Sensitivity Analysis

Optimization · Axiom Academy

Understanding how optimal solutions respond to changes in problem parameters Linear programming models contain parameters that are estimates or forecasts. When these parameters change, we need to understand how our optimal solution is affected. How much can parameters change before the optimal basis changes? What is the value of additional resources? How robust is our solution to uncertainty? 2. Shadow Prices (Dual Variables) The shadow price of a constraint represents the marginal value of relaxing that constraint by one unit. It tells us how much the objective value would improve if we had one more unit of the resource. If a constraint has shadow price λ = 50, then increasing its RHS by 1 unit increases profit by approximately 50 (within the valid range). 3. Right-Hand Side (RHS) Ranging Shadow prices are only valid within a specific range. RHS ranging determines how much a constraint's RHS can change before the current basis becomes suboptimal. Beyond these bounds, the optimal basis changes and a new shadow price applies. This is critical for investment decisions based on resource expansion. 4. Objective Coefficient Ranging How much can the profit (or cost) coefficient of a variable change before the optimal solution changes? This is crucial for pricing decisions and cost uncertainty analysis. A variable in the optimal solution can have its coefficient change within a range before a different solution becomes optimal. 5. Adding Variables or Constraints

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