The MILP formulation
The full mathematical formulation of VYAN's Decision Twin. Sets, indices, variables, constraints, objective.
VYAN's Decision Twin is a Mixed-Integer Linear Program at its compute core. The formulation has five structural pieces. Sets and indices — the entities the MILP reasons over: Order Lines, Supply Events, Pegging Links, Locations, Suppliers, Time Periods, Risk Events, Sample-set iterations. Decision variables — what the solver chooses: quantity to release, timing to commit, allocation to apply, substitution to offer, pricing to set, capacity to reserve. Constraints — hard (material balance, capacity limits, contractual SLAs) and soft (preferred sourcing, churn tolerance, customer-priority ordering). Objective function — the dollarized EVA composition with all seven KPI family terms, the CVaR tail-risk term, the risk-posture-derived percentile commitments. Solver mechanics — warm starting from prior solves, scenario decomposition, parallel iteration evaluation.
The formulation is the proprietary mathematical core of VYAN's optimizer, sized for production at customer-of-scale (144,000 active Order Lines × 60,000 active Supply Events for a representative $1B industrial customer). It sits behind the math-gate for the obvious commercial reasons — competitors would mine it; the genuine differentiation is in the running system, not the formulation alone, but we don't hand out the formulation casually either.