Glossary

Margin computed via Activity-Based Costing applied through the pegging cascade — direct and indirect costs flow back to the demand line that triggered them.

Standard COGS attributes a fixed unit cost per SKU. ABC-adjusted margin walks the pegging chain backward — every supply event that contributes to an order line carries its direct cost (purchase price, transport) plus its share of indirect costs (changeover labor, expedite freight, SLA-penalty exposure). The margin at commit reflects realized cost-to-serve, not standard cost. Captures what standard COGS misses: the customer whose orders chronically trigger expedites is dollarized as such.

The eight UX surfaces in VYAN: Driver Seat, Decisions, Policy, Frontier, Scenarios, Audit, Risk Events, Platform Admin.

Each Canvas surface serves a specific governance question. Driver Seat is the cockpit. Decisions is the per-decision queue. Policy is where the Decision Policy is edited. Frontier is the Pareto frontier review. Scenarios is the Mode 3 sandbox. Audit is the decision-provenance reference. Risk Events is the Risk Library editor. Platform Admin is the tenant-level configuration. Every Canvas surface has SAGE in the right pane.

VYAN's ability to run any deterministic solver — VYAN's own, the customer's incumbent, a solution provider's — inside the stochastic envelope.

VYAN constructs the iteration set from past variabilities and future risks, hands each iteration to a solver as an ordinary deterministic problem, collects the answers, and assembles the probability histograms. The solver never sees uncertainty. Any deterministic planner becomes a stochastic planner when VYAN orchestrates it. SAP MRP, a 1990s-architecture batch system, produces P10/P50/P90 ranges under VYAN — not because MRP changed, but because VYAN wrapped it.

A function describing the dependency structure between variables, separate from their marginal distributions.

Copulas let VYAN model the marginal distribution of Brent and the marginal distribution of FX independently, then bind them through the copula that captures how they actually co-move in history. Different copulas (Gaussian, Clayton, Gumbel) capture different tail dependency structures. The copula is what prevents the system from sampling Brent at P95 while FX sits at its independent median.

The bidirectional workflow where customers contribute forward demand signals with confidence intervals and receive predictability, allocation visibility, and transparent commercial math in return.

Customers submit forward signals weighted against their own learned forecast-vs-realized reliability. Consistent customers get their signals weighted heavily; optimistic customers get discounted. The discount is transparent and continuously updated. Customers see confidence-interval-aware order acknowledgments, early warnings when supply constrains, dollarized surcharges at pull-in time, and rule-based allocation under scarcity.

Conditional Value at Risk — the expected outcome conditional on being in the lower tail of the distribution. The dollarized cost of tail outcomes.

Standard VaR is a percentile (e.g., 5% of outcomes are worse than $X). CVaR is the average of those worst N% outcomes — a richer measure of tail risk. EVA's risk-adjusted term encodes a CVaR penalty so a policy that maximizes expected EVA at the cost of catastrophic tail outcomes scores worse than its expectation alone would suggest. The risk posture's percentile choice (P75 vs P90 vs P95) operationally encodes a CVaR preference.

The single configurable object that holds every behavioral choice — risk posture, objective weights, autonomy thresholds, engine selection, constraints. Versioned and audited.

Seven sub-policies organize the surface area: Demand, Supply, Optimization, Autonomy, Publishing, Scenario, Governance. Each is edited through the Policy canvas by the people in the organization who own that lever (Marketing edits the promo section; Operations edits production scheduling; the CSCO edits risk posture). Lifecycle: Draft → Active → Suspended → Retired, with versioning at each step and full audit trail for every change.

The probability a Day-1 decision still holds across the realistic distribution of futures, multiplied by its dollarized cost-of-break.

A 38% resilience score means 38% of sampled future trajectories still hold the decision at the lookahead horizon. The other 62% break — each with a dollarized cost (expedite premium, SLA penalty, displaced higher-margin order). The probability-weighted expected cost-of-break is what the policy's autonomy logic compares against. Every decision carries a named break day — the specific day the cliff arrives — and the iteration cluster that causes the break is traceable.

VYAN's compute engine. Produces decisions under the active Decision Policy.

The MILP solver wrapped in the stochastic envelope. Runs Mode 1 daily, Mode 2 weekly, Mode 3 on demand. Co-determines pricing, demand-shaping, supply replenishment, inventory positioning, customer allocation, and financial reconciliation in one solve. Outputs a range across the joint sample; the deterministic commit comes from the policy's risk posture percentiles. The Twin computes; the Policy governs; SAGE never decides — the architectural discipline from chapter 3.2.

The dollarized difference between any two policies on the same data over the same horizon, with confidence intervals.

