Multi-Level Marketing Network Bonus Calculation (MLM)

Problem Definition

In a multi-level marketing network, each member recruits other members, forming a recruitment tree. A member earns their own sales, plus a decayed share of the bonus earned by everyone they've personally recruited (who, in turn, already includes a decayed share of their own recruits' bonuses, and so on down the tree). This makes bonus computation a recursive aggregation over the recruitment tree: the payout for the whole downline collapses up towards the root, shrinking by a fixed decay factor at every level.

Test Data

# Recruit(sponsor, member): sponsor personally recruited member
Recruit("alice", "bob");
Recruit("alice", "carol");
Recruit("bob", "dave");
Recruit("bob", "erin");
Recruit("carol", "frank");

Sale("alice", 100.0);
Sale("bob", 200.0);
Sale("carol", 150.0);
Sale("dave", 300.0);
Sale("erin", 50.0);
Sale("frank", 400.0);

Solution

# A member's bonus starts with their own sales...
Bonus(x) += s :- Sale(x, s);

# ...plus half of the bonus earned by each person they recruited
Bonus(x) += 0.5 * Bonus(y) :- Recruit(x, y);

Expected Results

+-------+--------------+
| col0  | logica_value |
+-------+--------------+
| alice | 462.5        |
| bob   | 375.0        |
| carol | 350.0        |
| dave  | 300.0        |
| erin  | 50.0         |
| frank | 400.0        |
+-------+--------------+

Leaf members (dave, erin, frank) have no recruits, so their bonus is just their own sales. bob's bonus is his own sales (200) plus half of dave and erin's combined bonus (0.5 × 350 = 175), giving 375. alice's bonus then rolls up half of bob and carol's bonuses on top of her own sales: 100 + 0.5 × (375 + 350) = 462.5.