APEX: An Extensible Model for Agent-Assisted Production Scheduling

Felix J. Grumbach; Stefan Görlitz

cs.AISep 27, 2026

APEX: An Extensible Model for Agent-Assisted Production Scheduling

Authors: Felix J. Grumbach, Stefan Görlitz

Organizations: Qunevo GmbH, Germany

Abstract

Production scheduling requires realistic models that reflect operational constraints and efficient methods that balance competing goals. Putting these methods into use also requires data integration, model adaptation and specialist expertise. We present APEX, an extensible production scheduling framework built around a general model and hybrid multiobjective search. Agent assistance supports both scheduling and model refinement: agents prepare data and explore scenarios in natural language, while coding agents help implement and test new constraints and objectives. Shared construction and checking procedures connect these adaptations to the scheduling core. We benchmark eight APEX configurations against NSGA-II, SPEA2, MOEA/D and SMS-EMOA on 69 public job-shop, flexible job-shop and permutation flow-shop instances, assessing workload completion time (makespan), total job flowtime and computation time. Hybrid configurations achieve the best aggregate solution quality, although the leading method depends on the problem class and objective. A separate synthetic workflow study uses OpenAI's GPT-6-astra as an interaction layer between the human planner and the algorithmic core, testing rule additions, plan and objective changes, and what-if comparisons. All 24 sessions completed the requested changes and passed independent checks of saved models and schedules. A separate coding evaluation produced six native implementations of an additional objective or hard constraint through predefined extension hooks. All passed independent checks without modifying the core.

Figures & tables

Study and setting	Model coverage	Method and evidence setting
Lan and Berkhout (2025) ; multiple machine and project families	Common task, mode, resource and temporal-constraint interface	CP; cross-family public benchmarks; preprint
Kasapidis et al. (2025) ; flexible job shop	Tools, utilities, material resources, buffers and blocking	CP with adaptive large-neighbourhood search; established and generated combined-resource instances
Perrachon et al. (2025) ; multi-resource job shop	Resources required during selected operation stages	Simulated annealing with reinsertion; benchmark comparison with commercial CP
Yasari et al. (2025) ; operator–machine job shop	Operator assignment and physical-workload limits	MILP with row generation; extended benchmark instances
Terbrack and Claus (2025) ; flexible job shop	Energy costs, demand peaks and emissions, with setups and due dates	CP with lexicographic objectives; computational instances
Ferreira et al. (2026) ; hybrid flow shop	Parallel machines at stages; sequence- and machine-dependent setups	Column generation and iterated local search; generated two-stage instances

Table 1: Selected scheduling models and solution approaches. CP denotes constraint programming; MILP denotes mixed-integer linear programming.

Study	Agent role	Evidence setting
Bakopoulos et al. (2024)	Coordination of scheduling methods	Bicycle production; digital-twin validation
Ahmaditeshnizi et al. (2024)	Model formulation and solver-code generation	Natural-language LP/MILP modelling benchmarks
May et al. (2026)	Generation and critique of dispatching rules	Dynamic job-shop simulation
Wang et al. (2025)	Scheduling-tool selection and coordination	FJSP simulations and robotic experiments
Yuan et al. (2025)	Natural-language system operation	Simulated garment MES; designed requests
Ye et al. (2026)	Preference interpretation and Pareto explanation	Job shops, flow shops and flexible job shops; preprint

Table 2: Selected agent-assisted approaches. The studies address different tasks and do not constitute a common performance comparison.

Method	HV deficit (%)	MS gap (%)	FT gap (%)	Time (s)
XG	3.498	18.405	14.587	0.035
XH	0.898	3.025	4.490	39.820
XT	1.364	6.910	6.976	35.606
XE	1.700	11.226	8.841	19.784
XHT	0.728	2.537	4.001	39.819
XHE	0.466	1.844	3.053	30.068

Table 3: Overall results for the 69 instances: median over three seeds within each instance, then an arithmetic mean with equal instance weights. Lower is better. Quality is relative to the best observed result on the same instance. Time is measured internal wall time. Bold marks column minima; XG uses one construction and is excluded from the runtime minimum among search methods, which each receive 1,000 evaluations.

Workflow	Requested change	Passes	MS (s)	Mode cost (a.u.)
Rules	M1 unavailable on $[0,2400)$	3/3	6,300	30
	J3-2 within $[7200,10800]$	3/3	9,300	30
Plans	J2-1 on M2 at $3600$	3/3	8,400	30
	Freeze baseline starts before $1800$	3/3	4,800	30
Objectives	Tardiness first, then makespan	3/3	4,800	30
	Mode cost first, then makespan	3/3	9,000	12

Table 4: Configuration and planning workflows. Passes count complete sessions. Request times and makespan (MS) are in seconds. Mode cost sums synthetic production costs in arbitrary units (a.u.): four per operation on M1 or M3 and one on M2 or M4, irrespective of duration. Each request produced the same reported MS and cost in its three repetitions. The baseline has MS 4,800 s and cost 30.