The primitive that makes policy comparison rigorous. Three principal use cases: migration decisions (current policy vs recommended knee policy), A/B comparison (Conservative vs Lean), and engine arbitration (which solver in an engine tournament produces the best decisions for this customer). Delta PVA is computed across the joint sample, so it carries a confidence interval — a Delta PVA of $11.8M with 95% CI of [$8.4M, $15.2M] is defensible; with CI of [-$2M, $25M] is not yet defensible and the system says so.

A shape describing how a quantity varies — mean, standard deviation, percentiles, tails.

In VYAN every input driver — lead time, capacity, demand residual, scrap rate, FX, commodity price, supplier reliability — is represented as a distribution learned from transaction history, not a master-data scalar. Distributions update incrementally as new realizations land. The Decision Policy chooses, explicitly, which percentile of each distribution to plan against.

VYAN's cockpit. The home page of the in-product UX — operational pulse, today's signals, autonomous/pending split, recent activity.

Not a dashboard for reporting after the fact, an operating cockpit for governing the policy. The same Driver Seat serves planner, CSCO, and CFO with different default framings.

Driver Seat, Decisions, Policy, Frontier, Scenarios, Audit, Risk Events, Platform Admin. The UX surfaces in VYAN.

Every canvas surface has SAGE in the right pane. See the Canvas glossary entry for descriptions of each.

Running multiple solvers against the same iteration set and arbitrating by PVA. The neutral arena no planning-stack vendor can structurally offer.

A buyer evaluating SAP IBP, Kinaxis, and o9 today runs a year of dueling vendor POCs on cherry-picked data. VYAN feeds all three the same iteration set built from the buyer's own past variabilities and future risks. Three histograms emerge. Three PVA scores emerge. The buyer sees, on their own data, with identical inputs, which solver actually wins. Whichever solver wins, VYAN won the buyer.

The tenant boundary — one per customer company. Contains one or more Workspaces.

The outermost object in the hierarchy. User authorization, billing, and federated SAGE state live here. Cross-Workspace queries from a user with cross-Workspace authority are mediated at the Enterprise level.

Economic Value Add — the single dollarized metric capturing service, margin, cash, carbon, customer priority, plan stability, and tail-risk in one number.

EVA composes eight dollarized components into a single figure the CFO can defend: Margin Contribution, Service-Driven Revenue, Cash Flow Value, Carbon Cost, Customer Priority Score, Plan Stability Score, Working Capital Score, and a Risk-Adjusted CVaR Term. Each component is dollarized at the component level — no percentages, no normalization — so the CFO can drill into where every dollar comes from. A single plan run against the joint sample produces an EVA distribution; the mean is the headline, the P5 is the tail risk, the P95 is the upside.

Expected Value of Waiting — the dollar value of delaying a commit by one day. The second axis of auto-commit logic next to value at risk.

Computed as the expected EVA difference between committing today versus waiting one more day, where waiting gives the system another day of incoming events and refined distributions. High-EVW decisions surface to humans even when value at risk is low (the waiting buys information worth more than the decision). Low-EVW decisions auto-commit even at high value at risk (waiting destroys value because the supplier window closes).

A distribution with more probability mass in the extremes than a normal distribution would have.

Lead-time distributions in industrial supply chains are characteristically fat-tailed — the rare 31-day arrival on a lane that normally runs 14 is more common than a normal distribution predicts. Pricing in a 14-day mean as a master-data scalar misses the fat tail entirely. VYAN learns the actual distribution including the tail and the policy can choose how much of the tail to plan against.

The collection of deterministic scenarios built from past variabilities and future risks. Each scenario is one coherent future handed to the solver.

Typically 100-1000 iterations per Mode 1 solve. Each iteration is a coherent draw from the joint distribution — Brent at its sampled value, FX at the copula-bound corresponding value, demand at its sampled value, the named risk events firing or not according to their probabilities. The iteration set is the substrate for both the stochastic evaluation and the engine tournament.

The combined distribution over multiple variables, capturing how they move together — not independent marginals.

In a supply chain context, Brent and FX move together. GDP softening propagates through specific customer segments. Substitution graphs activate under shortage. The joint distribution captures these dependencies. VYAN samples jointly through copulas fitted from history, so every iteration is a coherent future — not an implausible draw from independent marginals.

Mixed-Integer Linear Program — the optimization formulation at the compute core of VYAN's Decision Twin.

Sets and indices, decision variables, hard and soft constraints, dollarized objective function. VYAN's formulation is sized for production at customer scale (~144K active Order Lines × ~60K active Supply Events for a representative $1B industrial). The full formulation lives in chapter 9.2 behind math-gate; the structural pieces are open.

A computational method that samples a distribution repeatedly to estimate statistics of interest — used by VYAN for stochastic evaluation.

Each Mode 1 stochastic solve runs N (typically 100-1000) Monte Carlo iterations of the joint distribution. Each iteration is a single coherent future; the histograms of outcomes across iterations are how VYAN reconstructs the EVA distribution, the service distribution, the working-capital distribution. The Stochastic Run Theater visualizes the process.

