Insights
How we think about decisions under uncertainty.
Articles and white papers on supply chain economics, optimization, and decision science, written by the people who do the work.
Field notes
Long-form write-ups of real work: the problem, the model, what was reported, and what transfers. Each states its evidence plainly.
All articles
- Optimization / Sep 22, 2026 Every Constraint Needs an Owner A practical guide to constraint provenance: how to trace optimization rules back to physical limits, contracts, economics, policies, and the people authorized to change them.
- Optimization / Sep 18, 2026 Measure Stability Before You Constrain It How to measure planning churn before adding stability constraints, separate natural stability from forced stability, and avoid fixing the wrong problem in production optimization.
- Optimization / Sep 15, 2026 Shadow Prices Are Business Signals A practical guide to using LP dual values to understand scarce resources, challenge constraints, prioritize capacity, and improve optimization models without pretending every dual is a literal price.
- Decision Science / Sep 11, 2026 Policy Parameters Are Products A practical guide to treating thresholds, horizons, penalties, service targets, and other optimization policy parameters as production decisions that need ownership, tuning, validation, and monitoring.
- Decision Science / Sep 8, 2026 Decision Latency Is a Model Input A practical guide to modeling the time between observing the world and executing a decision, and why ignoring that delay can make an otherwise good optimization policy fail in production.
- Optimization / Sep 6, 2026 The MIP Gap Is a Decision Bound A practical guide to interpreting MIP gaps as bounds on the modeled objective, connecting solver progress to business decisions, and deciding when a MILP is good enough to stop.
- Optimization / Sep 5, 2026 Infeasibility Is a Modeling Signal A practical workflow for debugging infeasible MILP models, separating bad data from bad assumptions, and turning solver diagnostics into better decision systems.
- Decision Science / Sep 4, 2026 Substitution Is Part of Demand Why SKU-level demand is not independent when customers switch products, and how to model substitution without turning inventory optimization into fiction.
- Decision Science / Sep 3, 2026 Forecast Bias Is an Economic Problem A practical guide to deciding when forecast bias matters, how it changes supply chain decisions, and why correcting every statistical bias can make the business worse.
- Decision Science / Sep 2, 2026 Inventory Position Is a State, Not a Number How to model on-hand, pipeline, commitments, receipts, and timing correctly before optimizing replenishment decisions.
- Optimization / Sep 1, 2026 Separate Search From Evaluation Why tuning and judging a supply chain policy on the same scenarios gives you confidence you did not earn—and how to build a clean search, validation, and confirmation workflow.
- Optimization / Aug 31, 2026 Shadow Prices Are Clues, Not Answers How to use dual values and marginal economics to understand constrained supply-chain models without pretending a local LP sensitivity number is a universal business truth.
- Optimization / Aug 30, 2026 The Planning Horizon Is a Modeling Choice How to choose a planning horizon from decision timing, uncertainty, lead times, commitments, and terminal economics instead of inheriting an arbitrary number of weeks.
- Optimization / Aug 29, 2026 Rounding Is Part of the Optimization Model Why solving a continuous approximation and rounding afterward can quietly destroy feasibility, economics, and the decision you thought you optimized.
- Supply Chain / Aug 28, 2026 Sales Are Not Demand Why observed sales become a censored view of demand during stockouts, and how that mistake can poison forecasts, inventory policies, simulations, and optimization models.
- Decision Science / Aug 27, 2026 Forecast at the Grain of the Decision Why weekly, monthly, SKU-level, and aggregate forecasts are not interchangeable once a real supply chain decision sits downstream.
- Optimization / Aug 26, 2026 Do Not Build Constraints You Do Not Need A practical guide to constraint generation: when a huge MILP is mostly enforcing rules that never bind, start small, find violations, and add only the structure the solution actually needs.
- Decision Science / Aug 25, 2026 Flexibility Has an Economic Value How to value optionality in supply chain decisions instead of treating flexible capacity, suppliers, transportation, and inventory as vague insurance.
- Decision Science / Aug 24, 2026 Decision Latency Is a Cost A practical guide to modeling the economic cost of slow decisions in supply chain systems, from stale state and delayed orders to frozen windows and missed recourse.
