ECCO’s Interactive Assortment Recommender co-designs seasonal shoe ranges and store allocations inside one stochastic Mixed Integer Programme, reaching the 2026 Edelman final; Google’s carbon-aware compute scheduler strips megatonnes of emissions by shifting batch jobs across regions and hours; and today’s term is Distributionally Robust Optimisation, the hedge against being wrong about the probability distribution itself.
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This is the Decision Optimisation Radar for 22 April 2026. Today’s thread: two INFORMS 2026 Franz Edelman finalists whose submissions translate cleanly into reference designs for practitioners, plus two arXiv papers that push exact and distributionally robust methods into production-adjacent territory.
First, ECCO Sko A/S is a 2026 Edelman finalist for its Interactive Assortment Recommender. The model treats seasonal assortment design and initial store allocation as a single two-stage stochastic Mixed Integer Programme: the first stage chooses which two hundred styles enter the seasonal range, the second stage best-responds with per-store first-shipment quantities under each demand scenario. A scenario-generation pipeline supplies the recourse uncertainty, and column generation over assortment templates carries the combinatorial load that would otherwise make the extensive form intractable. Reported production impact is double-digit margin uplift and a material reduction in end-of-season markdowns across ECCO’s global retail footprint. Today’s Case Study walks through the formulation and the two-layer decomposition.
Second, Google’s Edelman submission is a carbon-aware compute scheduler. The model fuses real-time grid carbon-intensity forecasts with datacentre region and time-window capacity, and makes the time-shift-versus-region-shift decomposition explicit. Reported impact is a multi-million-tonne annual carbon-dioxide-equivalent reduction with under one percent latency-budget impact on user-facing workloads, on the strength of a shadow-price interpretation of the carbon objective that tells the operator where further savings would cost what.
On the research side, arXiv 2604.16064 closes a long-standing gap in exact Vehicle Routing Problem methods by handling temporal-dependency constraints (synchronisation, precedence, and bounded lag between visits on different vehicles) inside an arc-flow branch-and-cut formulation. The authors report more than ninety percent of instances closed within an hour at fleet sizes up to fifty vehicles. A second paper, arXiv 2604.06548, tackles multi-season NBA franchise roster and payroll planning as a rolling-horizon stochastic programme with a Conditional Value at Risk objective and a Wasserstein-ball distributional hedge against cap-inflation and player-performance regime shifts. On twelve seasons of public contract data the authors report a four-to-six percent expected cap-efficiency gain versus a deterministic baseline and a forty-percent tail-cost reduction versus the same stochastic programme without the distributional hedge.
Today’s term is Distributionally Robust Optimisation. Distributionally Robust Optimisation is the practice of making decisions that perform well not against a single probability distribution, but against the worst-case expected cost over a whole family of plausible distributions sitting inside an ambiguity set around your empirical estimate. As the ambiguity set shrinks to a single distribution the model collapses to classical stochastic programming; as the set grows to include everything, the model collapses to classical robust optimisation. One-line version: Distributionally Robust Optimisation is a hedge against being wrong about the probability distribution you assumed, not just against bad outcomes under the distribution you trust. That’s the Radar.
Industry Signals
ECCO Sko Reaches 2026 Franz Edelman Final with Stochastic MIP Assortment Recommender Co-Designing Season Assortments and Store Allocations 🔗
Foundation: A global shoe retailer has to decide months before a season starts which roughly two hundred styles to include in its range and how to split each style’s first-shipment quantity across every store, under uncertainty about what will sell where. Historically this runs as two separate tools: a merchandising team picks the assortment against last season’s curves, an allocation engine then fans out initial quantities store by store, and the two optimise against different objectives. ECCO’s Interactive Assortment Recommender (IAR) rewrites the split as a single two-stage program — the first stage chooses which styles enter the range, the second stage best-responds with store-level quantities under each demand scenario, and the whole thing is solved as one Mixed Integer Programme (MIP)A linear program with some variables restricted to integer values; the workhorse of discrete optimisation..
INFORMS Analytics profiles ECCO Sko A/S as a 2026 Franz Edelman Award finalist for the IAR. The model runs over millions of store-week-SKU (Stock Keeping Unit) cells in the second stage and is solved with a custom pipeline that generates demand scenarios for the recourse layer and layers Column GenerationSolves linear programs with enormous variable counts by starting from a restricted master and iteratively pricing in new columns via a subproblem. over assortment templates at the first stage to carry the combinatorial load. Reported production impact is double-digit margin uplift and a material reduction in end-of-season markdowns across ECCO’s global retail footprint. The deployment write-up below details problem, formulation, decomposition, and operational impact.
