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What is sensitivity analysis? Why do we perform sensitivity analysis?

What is sensitivity analysis? Why do we perform sensitivity analysis? How far do we like to perform sensitivity analysis? In an LP sensitivity analysis, what type of conditions or information are considered? In an LP sensitivity analysis, what type of conclusions are considered?.

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What is sensitivity analysis? Why do we perform sensitivity analysis?

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  1. What is sensitivity analysis? Why do we perform sensitivity analysis? How far do we like to perform sensitivity analysis? In an LP sensitivity analysis, what type of conditions or information are considered? In an LP sensitivity analysis, what type of conclusions are considered? IE 416, Chap 5:1, July 98

  2. Shadow Price: SP page 199 Shadow price for the i th constraint of an LP is the amount by which the optimal z-value is improved if the rhs of the i th constraint is increased by 1. Reduced Cost: RC page 205 For any nonbasic variable Xk, the reduced cost is the amount by which the objective function coefficient of Xk must be improved before the LP will have an optimal solution in which Xk is a basic variable IE 416, Chap 4:3, July 98

  3. Terms Used in Different Books on Simplex method WinstonWinQSB System Binding Tight Non-binding Loose Slack Slack Excess Surplus Reduced cost Opportunity cost Shadow price Dual price IE 416, Chap 4:4, July 98

  4. Summary of LP Sensitivity Analysis, Notations O.F. Z=CBV*XBV + CNBV*XNBV S.T. ab1*X1 + ab2*X2 + … =< bb an1*X1 + an2*X2 + …. =<bn Where: CBV = coefficient of basic variable in Z CNBV = ….. nonbasic variable in Z XBV = basic variable in optimal solution XNBV = nonbasic variable in optimal solution bb = right hand side of binding constraint bn = right hand side of nonbinding constraint SPi = shadow price of constraint i RCi = reduced cost of XNBV C’BV = new CBV , C’NBV = new CNBV , b’b= new bb , b’n= new bn IE 416, Chap 5, Feb. 98

  5. Summary of LP Sensitivity Analysis Summary information from output of the Quant software: Coefficient of OF. RHS . Variable RC Min CurrentMaxConstraintsi/eiSPMinCurrentMax Summary sensitivity analysis: . IF .. THEN . Basis (var)bfs (value)Z (value) . min C’BV maxsame same Z+( CBV)XBV C’Bv out of rangechange change change min C’NBV maxsame same same C’NBv out of rangeXNBV ->X’BV change change min b’b maxsame change Z+SPb( bb) b’b out of rangechange change change min b’n maxsame same same b’n out of rangechange change change Note: y = y’ - y Note: If output of the Lindo is being used then Z SPb( bb); Use + if O.F. is max; Use - if O.F. is min IE 416, Chap 5, Dec. 98

  6. Managerial Use of Shadow Price What is the maximum amount that a manager would like to pay extra for an extra unit of a resource? Consider RMC problem and material 3 in the following table. IE 416, Chap 5, Sept. 2009

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