73-220-Lecture09

73-220-Lecture09 - 1 Sensitivity Analysis I 73-220 Lecture...

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Unformatted text preview: 1 Sensitivity Analysis I 73-220 Lecture 09 2 Agenda ● Last two weeks – Typical linear programming applications ● Sensitivity Analysis – Objective function coefficient changes (Range of optimality) – Changes in RHS of constraints (Shadow or Dual Price and Range of Feasibility) » Non-binding Constraints » Binding Constraints ● Interpretation of Excel sensitivity report – Excel Solver – Sensitivity Report ● Next Class 3 Sensitivity Analysis ● Sensitivity analysis (or postoptimality analysis) is used to determine how the optimal solution is affected by changes, within specified ranges, in: – the objective function coefficients – the right-hand side (RHS) values ● Sensitivity analysis is important to the manager who must operate in a dynamic environment with imprecise estimates of the coefficients. ● Sensitivity analysis allows the manager to ask certain what-if questions about the problem. 4 Impact of Possible Changes ● Change an objective function coefficient – May or may not change optimal solution (can be assessed by reading the Excel sensitivity report) ● Change an existing constraint – RHS change: shift a constraint line – LHS coefficient : change slope; may change size of feasible region (cannot be assessed by interpreting the Excel report). ● Add a new constraint – may decrease the feasible region (if binding) ● Remove a constraint – may increase the feasible region (if binding) 5 ● Kelson makes 2 different types of baseball gloves: a regular glove and a catcher’s mitt. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution for each product are shown below. Assume that the company is interested in maximizing the total profit contribution. LP Example Model Cutting& Sewing Finishing Packaging& Shipping Profit/glove Regular Catcher 1 (hr) 1.5 0.5 0.333 0.125 0.25 \$5 \$8 6 LP Formulation - Verbal 3 Components 1) Decision variables – number of regular gloves to be produced – number of catcher’s mitts to be produced 2) Objective function – maximize the total profit contribution. 3) Constraints – cutting&sewing: 900 hours available – finishing: 300 hours available – packaging&shipping: 100 hours available 7 LP Formulation - Mathematical 1) Let x 1 = number of regular gloves x 2 = number of catcher’s mitts 2) Max z = 5 x 1 + 8 x 2 3) s.t. 1 x 1 + 1.5 x 2 ≤ 900 (Cut&Sew) 0.5 x 1 + 0.333 x 2 ≤ 300 (Finishing) 0.125 x 1 + 0.25 x 2 ≤ 100 (Pack&Ship) x 1 , x 2 ≥ 0 (Nonnegativity) 8 Graphical Solution C R 900 400 (500, 150) 900 600 600 800 Pack&Ship Finish Cut&Sew 9...
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This note was uploaded on 11/28/2011 for the course FINANCE 101 taught by Professor Chan during the Spring '11 term at Aarhus Universitet.

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73-220-Lecture09 - 1 Sensitivity Analysis I 73-220 Lecture...

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