WOW, sort this bag, this is a paralleled mess !

Bagnon is an add-on by Jaliborc for World of Warcraft (WOW), which has a sorting feature included. The goal of this challenge is to make this sorting faster. The winner gets to be ported to Lua and gets to be proposed as a merge request in WildPants the sorting library that Bagnon and Combductor rely on. This would affect a lot of WOW players. Please don't flood Jaliborc with an inferior algorithm, the man is busy.

• In WOW, there are up to 5 bags with each a number of slots. From 20 slots (just the starting bag) to 164 slots (20 + 4 = 36 slot bags). There is also a 98 slots bag (the reagent bank), and the bank itself which has between 28 (starting bank space), and a maximum of 280 slots (28 + 7 = 36 slots bags).
• Bags and items have types: There are special bags that can only contain one type of object. For example, quivers can only contain arrows, but arrows can be stored everywhere.
• Items have a stack size: A stack of 200 arrows take a slot, but a sword takes a single slot.
• Item cannot be together in the same slot: One arrow alone takes the full slot.

Bagnon hides this from the user by creating a single bag that you can sort. Bank bags and reagent bags are sorted less often and independently to the player bags.

In order to sort the bag, you need to move the item. A move is done by calling the WOW API:

• Moving something can fail if the slot does not accept this type of object.
• Moving something to a slot where another item exists invert item position, and it can fail if one of the slots does not accept these types of items.
• Moving an item that can be stacked from a slot A to slot B where the same object exists, makes the stack in slot B bigger, and every item that overflow goes into slot A (slot A can become empty as a result).

Moving an item requires a server call and is one of the two limiting factors. Let's call this serverDelayTime. If you try to move an item again faster than the serverDelayTime it will fail.

The sorting can be parallelized: every serverDelayTime you can exchange the position of multiple items as long as no action occurred on any of them. Although some clients freeze when you move too many objects this way at the same time. This can vary between clients with their PC performances. Let's call this second limiting factor maxConcurrentMove (Value is from 1 for two objects moved at a time to 140 for every object in the biggest bank moved at the same time).

Input: List of items with their id, their bag, slot, the number of item in the stack and the type. Bags with their number, the type they accept and their size.

items = [
    {"id": 1, "bag": 1, "slot": 4, "stack": 20, "type": 0},
    {"id": 5, "bag": 1, "slot": 5, "stack": 200, "itemCount": 187, "type": 3},
    {"id": 5, "bag": 1, "slot": 15, "stack": 200, "itemCount": 25, "type": 3},
]
bags = [
    {"bag": 0, "types": [0, 1, 2, 3], "size": 20},
    {"bag": 1, "types": [0, 1, 2, 3], "size": 16},
    {"bag": 2, "types": [0, 1, 2, 3], "size": 14},
    {"bag": 2, "types": [3], "size": 14},
]

Output: List of tick calls. Each tick is a list of move calls.

[
    [
        "b1 s4 => b0 s0",
        "b1 s5 => b2 s0",
        "b1 s15 => b2 s0",  # This stack overflow, and 12 items will stay in b1 s15
    ],
    [
        "b1 s15 => b2 s1",
    ],
]

Applying all the moves must return sorted bags. Ie: item's id are from smallest to biggest.

This is a real-world algorithm, so of course, the theoretically faster algorithm wins ! The objective is to sort the bag in the less possible ticks of serverDelayTime while respecting the maxConcurrentMove limit and without moving anything to a forbidden bag. For the same number of ticks, the winner is the one with the least move call.