- Optimization / Aug 23, 2026 Simulation Noise Changes the Search How to tune decision policies when every objective evaluation is noisy, expensive, and only an estimate of the economics you actually care about.
- Optimization / Aug 22, 2026 The Objective Function Needs a Receipt A practical guide to validating optimization objectives against real economics before trusting the decisions they produce.
- Optimization / Aug 21, 2026 Warm Starts Are More Than a Solver Trick A practical guide to using yesterday's decisions, heuristics, and incumbent solutions to make repeated MILPs faster, more stable, and more useful in production.
- Optimization / Aug 20, 2026 Debug the Policy, Not Just the Model A practical guide to debugging optimization systems by tracing states, decisions, uncertainty, constraints, and downstream outcomes instead of stopping at solver status.
- Optimization / Aug 19, 2026 How Many Scenarios Do You Actually Need? Scenario count is not a sophistication contest. Use enough uncertainty to stabilize the decision, then spend the remaining compute where it changes the policy.
- Decision Science / Aug 18, 2026 Aggregation Can Change the Decision Why aggregating products, locations, time, or uncertainty can make an optimization model faster while quietly changing the business problem it solves.
- Optimization / Aug 17, 2026 Fix the Formulation Before You Tune the Solver A practical guide to comparing MILP formulations using relaxations, bounds, model structure, and controlled solver experiments instead of parameter folklore.
- Optimization / Aug 16, 2026 Decision Stability Is a Cost Why a mathematically better plan can still be operationally worse, and how to model replanning churn, commitment, and stability without freezing the business in place.
- Optimization / Aug 15, 2026 Not Every Business Rule Is a Constraint A practical guide to deciding which supply chain rules belong as hard MILP constraints, which belong in the objective, and which should be tested as policy choices.
- Decision Science / Aug 14, 2026 Uncertainty Matters at the Decision Boundary Why forecast uncertainty becomes economically important near discrete ordering, capacity, MOQ, and activation thresholds—and how to model those boundaries in practice.
- Decision Science / Aug 13, 2026 The Value of Information Depends on the Decision How to decide whether better forecasts, faster data, or another signal is actually worth paying for by measuring how information changes actions.
- Optimization / Aug 12, 2026 Cost Functions Are Policy Knobs How to turn a rigid optimization model into a tunable decision policy by using economic penalties, simulation, and out-of-sample evaluation instead of piling on rules.
- Decision Science / Aug 11, 2026 Recourse Is Part of the Policy Why a supply chain plan is incomplete unless it says what happens after demand, lead time, capacity, or inventory turns out differently than expected.
- Optimization / Aug 10, 2026 Scarce Capacity Should Go to the Next Best Unit A practical guide to allocating constrained supply, production, cash, and logistics capacity using marginal economic value instead of averages, priorities, or historical shares.
- Supply Chain / Aug 8, 2026 Ordering Costs Create Cadence Why fixed ordering costs, receiving effort, freight thresholds, and supplier economics naturally create lumpy replenishment—and how to model that cadence instead of imposing it by habit.
- Decision Science / Aug 7, 2026 Forecast Bias Is Not Symmetric Why the same forecast error can have radically different economic consequences depending on inventory position, lead time, margin, and the decisions your planning system makes.
- Supply Chain / Aug 6, 2026 Holding Cost Belongs to Time, Not Leftover Inventory Why period-specific inventory costs must be charged against the inventory that actually exists when the cost applies, and how terminal-cost shortcuts can distort ordering decisions.
- Supply Chain / Aug 5, 2026 Lead Time Is a Distribution, Not a Number Why planning with average supplier lead time can create systematically bad orders, and how to model lead-time uncertainty in replenishment, simulation, and optimization.
- Supply Chain / Aug 4, 2026 Safety Stock Is a Model, Not a Number Why the familiar z-sigma safety-stock formula is a set of assumptions about demand, lead time, replenishment, and cost—and what to do when those assumptions do not describe your supply chain.
- Optimization / Aug 2, 2026 Infeasibility Is a Business Signal How to debug an infeasible optimization model without treating the solver as the problem, and how to turn conflicting constraints into useful operational information.
