Noodle shop shift-structure analyzer - schedule to the order curve and the broth clock, break the lunch peak into half-hours, convert flat blocks into staggered shifts

You are a scheduling analyst for a noodle shop. Analyze how
well our shift structure matches the order curve and produce
a person-by-person revised roster.

Inputs I will provide:
- Four weeks of POS order counts per half-hour slot (every
  slot within opening hours)
- Current roster: each person / position / start / end /
  skill tags (can they pull noodles, make broth, run the
  register)
- Noodle-station load ceiling: how many bowls one noodle cook
  can steadily turn out per half hour (I will give our
  measured peak value, or give me the method to measure it
  first)
- Part-timer availability: the hours each current part-timer
  can work
- Hard constraints: the broth firing time (that shift may be
  re-staffed but never cut or delayed to just before lunch),
  the consecutive-days cap, and the maximum single-person
  weekly-hours change acceptable in one adjustment

Analysis steps:
1. Cut each day into five segments: broth and prep (before
   open) / lunch peak 11:00-13:30 / afternoon valley /
   dinner peak 17:00-20:00 / close, half an hour as the
   minimum granularity
2. For every half-hour slot compute three numbers: total
   staff on, noodle-station cooks on, and load as slot
   orders divided by noodle cooks on
3. Diagnose three failure modes (fixed categories, no
   additions):
   One, under-manning at peak: 3 or more consecutive
   half-hour slots inside lunch or dinner with load above
   the ceiling
   Two, crowding in the valley: total valley headcount above
   my stated fraction of peak headcount - the valley holding
   more people than the peak is a structure problem
   Three, skill gap: a peak slot with adequate total headcount
   but zero noodle cooks (or one, with load over the
   ceiling) - not short of hands, short of hands that can
   pull noodles

Output format:
- Load table: segment / representative half-hour slot /
  orders / total staff / noodle cooks / load / over ceiling
  (four-week averages)
- One detail table per failure mode: the slots involved /
  severity / which shifts they implicate
- Revised roster: one line per person "current shift ->
  suggested shift," part-timers with exact clock-in and
  clock-out; the broth shift on its own line naming who
  guards it; each adjustment with its verification method -
  which range next week's load in the same slots should fall
  into, or what should happen to peak ticket times
- A final column: each person's weekly-hours change (never
  beyond my stated acceptable margin)

Constraints:
- No forecasts of revenue, order count, or productivity
  percentages after the change - scheduling moves serving
  capacity, not customer traffic, and cannot claim credit
  for the latter
- Part-timer suggestions must land inside the availability I
  gave; do not invent part-timers who can come anytime
- The broth shift may be re-staffed, never cut or delayed to
  pre-lunch - delaying the firing time is not a scheduling
  suggestion, it is a different broth
- No "optimize the schedule" or "improve labor efficiency"
  phrasing; no generic advice beyond the roster itself

Why it is written this way

Half-hour granularity is the smallest usable tick for noodle-shop analysis. The lunch peak here is a spike, not a block: inside 11:00-13:30 the truly crushing stretch is 11:30-13:00, which hourly averaging flattens away and daily totals hide entirely. A half hour is the rhythm of one cook's pot and one table turn - capacity and demand line up at that scale. Any coarser, and the analysis describes an "average day" that never actually happens.

Separating headcount from noodle-station count makes the kitchen's real constraint explicit. A noodle shop BOH runs five or six people of whom perhaps three can pull noodles: at a slot with enough bodies but not enough noodle cooks, adding servers or bussers accomplishes nothing - the only fixes are staggering the noodle cooks' breaks or training another one. Generic scheduling analysis counts heads, which misdiagnoses such slots as "adequately staffed" or "generically short"; once the split exists, the skill gap separates out of the fog phrase "we're slammed" and becomes a nameable problem with nameable solutions (training, shadowing, station assignment).

Writing the broth shift as an uncancellable anchor guards against the model's favorite mistake: to a scheduling algorithm, any shift that produces no orders looks like waste. Cut the early broth shift and the roster instantly looks tighter - and the next day the broth runs short or wrong, a cost completely invisible in four weeks of order data. The firing time also hard-bounds the rest gap between closing shift and next morning's opener, which is exactly where noodle shops hide their compliance problems, so it must enter as a hard constraint from line one, not as a repair afterward.

Person-by-person changes with a bounded margin exist because the real resistance to a new roster is never the data - it is people whose routines get rewritten. Small moves with verification windows, then a second step informed by next week's numbers: shift-structure change is a sequence of small steps, not one teardown. The built-in verification window also protects the supervisor politically: if next week's numbers land outside the window, the assumption behind that adjustment was wrong, and it gets rolled back without an argument.

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