A constraint makes a mathematical recommendation feasible, but can also protect an unchallenged habit.
A constraint makes a mathematical recommendation feasible, but can also protect an unchallenged habit. Minimum presence, channel ceiling, sales capacity, contract, timing or risk rule needs a unit, period, owner and rationale. Shadow price measures the value of a small relaxation, distinguishing a limit that is genuinely costly to change from a rule whose review creates more value than it costs.
Decision and method.
Keep regulatory and physical constraints, but review internal-policy constraints when shadow price exceeds relaxation cost. Inventory budgets, minima, maxima, contracts, dependencies, capacities, risks and delays, removing duplicates and purely narrative rules. For each, document variable, direction, threshold, unit, window, owner, rationale and expiry; distinguish hard constraints from penalised preferences. Compare unconstrained, feasible and relaxation scenarios; calculate active constraints, slack and shadow price. Negotiate relaxation by comparing marginal value with operational or political modification cost, starting with active high-shadow-price, low-change-cost constraints.
Worked example.
Constrained solution yields 486 k€ contribution. CRM ceiling is active with shadow price €0.68 per extra euro. Adding 20 k€ capacity costs 9 k€. Brand floor opportunity cost is €0.25 per imposed euro. Gross CRM relaxation value: 20,000 × 0.68 = €13,600. Net after capacity: 13,600 − 9,000 = €4,600. Raising brand floor by 40 k€ destroys about 40,000 × 0.25 = €10,000. Accept CRM expansion locally; keep brand floor and review its rationale before any increase.
Checks and limits.
Each constraint has unit, period, owner and source; hard constraints are separate from negotiable preferences; inspect slack and shadow price for active constraints; decide relaxation on net value and validity range. Shadow price is local and can change after a large relaxation. Nonlinear or discrete constraints require specific analysis. Economic value never permits breaching legal obligation.
Resources and sources.
Download the constraint register. Related: compare scenarios, allocate budget growth, add uncertainty. Sources: Boyd and Vandenberghe (2004); Nocedal and Wright (2006); Asadpour et al. (2019).