The Model
Every plan is one mixed-integer program covering every recipe and facility at once, solved with HiGHS. Each recipe your facility levels and modules unlock, \(r\), gets a rate \(b_r\) (batches per second) and a whole number of units \(u_r\) set to it: plots for a crop, machines for a processed item.
\[ \max \ \sum_i p_i \, s_i \;-\; \sum_r c_r \, b_r \]
where \(s_i\) is how much of item \(i\) is sold per second at price \(p_i\), and \(c_r\) is a crop's seed cost. During the Harvest Moon Festival, season crops' seeds cost Moonray Wheat instead, which plans take as unlimited. Subject to:
- Whole units. \(b_r \, t_r \le u_r\), with \(u_r\) a whole number and \(t_r\) the time per batch. A unit runs one recipe and is left running.
- Item balance. Everything made covers what other recipes use plus what's sold. A quick variant makes the same item as the regular one.
- What you own. For every facility and level \(L\), the units on recipes needing level \(L\) or higher add up to at most what you own at that level. A higher-level plot can run a lower-level recipe.
- Growing environments. A crop wanting Cool, Warm, Freeze or Scorching grows at full speed on a plot covered by a Heat Furnace or Cooling Unit set to that mode, and more slowly on an uncovered one (see below). An Adequate crop needs a Sunlamp and grows nowhere else.
HiGHS proves the plan is the best possible. On the rare setup where that takes longer than 30 seconds, it stops with the best plan so far and the results say how far from the best it could be. Every plan is then re-checked on its own before it's shown.
Time per Batch
Crops and trees take their grow time, less the Aniimo's watering: a plot asks for water twice as it grows, at two thirds and at one third of its time left, and each watering takes an eighth of the crop's own time off. A 40-minute crop comes in at 30 and a 4-minute one at 3. A crop short of its environment grows slower but still loses the same minutes, so a Warm crop with no building takes 50 minutes and is watered down to 40; that part isn't checked in game yet.
Everything else has a workload, and how long it takes depends on the Aniimo's Efficiency \(e\), which the facility screen shows, and a base rate \(r\):
\[ t = \frac{\text{workload}}{r \times e \times 1.2^{\,\text{personality}}} \]
At a processor, \(r\) is one workload a second. At a gathering facility (Well, Mine, Sandcastle, Dewy House and the like) and at the Dance Pad Polisher and Aniipod Maker, it's higher on recipes needing a higher ability level: 1 a second at level 1, 1.25 at level 2 and 1.5 at level 3. A Growth Fruit, 5,400 workload, takes an hour at 100%.
Efficiency \(e\) depends on the Aniimo's ability level compared with the level the recipe needs. At exactly the needed level it's 100%. At a processor, one level above the recipe's need is 300%, and each level after that adds 100% (400%, 500%). At a gathering facility, each level above adds half a workload a second, whatever the recipe needs, so against the recipe's own base rate that reads as +50% a level on a level-1 recipe, +40% on a level-2 one and +33% on a level-3 one. The Dance Pad Polisher and Aniipod Maker add 40% a level. The personality term counts only when the Aniimo has the facility's personality (+20%); the Polisher and Aniipod Maker have none. Ability levels stop at 4.
Environment Coverage
Environments are steps of temperature: Freeze -2, Cool -1, no building 0, Warm +1, Scorching +2. A crop grows at 100% at its own, 80% one step away, 50% two steps and 20% beyond that. An uncovered plot is neutral, so a Cool or Warm crop still manages 80% and a Freeze or Scorching one 50%, which is why plans sometimes grow them with no building at all. Adequate is separate: those crops need a Sunlamp. Efficiency stretches the grow time, so a Rose at 80% takes 50m instead of 40m for the same 8 roses, before watering.
Temperatures add where two buildings both reach a plot, capped at -2 and +2, and the game shows the result on the plot itself: Scorching and Cool together read Warm, Warm and Cool read Room temp. Plans use that, so a Heat Furnace on Scorching with four tiles of space to a Cooling Unit on Cool covers three zones at once, Scorching, Warm between them and Cool. Where the second building sits decides the split: every placement whose coverage still overlaps the first is worked out, in a row or on the diagonal, from touching (6 plots, 24 in the middle and 6, for Farmland) out to a corner's worth of overlap (22, 10 and 22). Two buildings this close cover fewer plots in total than two standing apart, so a plan only does it when the third zone is worth more. Place the pair exactly as the plan's diagram shows, and keep any other building's area clear of them.
A Cooling Unit is 2×2 tiles, and a Heat Furnace and Sunlamp one tile each; each covers a 9×9 area centered on it. A plot counts as covered if any part of it is inside, and everything snaps to quarter tiles. Every useful way one building can cover a mix of Farmland, Woodland and the rest is worked out once by exact packing; the plan then picks a mode and one of those mixes for each building.
Level Up
A level-up costs Home Coins \(C_0\) plus the materials it asks for, \(C_1\) and \(C_2\) (raw Wood Blocks and Mineral Sand up to RV 6, a Woodworking Bench item and a Chimney Kiln item from RV 7), and you may already have some of each, \(S_j\). The plan finds the most level-ups per day, \(\lambda\), it could keep up, where for Home Coins and each item:
\[ \text{made}_j \ \ge\ \frac{\lambda \, (C_j - S_j)}{86400} \]
(\(\text{made}_j\) per second), so the level-up takes \(1/\lambda\) days. Stock of anything lower in a chain (Wood Blocks, Mineral Sand, a lower tier) counts toward what's made, since the Bench and Kiln process it up. Two more solves follow, each keeping what the last one found: the most Home Coins at that pace, then as much extra of the level-up items as spare Bench and Kiln time allows. That's why ore often finishes before wood and shows up as surplus.
Each tier takes 8 of the tier below (4 for the last), so the Bench and Kiln switch between tiers rather than running one recipe like other processors.
Priorities
The plan solves once per ticked priority, in your order. Each solve makes as much of its priority as it can while keeping at least what the earlier ones reached; a last solve then earns as many Home Coins as all of those leave room for. Aniimo EXP, Aniipods and, during the Harvest Moon Festival, Harvest Moon Points count as their own currencies, so the same model handles them like Home Coins.
Time to Reach a Goal
Each product starts adding up once its first batch clears its ingredient chain (its lead time), then keeps its steady rate:
\[ \text{amount}(t) = \sum_i \text{rate}_i \cdot \max(0,\ t - \text{lead}_i) \]
This only ever grows with \(t\), so the time to reach a target is found by binary search.
The Backup Planner
If the exact planner can't run (rare; reloading the page usually fixes it), an older planner steps in. It solves the same problem as a continuous linear program, rounds to whole plots and one recipe per machine, then re-solves. Its plans are usually close to the best but not guaranteed, and the results say when it was used.