The demand atom. Every customer order line carries its full attributes — quantity, requested date, customer, SLA, price, substitutions, channel, source-location constraint, temporal flexibility, cost-to-serve.

VYAN plans at this grain, not at aggregated SKU-location-week buckets. Aggregation hides exactly the information decisions need — customer priority, substitution acceptance, temporal flexibility, contract terms. The cost of this commitment is real (the MILP at a typical $1B industrial runs across ~144K active Order Lines), and it's what makes everything downstream — margin awareness at the line, per-decision resilience scoring, allocation under scarcity — actually possible.

The set of non-dominated policies — for each, no other policy is strictly better on every dimension.

In VYAN the frontier is constructed weekly by Mode 2 across 200-500 candidate policies, dollarized in EVA and decomposed by KPI family. The knee policy — the point where adding more of any one KPI starts requiring disproportionate sacrifices in others — is identified as the recommended active policy. Delta PVA between the current operating policy and the knee policy is what the CSCO and CFO use to decide migration.

The chain that traces each Supply Event back to the Order Lines it serves.

VYAN's pegging chain is the substrate for ABC-adjusted margin (cost-to-serve flows back from supply to demand), allocation under scarcity (we know which customer gets each unit), and the audit trail (every committed dollar has a provenance). Standard term, used here with deeper precision than most planning systems implement.

A point in a distribution below which a stated fraction of outcomes fall.

The P85 of a lead-time distribution is the value below which 85% of observed arrivals fell. VYAN's risk posture is expressed in percentile commitments — Conservative might plan to P95 of lead time, Balanced to P85, Lean to P65. The choice is explicit, dollarized, and surfaced at executive level rather than buried in master data.

Policy Value Add — the dollar lift VYAN policy-based decisions produce above a rule-based heuristic baseline, on the same data over the same horizon.

Every solve produces three plan anchors — Heuristic Baseline (what rules-based planning would have done), Constrained MILP (what the optimizer produced under the active policy), and Ideal Unconstrained (the upper bound if every constraint were relaxed). PVA = Constrained MILP - Heuristic Baseline. Decomposes by KPI family and by decision class. PVA accumulates continuously, so the quarterly board narrative becomes "policy delivered $X over the quarter, decomposed as Y, with confidence interval Z."

A learned distribution of a partner's actual performance against their commitments — supplier delivery vs commit date, customer realized demand vs forecast, 3PL transit time vs tender.

VYAN's collaboration channels feed back realized performance into a learned distribution per partner. A supplier that consistently delivers 2 days early on a 14-day committed lead time has its reliability distribution learn that asymmetry. The buyer's plans against that supplier reflect the actual shape, not the committed value. Same pattern for customers (forecast accuracy) and 3PLs (lane transit reliability).

The structured exchange between buyer and supplier (or buyer and contract manufacturer) before a PO is placed.

Buyer sends a structured request — specific SKU, quantity, requested date, with the buyer's posture context. Supplier responds with their commit confidence and any counter-proposals (different quantity, different date, substitute material, partial fulfillment). Both sides agree before the PO is placed. The handshake closes the structural one-way relationship that produces today's silent failures.

The deliberate organizational posture for converting uncertain environments into resilient recommendations. Named, dollarized, set at executive level.

Three reference postures — Conservative, Balanced, Lean — each carrying explicit percentile commitments per driver and explicit dollarized implications for working capital, service, and tail risk. The posture is the executive choice the CSCO and CFO commit to deliberately. Drives every downstream decision: safety stocks, PO release timing, allocation under scarcity, margin-floor enforcement.

VYAN's conversational layer. Translates intent, reasons over state, orchestrates bounded actions. Never decides.

Three bounded roles: Translation (converting user intent into structured system requests), Reasoning (drawing on cached state to answer questions without invoking the engine), Bounded Orchestration (executing operations within the Decision Policy's authorized limits). Three depths of explanation: Headline, Decomposition, Deep Lineage. Root-cause traversal is mechanical, not generative — every link cites the audit trail. The discipline that "SAGE never decides" is what makes SAGE safe to trust.

Customer Service, Margin, Cash Flow, Carbon, Customer Priority, Plan Stability, Risk Posture. Each continuously measured, each dollarized.

Every component of EVA and every component of PVA breaks down by these seven families. The decomposition is what makes posture choices defensible — the CSCO can see which families the policy is winning on and which it's giving up, and adjust accordingly.

Demand, Supply, Optimization, Autonomy, Publishing, Scenario, Governance. The seven sections inside the Decision Policy object.