- Decision Science / Aug 1, 2026 Your Planning Horizon Is Not Your Commitment Horizon Why supply chain models should look farther into the future than they commit, and how rolling-horizon decisions reduce forecast dependence without pretending uncertainty disappears.
- Decision Science / Jul 27, 2026 Data Access Is a Decision Constraint How to reason about decisions when the best information exists but cannot be legally, commercially, or organizationally accessed in raw form.
- Supply Chain / Jul 27, 2026 Lost Sales Are Silent Demand Why stockouts usually disappear from the systems finance trusts, and how to build defensible lost-sales estimates for real replenishment decisions.
- Optimization / Jul 27, 2026 MOQ Trees Are Business Logic Why nested minimum-order structures should be treated as explicit decision logic, not as an awkward data shape hiding inside preprocessing code.
- Optimization / Jul 27, 2026 Scenario Count Is Not Model Quality Why running more simulation samples does not automatically make better decisions, and how to spend stochastic compute where it actually changes the policy.
- Supply Chain / Jul 27, 2026 Service Levels Are Not Control Knobs Why target service levels often hide the real economic decision, and how to replace them with marginal value, stockout cost, and risk-adjusted inventory logic.
- Decision Science / Jul 27, 2026 The Aggregation Level Is a Modeling Decision Why aggregating demand, inventory, or decisions can make a model faster while quietly removing the operational tradeoffs the business actually cares about.
- Decision Science / Jul 27, 2026 Vendor Outages Belong Outside the Planning Engine How to model supplier shutdowns, capacity interruptions, and temporary buying restrictions without burying fragile business logic inside the optimization core.
- Decision Science / Jul 19, 2026 Forecast Vintage Leakage Why many planning systems look brilliant in testing and disappoint in production because they accidentally use information that was unavailable at decision time.
- Optimization / Jul 18, 2026 The Constraint That Creates the Decision Most optimization models have thousands of constraints, but only a handful actually create the decision. Learn how to identify the constraints that drive economic tradeoffs and focus modeling effort where it matters.
- Optimization / Jul 10, 2026 A Timeout Is Not a Model Benchmark A MILP that times out in one environment may solve in seconds somewhere else. Learn how to separate model difficulty, formulation quality, solver behavior, and implementation overhead before tuning the wrong thing.
- Optimization / Jul 10, 2026 The Atomic Move Defines the Algorithm Why practical optimization under MOQs, case packs, shared vendors, and nested constraints starts by defining the smallest legal decision change—not by choosing a search algorithm.
- Optimization / Jul 9, 2026 An Optimal Solution Is Not the Only Optimal Decision MILP models can have many equally good solutions. Learn why tie-breaking, stability, replay, and operational preferences matter after the solver proves optimality.
- Optimization / Jul 9, 2026 An Optimal Solution Is Not the Only Optimal Solution A MILP solver returns one optimal solution, but the model may contain many. Learn what presolve fixing means, why alternate optima matter, and how to make operational decisions stable on purpose.
- Optimization / Jul 8, 2026 Optimize the Coupled Decision Why multi-echelon supply chain optimization fails when teams tune SKUs, regions, and horizons independently even though the economics are shared.
- Optimization / Jul 8, 2026 When Local Improvements Lie A supply chain decision can improve one SKU, scope, or echelon while making the total system worse. Learn how to optimize coupled decisions without fooling yourself with local metrics.
- Optimization / Jul 7, 2026 Profile Before You Optimize When an optimization or simulation pipeline is slow, the solver is often not the bottleneck. Measure the full decision pipeline before tuning the wrong thing.
- Supply Chain / Jul 7, 2026 The Buying Cadence Is the Policy Why inventory optimization should treat buying cadence as a controllable decision policy, not a background calendar assumption.
- Decision Science / Jul 6, 2026 Planner Overrides Are Training Data Why manual changes to analytical recommendations should be captured as structured evidence, not dismissed as noise or treated as proof that the model failed.
- Optimization / Jul 6, 2026 Same Logic, Different Relaxation Two MILP formulations can describe the same integer decisions and still behave very differently. The difference often lives in the LP relaxation.
- Decision Science / Jul 5, 2026 The Search Space Is a Business Decision Why simulation optimization often succeeds or fails before the search algorithm starts, and how practitioners should design candidate decisions around operational reality.
