Three companies. Fewer payments.
Imagine three businesses all owing money to one another. Before moving any cash, add up what each business should receive and what it should pay. Only the difference needs to move.
Try the numbers ↓Write down the promises.
A owes B, B owes C, and C owes A. Adding those promises gives gross settlement: the amount that would move if every invoice were paid separately.
Find the net position.
For each company, subtract money owed from money due in. A negative result means it pays; a positive result means it receives. The three results always add to zero.
Send only what is still owed.
Match net payers directly to net receivers. With unrestricted routes and equal costs, the smallest amount that must move is the sum of all positive net balances.
Money moved = sum of the amounts net receivers are owed
A worked example
If A owes B $100,000, B owes C $80,000, and C owes A $60,000, the original payments total $240,000. A ends up owing $40,000, while B and C each receive $20,000. Just $40,000 moves; $200,000 of movement disappears.