Each sub-policy is a configurable surface. Marketing edits Demand's promo section. Operations edits Supply's production scheduling. The CSCO edits Optimization's risk posture. The policy becomes a shared artifact rather than a buried IT setting.

Any engine — VYAN's or third-party — that accepts a deterministic planning problem and returns a deterministic plan. Pluggable inside VYAN's stochastic envelope.

VYAN already ships two solvers internally — the heuristics engine and the optimizer engine. Both implement the same scenario-in, plan-out contract. Third-party solvers extend a proven internal pattern; they're not a new concept. Composability is safe to advertise precisely because the solver runs inside two layers of VYAN IP it never sees.

The iteration-construction-plus-histogram-assembly layer VYAN wraps around any solver. VYAN owns both sides; the solver in the middle is pluggable.

The proprietary IP that turns any deterministic solver into a stochastic one. Modeling past variabilities is VYAN. Modeling future risks is VYAN. Building the joint sample is VYAN. Assembling histograms and computing PVA from the solver's deterministic answers is VYAN. The solver in the middle never sees the stochastic intelligence, only the deterministic problem.

The bidirectional workflow where the buyer sends request-for-commits before placing POs and the supplier responds with their own commit confidence and counter-proposals.

The handshake completes before the formal PO is placed. The PO that gets placed reflects the supplier's actual current state, not a master-data lead-time assumption. The supplier becomes a participating intelligence in the planning loop — they see the buyer's forward demand distribution, named risk events at their probabilities, and a stability score that justifies capacity investments to their own board. The buyer gets supplier reliability distributions learned from realized commits-vs-deliveries.

The supply atom. Every PO, every production order, every STO, with its own pegging chain and realized cost accumulator.

The counterpart to Order Line on the supply side. Every Supply Event carries its source (which supplier, plant, or DC), its committed delivery shape (mean + distribution from the supplier reliability model), its pegging links to the Order Lines it serves, and its realized cost accumulator that totals direct and indirect costs as the event executes.

The architectural layer above existing planning stacks that adds policy governance, distribution-driven planning, stochastic evaluation, meta-optimization, resilience scoring, and a conversational interface. VYAN is the System of Intelligence.

Sits above Systems of Planning (which it replaces) and above the control tower (which it absorbs), reading from and writing back to Systems of Record (which it augments, not replaces). The category didn't exist before VYAN drew the boundary; it's the right architectural frame for the work the planning layer hasn't been doing.

The planning-software layer: IBP, Kinaxis, o9, Blue Yonder, Anaplan. The layer VYAN replaces.

Their architecture is what produces the seven failures from chapter 1.3; replacing them is the point. VYAN can also orchestrate them as solvers through composability, which is how the evidence-driven migration works.

ERP, PLM, CRM, MES, WMS, TMS — the transactional truth as recorded. The layer VYAN augments, not replaces.

VYAN reads transaction history from the SoR and writes back committed decisions. The customer's ERP remains the source of truth as recorded; VYAN holds the truth as decided. The boundary is decisions versus records.

The seven specific reasons decision quality fails in current planning architectures. Each compounds the next. Each has an architectural answer in VYAN.

(01) Sequential, single-future planning → single-pass joint stochastic solve. (02) Stale master data dressed as single values → distributions, not values. (03) No order-line margin awareness → pegging-based realized cost cascade. (04) No explicit risk posture → named, dollarized executive choice. (05) Risk modeled as binary not probabilistic → every percentage point dollarized. (06) No optimization of the policy itself → weekly meta-optimization across the candidate policy universe. (07) No decision resilience scoring before commit → lookahead-driven score and break-day projection on every commit.

Mode 1 — daily stochastic operational solve. Mode 2 — weekly policy optimization. Mode 3 — on-demand user scenarios. The event-driven loop runs continuously beneath all three.

Mode 1 produces today's commits; Mode 2 refreshes the Pareto frontier across the candidate policy universe; Mode 3 is the planner/CSCO/CFO sandbox for "what if" exploration. The CSCO's weekly cadence anchors at Mode 2; the planner's daily rhythm anchors at Mode 1; ad-hoc analysis lives in Mode 3.

VYAN's sampling discipline — each iteration is a coherent future with joint dependencies preserved across the horizon.

Standard Monte Carlo samples each variable independently per iteration. Trajectory-coherent sampling preserves the joint distribution across iterations and across the planning horizon — Brent's path stays correlated with FX's path across days, demand shocks propagate consistently across the substitution graph. Each iteration is a story the world could plausibly tell, not a random draw from marginals.

The data-isolation boundary inside an Enterprise. Typically one per product family or geography.

Each Workspace holds its own Decision Policy, runs its own Decision Twin, has its own SAGE state, and presents its own Canvas surfaces. A customer with three business units typically runs three Workspaces under one Enterprise. Policies and learnings can be shared across Workspaces deliberately; data does not leak across the boundary by default.