- Optimization / Jul 5, 2026 The Search Space Is Part of the Model Why simulation optimization often fails before the simulator runs, and how to design candidate decisions, neighborhoods, and search spaces that reflect the real operation.
- Supply Chain / Jul 4, 2026 A Demand Distribution Is Not a Demand Path Why total demand over a horizon can be enough for one decision and dangerously incomplete for another, and how to choose the right uncertainty representation for the job.
- Decision Science / Jul 4, 2026 The Decision Meeting Is the User Interface Why optimization systems only become valuable when their recommendations fit the real meeting, cadence, ownership model, and operating rhythm where decisions actually happen.
- Decision Science / Jul 3, 2026 A Simulator Is Not a Policy Why simulating a supply chain is different from deciding what to do, and how to connect simulation, optimization, and policy design without confusing their roles.
- Optimization / Jul 3, 2026 Allocate by Breakpoint, Not by Unit How to turn slow unit-by-unit supply allocation into a fast, auditable algorithm using marginal value curves and breakpoints.
- Optimization / Jul 1, 2026 Solver Logs Are Management Artifacts Why optimization logs should be treated as operational evidence, not just technical noise, when moving supply chain decision systems from prototype to production.
- Decision Science / Jun 29, 2026 Policy Tuning Is Not Model Cheating Why practical supply chain decision systems need tunable policies, controlled experiments, and economic judgment after the first optimization model works.
- Decision Science / Jun 27, 2026 The Operational Shadow Model Why every supply chain optimization system needs to model the decisions people already make outside the formal system.
- Decision Science / Jun 24, 2026 Replay Before You Deploy Why replay testing is one of the most important and overlooked disciplines in supply chain optimization, decision science, and analytical system adoption.
- Decision Science / Jun 24, 2026 Why Your Simulation Is Not a Decision Policy Many supply chain teams build sophisticated simulations but still struggle to make better decisions. Learn the difference between evaluating a decision and generating one.
- Optimization / Jun 23, 2026 Solver Logs Are Economic Documents Why production optimization teams should treat solver logs as operational evidence instead of technical noise.
- Optimization / Jun 23, 2026 The Most Expensive Constraint Is the One You Forgot Why optimization projects fail when the model captures the mathematics but misses the operational realities that actually drive decisions.
- Decision Science / Jun 22, 2026 Decision Ownership Is the Missing Constraint Why supply chain optimization systems fail when no one owns the decision policy, and how to move from prototype math to operational adoption.
- Decision Science / Jun 22, 2026 Decision Variables Are Not Spreadsheet Columns A practical guide to framing optimization models around real operational decisions instead of copying the shape of a planning spreadsheet.
- Supply Chain / Jun 21, 2026 Buying Cadence Is a Policy, Not a Calendar Habit A practical supply chain framing of order frequency, buying horizon, lead time, inventory position, and uncertainty as one policy decision instead of a fixed planning ritual.
- Optimization / Jun 21, 2026 Read the Solver Log Before You Blame the Model A practical guide to treating MILP solver logs as operational evidence instead of noise, with a checklist for diagnosing formulation, data, scaling, and timeout problems.
- Perspectives / Jun 20, 2026 Why Analytical Systems Fail in the Last Mile The hardest part of decision science is often not the model. It is getting a real organization to trust it, use it, and change how decisions are made.
- Optimization / Jun 12, 2026 Optimizing Expensive Simulators Without Pretending You Need Global Optimality How to search huge combinatorial spaces when each Monte Carlo simulation is expensive and a good decision matters more than a proof.
- Supply Chain / Jun 9, 2026 Multi-Echelon Inventory Is Applied Economics A practical way to think about offshore storage, marketplace inventory, lead time, speed, cash, and service as one economic decision system.
- Optimization / Jun 4, 2026 MILP Optimality Is a Business Claim, Not a Slogan Why solver optimality is powerful, but only after the model, data, objective, constraints, and time budget actually represent the business problem.
- Decision Science / Jun 2, 2026 Point Forecasts Are Not Point Decisions Why point forecasts often hide uncertainty, but production decision systems still need to produce one executable recommendation with visible tradeoffs.
