Excel Sensitivity Report¶

Definition¶

The course's Excel sensitivity report summarizes a solved continuous LP through variable values, reduced costs, objective coefficients and their allowable changes, constraint left-hand-side values, shadow prices, right-hand sides, and their allowable changes. The course obtains this report after solving with Simplex LP.

Interpretation¶

The sensitivity report answers what-if questions about a solved linear program without solving it again: how far a coefficient may change before the optimal plan changes, and what one more unit of a resource is worth. Every number refers to the final solution of Excel Solver.

The variable table concerns the objective: each variable's final value, reduced cost, objective coefficient and its allowable increase and decrease. Within that range the optimal variable values stay the same, while the optimal objective value moves with the coefficient. The constraint table concerns the right-hand sides: the final value of the left-hand side, the shadow price, the right-hand side and its allowable range. Within that range each extra unit changes the optimal value by the shadow price, while the variable values may change.

The entries are linked. A constraint whose final value differs from its right-hand side is not binding and has shadow price $0$: more of a resource that is not used up is worth nothing. In the pipes example processing time is used for $624$ of $2{,}400$ units, so its shadow price is $0$.

The ranges need the most care. They are changes relative to the current value, not new totals: a coefficient $5$ with allowable increase $2$ may rise to $7$. Each range also assumes that only that one number changes.

Key Results¶

• For a constraint, Final Value is the evaluated left-hand side, not its right-hand side.
• An allowable increase is an increment, not a new total.
• The report's very large bound notation is used for an effectively unlimited allowable change in these examples.
• Interpret the ranges for separate single-parameter changes.

Examples¶

• The pipes plan produces 72 large pipes, 48 small pipes, and no sheets, with profit 816.
• Processing time used is 624 out of 2,400, leaving 1,776 units of slack.

Prerequisites¶

• Excel Solver for Linear Programming
• Sensitivity Analysis

Related Concepts¶

• Reduced Cost
• Objective Coefficient Range
• RHS Sensitivity Range

Sources¶

• OR Modelling · Week 3

Aliases: sensitivity report, Solver sensitivity report

Last updated: 20 October 2026 03:02