The five strategies

Also in the app

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All five strategies share one constraint engine and one cost function. They differ only in how they decide the order and scope of assignments, which is what makes the comparison fair.

Greedy

Takes jobs in priority, then deadline, order, and gives each to the cheapest feasible engineer. Never revisits a choice. Instant and the easiest to explain, but an early choice can block a later, tighter job.

Hungarian

Finds the optimal engineer-to-job matching for one round (Kuhn–Munkres), commits it, and repeats until no feasible pair is left. The fastest response to tool-downs and the most even workload, but it builds up idle time because it plans one round at a time, so its plans cost more.

Regret-2

Places first the job with the most to lose: the largest gap between its best and second-best engineer. That protects scarce certifications, so a job only one person can do isn't left stranded.

ALNS

Adaptive large neighbourhood search: repeatedly removes part of the plan and repairs it, keeping changes that lower the cost. It optimises the exact objective, including workload balance. About 6% from the proven optimum on full-size shifts, and the closest of the five in the lithography crunch, where scarce certifications dominate the cost.

PyVRP

The PyVRP library's iterated local search (C++ core), warm-started from Regret-2. PyVRP is the open-source solver whose hybrid genetic search won the recent VRPTW competitions; the version used here runs its iterated local search, a different algorithm from the same library. It had the lowest cost in 50 of 80 benchmark shifts (ALNS in 31), mostly by cutting idle wait, and is about 4% from the proven optimum on full-size shifts. On the normal shift it is tied with ALNS; when tool-downs are only known as they happen, it is rarely measurably cheaper than the simple strategies.

Exact solver

Not a live dispatch option: it enumerates every feasible route and solves a set-partitioning problem to find the proven optimum. It works at full shift size (about a minute on average on a laptop, up to about 13 minutes for the hardest shift; it depends on the hardware), which suits planning ahead but not a hosted request: the live app's API has a 60-second limit, so the Benchmark view's Measure gaps proves small shifts (4 engineers × 12 jobs) and returns in seconds. The full-size proofs, 80 shifts at 14 × 45, are in the analysis.

When each one wins

Situation	Best choice
You need an answer instantly	Greedy
Tool-downs arrive during the shift (live)	Greedy is a sound choice: in a replay with tool-downs revealed as they happen, it was never measurably dearer than PyVRP
Tool-downs must be answered fastest, or fairness matters most	Hungarian
Scarce certifications	Regret-2 at minimum; ALNS in a lithography crunch
Lowest cost on a shift known in advance	PyVRP or ALNS (tied on a normal shift; PyVRP ahead in a surge or when overstaffed)
Closest to the proven optimum at full shift size	PyVRP overall (3.9% mean gap over 80 proven shifts; ALNS 5.7%), ALNS in the lithography crunch. On small 4 × 12 shifts both are within 0.2%, which is why small shifts can't tell them apart: see the analysis.
Certified engineers have run out	None: every strategy hits the same ceiling. It's a staffing problem.