. Müller, F. Grumbach, F. Kattenstroth

    IEEE Access · 2024

  5. Demystifying Reinforcement Learning in Production Scheduling via Explainable AI (opens in a new tab)

    D. Fischer, H. M. Hüsener, F. Grumbach, L. Vollenkemper, A. Müller, P. Reusch

    arXiv · 2024

  6. Robustness Prediction in Dynamic Production Processes—A New Surrogate Measure Based on Regression Machine Learning (opens in a new tab)

    F. Grumbach, A. Müller, P. Reusch, S. Trojahn

    Processes · 2023

  7. Smaller Batches, Bigger Gains? Investigating the Impact of Batch Sizes on Reinforcement Learning Based Real-World Production Scheduling (opens in a new tab)

    A. Müller, F. Grumbach, M. Sabatelli

    IEEE ETFA · 2024

  8. Humanzentrierte Ablaufplanung von Montagelinien (opens in a new tab)

    L. Vollenkemper, F. Grumbach, M. Kohlhase, P. Reusch

    wt Werkstattstechnik online · 2023

  9. Robust Human-Centered Assembly Line Scheduling with Reinforcement Learning (opens in a new tab)

    F. Grumbach, A. Müller, L. Vollenkemper

    Dynamics in Logistics · LDIC · 2024

  10. Predicting processing times in high mix low volume job shops (opens in a new tab)

    A. Müller, F. Grumbach

    International Doctoral Students Workshop on Logistics, Supply Chain and Production Management · 2023

Compare with your current plan

Compare Apex with your current plan using the same orders, shifts and rules. Assess delivery dates, setup effort and workload against your priorities. The benchmark provides evidence for the algorithm; this comparison shows its value for your production.

Discuss your planning goals

Define what a good plan means

Optimise delivery performance, setup effort, workload or a company-specific measure. Additional objectives can be implemented and validated through Apex extensions.

Make trade-offs explicit

Compare alternatives when one goal improves at the expense of another. Set priorities and weights that reflect your production needs.

Keep your operating rules binding

Model machine eligibility, staff, material, calendars and fixed commitments. Customer-specific constraints become part of planning and validation.

Start with Apex

Run Apex locally with your own AI models; we can help with setup and integration. Or request hosting by Qunevo with a Custom license. Custom also supports local operation, with services tailored to your needs.

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Data integration.
Planning rules.
Implementation and training.

Benchmark questions

All questions about ApexAsk a question

What does the Apex production scheduling benchmark compare?

Apex and four established optimization methods solve the same benchmark problems. The comparison covers total completion time and total flow time. The published charts aggregate the shared datasets; the methodology explains how runs, configurations and reference values are selected. This is a comparison of algorithms, not commercial APS products.

Results & research

How much can Apex improve our production planning?

That depends on your orders, capacity, data and current planning process. Benchmark averages are not a forecast for your factory. Compare Apex with your current plan using the same inputs and rules, then assess delivery dates, production times, setup effort and the time your team spends planning.

Can researchers inspect the methods and reproduce results?

The Apex source code is public. The study is available on arXiv, and the benchmark page describes the results and methodology. Reproduction requires the same datasets, configuration, run budget and aggregation.

Explore the research foundations

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