InteractiveMap of Operations Research
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MethodIntermediate02.20
Optimization Core

Postoptimal & Parametric Analysis

Understand how optimal solutions change when inputs move.

Overview

Postoptimal and parametric analysis asks what happens after a model has been solved. It studies how objective coefficients, right-hand sides, bounds, and other parameters can move before the current basis or recommendation changes.

This topic appears repeatedly in textbook LP coverage because OR recommendations are rarely consumed as one fixed answer; managers ask what capacity is worth, which assumptions matter, and how robust the plan is.

Core ideas

Sensitivity ranges

Sensitivity ranges describe intervals over which parts of the current LP solution interpretation remain valid.

Shadow prices

Shadow prices estimate the marginal value of relaxing a binding resource constraint inside its valid range.

Parametric RHS

Parametric right-hand-side analysis tracks how solutions change as capacities, demands, or requirements move.

Parametric costs

Parametric cost analysis tracks how objective changes affect the basis, reduced costs, and selected activities.

Reoptimization

Reoptimization uses the previous solve as a starting point when model data changes.

How to use it

  1. 1Identify which coefficients or constraints decision-makers are likely to challenge.
  2. 2Inspect binding constraints, slack, dual values, and reduced costs.
  3. 3Compute or estimate valid ranges before interpreting marginal values.
  4. 4Run targeted scenarios for changes outside the reliable sensitivity range.
  5. 5Translate the results into business statements about bottlenecks, breakpoints, and value of flexibility.

Applications

Capacity planningPricingBudget changesScenario reviewManagement reports
  • Capacity planning: estimate the value of one more machine hour, vehicle, bed, or worker.
  • Pricing: understand which cost or revenue changes would alter a plan.
  • Budget changes: show when an additional dollar changes the optimal allocation.
  • Scenario review: identify assumptions that deserve full re-solving rather than local interpretation.
  • Management reports: explain why a recommendation is stable or fragile.

Common pitfalls

  • Using shadow prices after a parameter change has left the valid range.
  • Assuming sensitivity output from an LP applies unchanged to a MIP.
  • Reporting too many solver-table numbers without explaining the operating implication.
  • Ignoring alternate optima and degeneracy when interpreting marginal values.

Resources