New implementation	Accepted/submitted	Checks	Median time (s)
Squared-tardiness objective	3/3	68	198.0
Exposure-balance constraint	3/3	61	249.6

Table 5: Acceptance of submitted native implementations, including the additional constraint attempt. Counts give accepted final modules over submitted final modules. Checks are acceptance assertions per module. Median time covers sessions that produced a final module and includes code generation, compilation and public-example feedback. The seven attempts, including one without a submission, are documented in Appendix A.7 .

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Class	Method	HV (%)	MS (%)	FT (%)	Time (s)
JSP	XG	3.560	16.837	11.323	0.022
JSP	XH	0.271	1.366	1.729	26.454
JSP	XT	0.434	3.013	3.335	22.143
JSP	XE	2.309	12.461	9.965	5.580
JSP	XHT	0.192	1.193	1.145	27.275
JSP	XHE	0.331	1.516	2.116	16.561

Appendix

Table 6: Class summaries: means of instance-level seed medians. Lower is better. Bold marks minima within each class; XG is excluded from the runtime minimum.

Method	HV deficit (%)	MS gap (%)	FT gap (%)	Time (s)
XG	3.666	17.639	14.482	0.037
XH	1.098	3.604	5.231	42.164
XT	1.447	6.714	7.061	37.972
XE	1.585	10.007	7.963	24.281
XHT	0.877	2.981	4.504	42.452
XHE	0.520	1.965	3.165	33.577

Appendix

Table 7: Supplementary overall summary with equal weights for JSP, FJSP and PFSP. Each entry is the mean of the three class-level values in Table 6 . Lower is better; bold marks column minima, excluding the one-construction XG reference from the runtime minimum.

Class	Instance	Family	Jobs	Machines	Operations
JSP	abz5	OR-Library	10	10	100
JSP	ft06	OR-Library	6	6	36
JSP	la01	OR-Library	10	5	50
JSP	la06	OR-Library	15	5	75
JSP	la16	OR-Library	10	10	100
JSP	tai_jsp002	Taillard	15	15	225

Appendix

Table 8: The 69 instances included in the manuscript. Source identifiers are retained; Taillard JSP and PFSP use separate identifier prefixes.

Class	Instance	XG	XH	XT	XE	XHT	XHE	XTE	XHTE	NSGA-II	SPEA2	MOEA/D	SMS-EMOA
JSP	abz5	10.320	0.431	0.669	6.432	0.157	0.498	0.643	0.306	1.694	1.503	1.421	1.746
JSP	ft06	18.652	0.206	0.008	5.782	0.200	0.195	0.044	0.208	0.557	0.194	1.388	1.096
JSP	la01	4.817	0.687	0.243	2.153	0.498	0.785	0.252	0.489	1.807	1.690	1.117	1.168
JSP	la06	2.187	0.780	0.249	1.930	0.367	0.942	0.326	0.315	1.607	1.553	1.533	1.356
JSP	la16	4.661	0.719	0.000	2.760	0.634	0.869	0.219	0.217	0.887	0.987	1.396	1.150
JSP	tai_jsp002	3.181	0.140	0.327	2.707	0.025	0.103	0.327	0.025	1.726	1.566	1.617	1.840

Appendix

Table 9: Per-instance HV deficit (percent): median over three seeds. Bold marks the lowest unrounded value within each instance; ties are retained.

Class	Instance	XG	XH	XT	XE	XHT	XHE	XTE	XHTE	NSGA-II	SPEA2	MOEA/D	SMS-EMOA
JSP	abz5	0.003	2.644	2.117	1.186	2.459	1.838	1.648	2.030	0.193	0.222	0.329	0.188
JSP	ft06	0.001	0.701	0.585	0.430	0.727	0.534	0.543	0.637	0.090	0.123	0.235	0.097
JSP	la01	0.001	1.245	0.967	0.575	1.113	0.864	0.820	1.010	0.116	0.142	0.261	0.121
JSP	la06	0.002	2.154	1.889	0.914	1.968	1.542	1.361	1.699	0.168	0.188	0.327	0.160
JSP	la16	0.002	2.312	1.926	1.103	2.379	1.891	1.615	1.938	0.190	0.219	0.380	0.208
JSP	tai_jsp002	0.007	7.756	6.485	2.696	7.614	5.159	4.619	5.985	0.378	0.435	0.601	0.385

Appendix

Table 10: Per-instance internal wall time (seconds): median over three seeds. Bold marks the lowest unrounded time among the search methods. XG uses one construction.

	Stage 1		Stage 2
Job	M1	M2	M3	M4	Stage-2 due time
J1	1,200	1,500	900	1,200	4,200
J2	900	1,200	1,500	900	4,800
J3	1,800	1,200	1,200	1,500	5,400
J4	1,500	900	1,800	1,200	6,000
J5	1,200	1,800	900	1,500	6,600

Appendix

Table 11: Entirely synthetic workflow fixture. Entries under M1–M4 are alternative processing times in seconds, not consecutive visits to both machines. Each job uses one machine per stage.

Measure	Value
Sessions	24
Median session time (s)	44.5
Median tool calls	7
Median internal XH time (ms)	16.7
Median input tokens	163,176.5
Median output tokens	770.5

Appendix

Table 12: Measured effort for the 24 configuration and planning sessions. Token usage was recorded for every session. Input counts include cached context and repeated input across model calls.

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