Source: INFORMS Analytics · 2026 Edelman Finalists · Apr 2026📋 Case Study below ↓Google Wins Edelman Finalist Recognition for Carbon-Aware Compute Scheduler That Shifts Batch Jobs Across Regions and Hours at Hyperscale 🔗
Foundation: Hyperscale datacentre workloads divide into two tiers: user-facing queries that must run now in the region the user hit, and batch jobs such as training, indexing, and analytics that can tolerate minutes or hours of deferral and can be routed to a different region entirely. Electricity grid carbon intensity, measured in grams of carbon dioxide per kilowatt-hour, varies by a factor of three across regions and hours of the day. A scheduler that moves batch work toward low-carbon regions and low-carbon hours can strip megatonnes of emissions from the compute footprint without slowing user requests, provided it respects latency budgets and capacity limits at the target destinations.
INFORMS announced the 2026 Franz Edelman Award finalists at the Analytics+ conference in Indianapolis on 12 to 14 April 2026. Google’s submission documents a multi-objective MIP that fuses real-time grid carbon-intensity forecasts with datacentre region and time-window capacity, and makes the time-shift-versus-region-shift decomposition explicit. Reported impact is a multi-million-tonne annual carbon-dioxide-equivalent reduction with under one percent latency-budget impact on user-facing workloads.
Research Papers
Exact Branch-and-Cut Formulation Closes Ninety Percent of Temporally Coupled Vehicle Routing Problems in an Hour at Fifty-Vehicle Fleets 🔗
Foundation: Consider a home-care worker doing a blood draw at a patient’s house followed by a sample drop at a regional lab: the two visits must be in order, and the gap cannot exceed a fixed window or the sample spoils. Classical Vehicle Routing Problem (VRP)Assigns a fleet of vehicles to visit customers, minimising total travel while respecting capacity and time-window constraints. models enforce only per-visit time windows, so they cannot express precedence, synchronisation, or bounded lag between two visits on two different vehicles. Temporal dependency constraints fill that gap, and getting them into an exact branch-and-cut formulation at realistic fleet size is what this paper does.
Submitted to arXiv on 17 April 2026, the paper (arXiv:2604.16064) introduces VRP variants with explicit temporal-dependency constraints over pairs of visits: synchronisation (visits must occur together), precedence (one must precede another), and bounded lag between service times. Two exact formulations are developed, a compact MIP and an arc-flow reformulation with dependency cuts, alongside a hybrid column-generation plus branch-and-cut approach. On newly generated benchmarks the arc-flow formulation closes more than ninety percent of instances within an hour at fleet sizes up to fifty vehicles.
Rolling-Horizon DRO-CVaR Trims NBA Franchise Tail Payroll Cost Forty Percent Versus Risk-Neutral Stochastic Programming on Twelve Seasons 🔗
Foundation: A National Basketball Association (NBA) general manager signs a four-year contract today whose cost will depend on where the salary cap lands three years out, whether the player stays healthy, and how trade value evolves across two collective-bargaining windows. Each of those drivers is uncertain, and the empirical distributions estimated from historical data are themselves suspect because the league’s economic regime shifts with every new television deal. Distributionally Robust Optimisation is the tool that hedges against this second-order uncertainty: instead of trusting one empirical distribution, it takes the worst-case expected cost over a whole ambiguity set of plausible distributions close to the one observed.
Submitted to arXiv on 8 April 2026, the paper (arXiv:2604.06548) formulates multi-season roster and payroll planning as a Stochastic Programming (SP)Optimisation under uncertainty modelled by explicit probability distributions, typically expressed via scenarios and recourse. model solved on a Rolling HorizonRe-solves a finite-horizon planning problem periodically, applying only the first-period decisions and rolling forward as new data arrives. with a Conditional Value at Risk (CVaR)A coherent tail-risk measure equal to the expected loss conditional on exceeding the Value-at-Risk threshold; admits a linear-program reformulation via the Rockafellar-Uryasev identity. objective, and adds a Wasserstein-ball ambiguity set that hedges against cap-inflation and player-decay regime shifts. Contracts, draft picks, and free-agent signings are decision variables. On twelve seasons of public contract data the authors report a four-to-six percent expected cap-efficiency gain versus a deterministic rolling-horizon baseline and a forty-percent tail-cost reduction versus the same risk-neutral stochastic programme.
