ISYE3400_Ch.7_Sensitivity Analysis_Part1_Spring2018.pdf

ISYE3400_Ch.7_Sensitivity Analysis_Part1_Spring2018.pdf -...

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Chapter 7 Sensitivity Analysis/ Part 1 Slides contain significant supplemental material from “Operations Research” by Wayne Winston (3 rd edition) 1
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2 Deterministic OR Stochastic OR Operations Research Math modeling LP IP NLP Simulation Queuing Decision Analysis Stochastic Programming Network models ISYE 3400 DP ISYE 4200
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Learning Objectives Correctly use the terminology of sensitivity analysis, such as slack/surplus variables, reduced cost, shadow/dual price Graphically illustrate the intuition behind the impact of a change in the RHS or objective coefficients in a LP with 2 variables Understand the economic interpretation of dual variables/shadow prices Produce, read and understand computer output for Sensitivity Analysis Identify the impact of changing objective costs from Lingo output Identify the impact of changing right hand sides from Lingo output 3
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Sensitivity Analysis 4 Coefficients in an LP formulation are assumed to be known with absolute certainty Sensitivity analysis is concerned with how changes in an LP’s parameters affect the optimal solution. What is the effect upon the optimal solution of: Variations in the cost/profit coefficients in the objective function Variations in the resource availabilities (right hand side) of the constraints. “What If” analysis
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5 Reconsider the Giapetto problem x1 = number of soldiers produced each week x2 = number of trains produced each week Maximize Z = 3x1 + 2x2 (profit) Subject to: 2 x1 + x2 ≤ 100 (finishing constraint) x1 + x2 ≤ 80 (carpentry constraint) x1 ≤ 40 (demand constraint) x1, x2 ≥ 0 (non-negativity) Optimal Solution: x1 = 20, x2 = 60, Z = 180 Example
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Finishing and carpentry constraints are binding . At the optimal solution (x1=20, x2=60), we are using up all the available 100 finishing hours and 80 carpentry hours. The optimal solution is at the intersection of those constraints, graphically. You might wonder, should we buy more finishing or carpentry hours? If so, how much should we pay for these hours? What will this do to our solution? Increase profit? Change how many soldiers and trains we make? To answer these questions we could Increase # finishing or carpentry hours (i.e. change RHS) and re-solve, over and over and over and over and ……Or use sensitivity analysis 6 Why Sensitivity Analysis?
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Currently we make $3 profit for each soldier (x1) and $2 profit for each train (x2). What if these profits changed (up or down)? Maybe we did not estimate our costs correctly or sale prices change What will this do to our solution? Change how many soldiers and trains we make? How? To answer these questions we could Change profits (i.e. change objective function coefficients) and resolve, over and over and over and over and ……Or use sensitivity analysis.
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