Which job on which machine, in what order, so the whole line finishes soonest? Job-shop scheduling is NP-hard the moment it matters. Our time-indexed formulation solves a real instance with QAOA and draws the answer as a Gantt chart your planner would recognise.
Machines wait on jobs and jobs wait on machines; the makespan hides in the ordering. Our demonstration found the exact weighted-shortest-processing-time optimum — at 19.5× the guessing rate, our strongest QAOA result.
Setup times turn a schedule into a routing problem in disguise. Both live naturally in the same time-indexed QUBO.
Crewing the line has the same shape as sequencing it — coverage, quals, fairness — and reuses the same machinery.
One cell, one week of orders — we encode jobs, machines, and precedence into a time-indexed QUBO, with your planner checking that the constraints are the real ones.
QAOA training with every evaluation a real circuit run; results rendered as Gantt charts next to the optimum your current scheduler produces.
Instance sizes that work, the projected crossover, and what to instrument now so your data is formulation-ready — pursue, park, or drop.
These programs are published in our algorithm library. The numbers below come from recorded executions we can reproduce on demand.
Time-indexed job-shop scheduling trained with QAOA.
Measured: Best feasible sample was the exact weighted-shortest-processing-time optimum, at 19.5× the guessing rate.
Crew rostering with coverage and fairness penalties.
Measured: Best sampled roster satisfied every hard constraint.
Results are from the library items' own recorded runs on our simulator — the same one your browser uses.
A production MES schedules thousands of operations; today's quantum instances are tens. The value now is the formulation and the team that knows how to write it — not a swap-in scheduler.
Jobs, machines, precedence — anonymised is fine. An engineer replies with the formulation sketch.