Term of the Day
Distributionally Robust Optimisation
“Essentially, all models are wrong, but some are useful.” — George E. P. Box, Science and Statistics (1976)
Distributionally Robust Optimisation (DRO) is the practice of making decisions that perform well not against a single probability distribution, but against the worst-case expected cost over a whole family of plausible distributions. You specify an ambiguity set, a ball of distributions around the one you estimated from data, and the optimiser hedges against everything inside it. The output is a decision whose expected cost is guaranteed regardless of which distribution in the set turns out to be correct, and the cost of that hedge is a single tunable parameter: the radius of the ball.
A concrete example
A retailer needs to set next season’s order quantity for a new product and has two years of demand history, giving an empirical distribution of historical weekly demand. Classical Stochastic Programming would plug that empirical distribution directly into an expected-cost objective. The trouble is that two years is a short sample, and next year might look nothing like the last two if a competitor enters the category or a recession starts.
A Distributionally Robust planner does not trust the empirical distribution. The planner draws a ball around it in Wasserstein distance (an optimal-transport metric that measures how much probability mass must be moved to turn one distribution into another) and says: whatever the true demand distribution is, it lives somewhere inside this ball. The order quantity is then chosen to minimise the worst-case expected cost over every distribution in the ball.
As the ball shrinks to a single point, DRO collapses to classical Stochastic Programming. As the ball grows to include every distribution on the demand support, DRO collapses to worst-case robust optimisation (which hedges against the worst parameter value, not the worst distribution). The radius is a tunable knob between the two extremes, and its value is usually chosen so the ball covers the data-generating distribution with a specified confidence.
Why practitioners misread this
It is not classical robust optimisation. Classical robust optimisation specifies an uncertainty set over parameter values, not distributions, and hedges against the worst parameter realisation inside that set. Distributionally Robust Optimisation specifies an ambiguity set over distributions and hedges against the worst expected value across that set. The distinction matters because DRO’s optimal decision is typically less conservative than classical robust optimisation’s: it exploits the fact that all distributions inside the ball share structure (for example, the same empirical mean), even when you cannot say which one is correct.
The distributional hedge is cheaper than it looks. Because DRO only needs to defend against distributions close to the empirical estimate (not all distributions on the support), its expected cost lands between Stochastic Programming and classical robust optimisation. For Wasserstein-ball DRO, recent results show the distributional hedge often costs only a fraction of a percent in expected performance while eliminating most tail risk, which is why it has become the default for risk-sensitive decision problems where data is short and regimes shift.
Not all ambiguity sets are equivalent. Two constructions dominate in practice. Wasserstein balls define neighbourhood via optimal-transport cost and are data-driven (the centre is the empirical distribution). Moment-based sets fix the mean and covariance and allow anything satisfying those moments. Wasserstein gives tighter results when data is available and a story about data noise is defensible. Moment-based gives tighter results when you have strong prior information about moments but not the full distribution. The two reformulate into different convex optimisation problems, so the choice of ambiguity set determines both the answer and the solver.
Where this shows up in practice
Distributionally Robust Optimisation appears in supply-chain inventory positioning when demand history is short or the market is shifting, in energy dispatch and storage control when renewable-generation forecasts drift, in portfolio optimisation where return distributions cannot be trusted beyond a window, and increasingly in machine learning (specifically distributionally robust risk minimisation) where the training distribution differs from the deployment distribution. The diagnostic question when you see a paper or product claim ‘robust optimisation’ is whether the uncertainty is over outcomes (classical robust), over distributions (DRO), or simply over a known distribution (stochastic). The choice determines the conservatism profile, the solver structure, and the tuning surface the user actually interacts with.
- ECCO IAR ECCO’s Interactive Assortment Recommender shows that a seasonal assortment decision (which styles enter the range) and a per-store first-shipment allocation can be co-designed inside one two-stage stochastic Mixed Integer Programme, provided column generation over assortment templates is used to manage the combinatorial load on the master.
- Google Carbon Google’s carbon-aware compute scheduler treats region-shift and time-shift as explicit decomposition layers and fuses real-time grid carbon intensity with datacentre capacity, demonstrating that carbon can be a first-class second objective on an existing scheduling Mixed Integer Programme with under one percent latency-budget impact on user-facing workloads.
- Temporal VRP Exact branch-and-cut for Vehicle Routing Problems with temporal-dependency constraints (synchronisation, precedence, bounded lag) closes more than ninety percent of instances within an hour at fleet sizes up to fifty, filling a gap that field-service and home-delivery teams have patched with heuristic extensions on top of standard time-window solvers.
- NBA DRO-CVaR Multi-season NBA roster and payroll planning under a rolling-horizon stochastic programme with a Conditional Value at Risk objective and a Wasserstein-ball distributional hedge reports a forty-percent tail-cost reduction versus the same model without the hedge, across twelve seasons of public contract data.