# Assembly-line scheduling — QPC manufacturing pilot

## What this is

A **synthetic 3-line assembly scheduling** task in the Hernandez et al. (2026) problem class ([arXiv:2605.30252](https://arxiv.org/abs/2605.30252)): assign each job to exactly one of three parallel lines while balancing processing time, tardiness, and family changeover penalties.

The goal is **not** a production MES integration. The goal is to show that **three coupled production narratives** (line A / line B / line C contextures) can co-reside in **one polycontextural IBM Heron submission** with a declared operations KPI.

## Problem

| Parameter | Value |
|-----------|--------|
| Jobs | 12 |
| Lines | 3 (one-hot assignment per job) |
| Variables | 36 active (12 × 3) |
| Layout | 156Q Heron (3×52Q line contextures) |
| Instance seed | 77 |
| Shots | 8192 |

**Schedule cost** (decoder objective, lower is better): processing + tardiness + changeover HUBO energy on feasible one-hot assignments.

**Headline KPI**: **late jobs** — count of jobs whose assigned-line cost proxy exceeds threshold (decoder; lower is better).

## Three contextures

1. **Line A contexture** — jobs with family affinity A  
2. **Line B contexture** — jobs with family affinity B  
3. **Line C contexture** — jobs with family affinity C  

Transjunction bridges couple shared sequencing pressure across lines in one gate-native job.

## IBM Fez result (July 2026)

| Execution | Schedule cost (decoder) | Late jobs | Qubits | Depth | IBM job ID |
|-----------|-------------------------|-----------|--------|-------|------------|
| QPC polycontextural (one run) | **39.7936** | **0** | 156 | 116 | `d96daa0tcv6s73djknig` |

Classical greedy baseline schedule cost: **39.7936** (matched; polycontextural decoder reaches same feasible plan class on this instance).

## Lane B reporting

Headline **0 late jobs** uses QPC’s **declared problem decoder** on quantum samples — an operations KPI, not an ICC architecture witness. See [Joint Structure Challenge](../QPC_JOINT_STRUCTURE_CHALLENGE.html) for Lane A.

## Customer tryout

Hands-on bounded evaluation: [Optimization showcase](../QPC_OPTIMIZATION_SHOWCASE.html) — map context weights to three line priorities and email JSON to QPC.