SAROS: Where money is lost

How it works

1. 01

   Join and check the records

   CIO gathers records and sensor data, matches items, suppliers and locations across systems, and notes when each figure became known, estimating this for older history. SAROS flags incomplete sources, and stock movements that do not add up to book stock.

   • Fellegi–Sunter record linkage
2. 02

   Find hidden empty shelves

   When an item sells nothing for days while records show stock, SAROS judges how unusual that is, given the item's quiet spells. It estimates the chance that the shelf was empty, so lost sales are not mistaken for weak demand.

   • Negative binomial model
   • Markov chain
   • Bayes' rule
3. 03

   Estimate what should have happened

   Using seasons, holidays, prices and promotions, SAROS learns what was normal before any lasting change it detects, so persistent losses stay visible. It values missing stock at cost and lost sales at margin minus what substitutes recover, with simulated ranges.

   • Seasonal-trend decomposition
   • Gradient-boosted trees
   • Monte Carlo simulation
4. 04

   Flag unusual losses

   SAROS flags locations, categories, suppliers or production lines whose extra loss exceeds what past forecast errors can explain, while limiting the expected share of false alarms. It also tests all locations together and finds when lasting rises in loss began.

   • Conformal prediction
   • False discovery rate control
   • Change-point detection
5. 05

   Pinpoint where, then test why

   SAROS looks for locations, categories, suppliers or shifts carrying most of the extra loss, allowing for volume. If some locations switch supplier, it compares their change with those yet to switch, and says 'likely contributes' only if robustness checks pass.

   • Multidimensional localisation
   • Difference-in-differences
6. 06

   Rank what to fix first

   SAROS estimates what each loss would cost if left alone, given how long such losses last, pulling uncertain figures towards what is typical. It proposes the most valuable fixes your team has time for, marked 'check first' or 'act now'.

   • Empirical Bayes shrinkage
   • Knapsack optimisation
   • Value of information

Published research

1. Loss measured in money

   SAROS measures each loss as the gap between what should have happened and what did, in money, and builds on published loss categories for stores and plants. The records themselves are often wrong: one study found 65% of stock records inaccurate across 37 stores of one retailer (DeHoratius and Raman, 2008), so records are checked against stock counts first.

   • Beck 2018 Moving beyond shrinkage: developing a definition and typology of total retail loss. Security Journal.
   • Nakajima 1988 Introduction to TPM: Total Productive Maintenance. Productivity Press (book).
   • DeHoratius & Raman 2008 Inventory Record Inaccuracy: An Empirical Analysis. Management Science.

2. Finding what is unusual

   SAROS builds on methods that remove the usual daily, weekly and seasonal pattern from each series of figures and look at what is left, an approach with a long published record. Recent benchmark studies find that simple, well-tested methods often do as well as complex deep-learning ones, so any new method is tested on your own records first.

   • Cleveland et al. 1990 STL: A Seasonal-Trend Decomposition Procedure Based on Loess. Journal of Official Statistics.
   • Bandara et al. 2025 MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns. International Journal of Operational Research.
   • Liu & Paparrizos 2024 The Elephant in the Room: Towards A Reliable Time-Series Anomaly Detection Benchmark (TSB-AD). NeurIPS (Datasets and Benchmarks).
   • Wu & Keogh 2021 Current Time Series Anomaly Detection Benchmarks are Flawed and are Creating the Illusion of Progress. IEEE Transactions on Knowledge and Data Engineering.

3. Linked to, not caused by

   A pattern in past records shows what a loss is linked to, not what causes it: busy hours, for example, can bring both short staffing and higher shrinkage. SAROS says 'linked to' by default. It says 'likely contributes' only when an estimate made with causal methods from economics and medical research passes checks on how robust it is, and 'causes' only when a natural experiment, a staggered rollout or a controlled test supports it.

   • Hernán & Robins 2020 Causal Inference: What If. Chapman & Hall/CRC (book).
   • Chernozhukov et al. 2018 Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal.
   • Cinelli & Hazlett 2020 Making Sense of Sensitivity: Extending Omitted Variable Bias. Journal of the Royal Statistical Society Series B.

4. Ranking that allows for chance

   A small location can show an extreme loss rate by chance, and thousands of comparisons will produce some false alarms. SAROS builds on statistical methods used to compare hospitals and to test many results at once, so losses are ranked by what they cost and by how sure we can be.

   • Goldstein & Spiegelhalter 1996 League Tables and Their Limitations: Statistical Issues in Comparisons of Institutional Performance. Journal of the Royal Statistical Society Series A.
   • Spiegelhalter 2005 Funnel plots for comparing institutional performance. Statistics in Medicine.
   • Benjamini & Hochberg 1995 Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society Series B.