Overview
This study investigates methods for clearing invoices within supply networks to alleviate working-capital pressure caused by late payments. It introduces an atomic-record temporal invoice-graph methodology for path-enabled clearing and compares its performance against complete-candidate bounded-cycle netting. Both methods are evaluated under a causal daily greedy scheduling framework.
Research Context
Supply networks experience working-capital pressure propagation due to late payments, where individual firms often function as both creditors and debtors simultaneously. The research addresses this issue by focusing on mechanisms for efficient invoice clearing.
Approach
The core of the approach is an atomic-record temporal invoice-graph method. Each invoice is maintained as a residual record, detailing its issue date, due date, amount, and a unique identifier. A 'candidate' for clearing is defined as executable if sufficient source capacity is active on every supporting edge on a common day.
The study specifically details two primary clearing policies:
- Path-Enabled Clearing: This policy involves a non-bilateral two-edge path. Its function is to reduce two invoice legs and create a direct settlement instruction between the path's endpoints. This process preserves the net positions for all participants on the combined invoice-plus-instruction state. The methodology distinguishes between payable-mass reduction and invoice compression.
- Complete-Candidate Bounded-Cycle Netting: This is compared against the path-enabled clearing. The specific variant used for comparison is length-eight cycle netting.
Both policies operate within a causal daily greedy schedule. The empirical sequence used for evaluation comprised 749,952 invoices. These invoices were issued between 2012 and 2023, representing a total value of EUR99.705 billion. The system maintained one rolling state across annual boundaries, which allowed bridge invoices to be introduced once and ensured residual balances continued. The findings were tested for robustness through alternative ordering, mixed path-cycle policies, sensitivity to cycle length, component resampling, acceleration constraints, and fragment replay. Tractable full-information linear programs were also utilized to demonstrate path advantage and path-cycle complementarity.
Findings
- Path clearing achieved a 48.202% reduction in issue-cohort mass.
- Length-eight cycle netting achieved a 43.347% reduction in issue-cohort mass.
- Path clearing demonstrated an advantage of EUR4.841 billion and 4.855 percentage points over length-eight cycle netting.
- Path clearing materially led in ten issue cohorts.
- Path clearing was practically tied with cycle netting in the 2013 cohort.
- Path clearing trailed cycle netting in the 2012 cohort.
- In reciprocal 2022, where almost all local paths are contained within the cyclic core, path clearing maintained its lead.
- Tractable full-information linear programs indicated both a path advantage and a path-cycle complementarity.
Why This Matters
The findings establish a policy-level benefit for the proposed clearing mechanisms, particularly path clearing, in reducing invoice mass. This suggests potential for mitigating working-capital pressure within supply networks by enabling more efficient invoice settlement processes.
Potential Applications
The research motivates future development of asynchronous agent-to-agent clearing systems. Such systems could be built around specific operational components including deterministic common-day verification, private mandates, reservations, explicit consent, and atomic commit.