COMMERCE 3QA3 Lecture Notes - Lecture 6: Shadow Price, Slack Variable, Sensitivity Analysis

• School: McMaster University
• Department: Commerce
• Course: COMMERCE 3QA3
• Professor: John Miltenburg

Document Summary

In an lp problem, the values of the objective function coefficients and the constraint right-hand-sides may change (e. g. they may be uncertain). For example, profit margins, available hours, demands, labour requirements, costs of advertising, expected financial return, etc. may change. Sensitivity analysis gives ranges of values of the objective function coefficients and the constraint right- hand-sides over which the optimal solution does not change. A sensitivity analysis corresponds to an optimal solution. So the optimal solution is found first, then the sensitivity analysis is done. You must know what the optimal solution is in order to understand the sensitivity analysis. Solve the lp model to find the optimal solution. Range of optimality for the coefficient of a decision variable in: binding or nonbinding, slack or surplus for a constraint. Shadow price for a non-negativity constraint (= reduced cost for a decision variable: range of feasibility for the right-hand-side (rhs) of a constraint the objective function.