- Decision Science / Jun 2, 2026 Show the Options, Not Just the Answer Why decision systems should produce a recommendation, but also expose the tradeoffs, alternatives, and risk profiles behind it.
- Supply Chain / Jun 2, 2026 The Critical Ratio Is Not a Supply Chain Strategy The newsvendor critical ratio is useful intuition, but it is too thin to run modern supply chains with real constraints, portfolios, and repeated decisions.
- Decision Science / May 29, 2026 Dynamic Programming Is a Policy Language, Not a Silver Bullet Dynamic programming is one of the most important ideas in decision science, but production supply chains need approximations, structure, and economics.
- Decision Science / Apr 26, 2026 Forecast Accuracy Is Not Decision Quality Why better forecasts can still produce worse business decisions, and how to evaluate decisions under uncertainty instead.
- Decision Science / Feb 2, 2026 Knowledge Gradient for Expensive Decisions A practitioner explanation of knowledge gradient: learning is valuable only when it can change the final decision.
- Decision Science / Nov 27, 2025 ML Predictions Are Random Variables, Not Truth A practical way to use machine learning inside decision systems without pretending the prediction is the future.
- Supply Chain / Sep 1, 2025 From Distribution to Decision: How Probabilities Become Order Quantities Probabilistic forecasts don't mean fuzzy answers. You still land on a single number — you just land on the right one.
- Perspectives / Aug 15, 2025 Decisions Under Uncertainty: An Introduction Every business decision is a bet. The question is whether you're making informed bets or blind ones.
- Supply Chain / Aug 1, 2025 The Deterministic Planning Trap Your supply chain plan was optimal at 9am. By 10am, reality had other ideas.
- Optimization / Jul 25, 2025 The Art of the Big-M Constraint Big-M constraints are the duct tape of MILP modeling. Used well, they're indispensable. Used badly, they'll destroy your solver performance.
- Decision Science / Jul 15, 2025 Simulation as a Laboratory for Decisions Why building a simulator is the most underrated step in solving complex decision problems.
- Optimization / Jul 10, 2025 When to Use Mixed-Integer Programming MILP is powerful — but it's not always the right tool. Here's a practical guide to when integer programming shines and when you should reach for something else.
- Decision Science / Jul 1, 2025 Sequential Decision Analytics: A Better Framework Why single-shot optimization isn't enough and how to think about decisions that unfold over time.
- Supply Chain / Jun 15, 2025 Why Probabilistic Forecasts? Point forecasts are comfortable. They're also dangerously wrong. Here's what to do instead.
- Perspectives / Jun 1, 2025 Why We Embrace Uncertainty The case against deterministic planning and why probabilistic thinking changes everything.
- Optimization / May 5, 2025 How to Explain Optimization Models to Executives Without Losing Them in the Math
- Supply Chain / Apr 28, 2025 How Slowing Down Your Deliveries Can Speed Up Your Business Why deferring packages can cut costs, ease peak-day chaos, and drive smarter delivery decisions
- Supply Chain / Apr 22, 2025 Planning for Tariffs You Can't Predict How Robust Optimization Helps You Make Smarter Decisions Under Uncertainty
- Perspectives / Apr 21, 2025 So You Want to Build a Decision Intelligence Product? The questions to ask, the traps to avoid, and how to build something that actually improves decisions
- Supply Chain / Apr 19, 2025 How Stochastic Decision Analytics Transforms Last-Mile Delivery Applying sequential decision analytics to the hardest logistics problem
- Decision Science / Feb 24, 2025 Stochastic Optimization vs. Sensitivity Analysis Understanding when to use each approach for decisions under uncertainty
- Decision Science / Feb 17, 2025 Optimizing the Uncertain: How Stochastic Optimization Transforms Decision-Making in Supply Chains From deterministic models to embracing uncertainty
- Perspectives / Feb 13, 2025 Why Digital Transformation Is Really About Better Decisions — Not Just More Data Shifting the focus from data collection to decision-making
White papers
A Practical Architecture for Simulation-Based Supply Chain Policy Optimization
How to search for good supply chain policies when every evaluation requires an expensive simulation.
Read the paper →The Future of Coding Looks Like Optimization
Why agentic software engineering increasingly resembles constraint satisfaction and search.
Read the paper →