AZIMUTH: What to plan for

How it works

1. 01

   Reconstruct the real demand

   AZIMUTH weights each day by the chance of an empty shelf, using SAROS's estimate, or sales and stock records. Sold-out days' sales set a minimum for demand; for items without SAROS's estimate, hourly sales project demand into the empty hours.

   • Posterior-mean imputation
   • Censored likelihood
2. 02

   Forecast the range of demand

   From corrected sales, prices, promotions, holidays and weather, AZIMUTH predicts each item's daily demand per location as a range of linked scenarios, capturing swings that many items and locations share. The simplest forecast stands unless another clearly lowers order costs.

   • Gradient-boosted trees
   • Negative binomial model
   • Gaussian copula
3. 03

   Turn scenarios into orders

   AZIMUTH corrects the scenarios for past forecast errors, projects stock until delivery and proposes orders in case packs, at the service level your costs justify. It picks the replenishment rule using a historical replay that reproduces past stock-outs and waste.

   • Newsvendor model
   • Isotonic regression
   • Simulation-based policy search
4. 04

   Measure the effect of price

   AZIMUTH proposes tests: paired sets of stores alternate high and low prices on groups of interchangeable items, measuring each group's response (and in some groups each item's), allowing for stock-outs. Past-sales estimates count only after tests correct and confirm them.

   • Randomised crossover design
   • Hierarchical Bayesian model
   • Random-effects meta-regression
5. 05

   Plan staffing and production output

   From forecast customer arrivals, AZIMUTH calculates how many people the checkouts need each hour and drafts rosters respecting Azerbaijan's Labour Code and your safety minimums. On production lines, it simulates stops, changeovers and scrap, then suggests how much output to commit.

   • Erlang queueing models
   • Constraint programming
   • Discrete-event simulation
6. 06

   Learn from each decision

   Each proposal reaches a person, who accepts it, overrides it or adjusts a forecast input. AZIMUTH logs every choice with its outcome, tracks which kinds of adjustment add value, and openly gives less weight to those shown to cost money.

   • Forecast value added
   • Empirical Bayes shrinkage
   • False discovery rate control

Published research

1. Sales are not demand

   When a shelf is empty, sales records understate demand, so forecasts built on them are too low for exactly the items that run out, and the next order is too small again. AZIMUTH builds on research that corrects for these gaps before forecasting, with what SAROS finds about when shelves were empty in the past as one input.

   • Huh et al. 2011 Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator. Operations Research.
   • Conlon & Mortimer 2013 Demand Estimation Under Incomplete Product Availability. American Economic Journal: Microeconomics.
   • Wang et al. 2025 FreshRetailNet-50K: A Stockout-Annotated Censored Demand Dataset for Latent Demand Recovery and Forecasting in Fresh Retail. arXiv preprint.

2. A range, not one number

   Forecasting research favours a range of likely outcomes over a single number, because a range shows how much stock or how many staff are needed to cover likely demand. In the M5 competitions on Walmart sales data, the leading methods for both single forecasts and ranges were gradient-boosted tree models (LightGBM) that learn from many items at once, rather than one item at a time. AZIMUTH builds on both findings.

   • Makridakis et al. 2022a M5 accuracy competition: Results, findings, and conclusions. International Journal of Forecasting.
   • Januschowski et al. 2022 Forecasting with trees. International Journal of Forecasting.
   • Makridakis et al. 2022b The M5 uncertainty competition: Results, findings and conclusions. International Journal of Forecasting.

3. The team decides

   An order depends on costs as well as on the forecast: the cost of an unsold loaf, set against the cost of an empty bread shelf, decides how much bread to order. Two field experiments in spare-parts retail, one of them at a car-parts retailer, found that letting buyers adjust the forecast that feeds the inventory system raised profit, while overriding the system's final decisions lowered it overall. So AZIMUTH proposes, the team corrects the forecast where it knows something the data do not, and a person signs off each order.

   • Huber et al. 2019 A data-driven newsvendor problem: From data to decision. European Journal of Operational Research.
   • Kesavan & Kushwaha 2020 Field Experiment on the Profit Implications of Merchants' Discretionary Power to Override Data-Driven Decision-Making Tools. Management Science.
   • Kesavan et al. 2026 Profit Implications of Judgmental Adjustments to Forecast Inputs: Evidence from a Large-Scale Field Experiment. Management Science.

4. Testing prices first

   Price effects estimated from ordinary sales data can mislead: in a 35-week price experiment at a grocery chain in the US Midwest, shoppers reacted to price about a sixth as strongly as the chain's ordinary scanner data suggested (Bray, Sanders and Stamatopoulos, 2024). AZIMUTH's estimate before a change is therefore a starting point, checked where it matters by a price test across matched groups of stores, and it allows for the part of a promotion's extra sales that comes from other items or other weeks.

   • Bray et al. 2024 Observational Price Variation in Scanner Data Does Not Reproduce Experimental Price Elasticities. SSRN working paper.
   • Gaur & Fisher 2005 In-Store Experiments to Determine the Impact of Price on Sales. Production and Operations Management.
   • van Heerde et al. 2004 Decomposing the Sales Promotion Bump with Store Data. Marketing Science.