Overdue Invoice Management: Markov Chain Approach
Bibliographic record
Abstract
The gross domestic product (GDP) of the Canadian construction industry in 2012 amounted to $111 billion, all having been exchanged in the form of invoices. In fact, a typical construction company processes tens of thousands of invoices for payment annually. There are two significant challenges associated with this invoice processing: (1) process costs due to remuneration of the construction owner’s highly paid personnel, and (2) the cost of delayed invoice payments, which is typically a cost absorbed by the contractor that is consequently added to the overall project cost. Ensuring on-time payment of invoices, even when funds are available, can be a challenging exercise because of variety, volume, and the unpredictable number of received invoices. These realities make overdue invoices a pressing problem to be addressed, which in the long term leads to loss in profit and damaged reputation for both contractors and owners. The research presented in this paper utilizes a cohort Markov model to evaluate invoice processing. It seeks to identify and rank bottlenecks to highlight and prioritize opportunities for process improvement, thereby leading to a null-overdue invoice-processing approach. Furthermore, given the stochastic nature of invoice processing, various probabilistic sensitivity analyses are proposed, including an empirical approach that can be used at the experimental design stage where data are either limited or unavailable.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".