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

Shadow Price: SP page 230 Reduced Cost: RC page 236 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 236 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

Terms Used in Different Books on Simplex method Winston WinQSB 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

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

Summary of LP Sensitivity Analysis Summary information from output of the Quant software: Coefficient of OF . RHS . Variable RC Min Current Max Constraint si/ei SP Min Current Max Summary sensitivity analysis: . IF . . THEN . Basis (var) bfs (value) Z (value) . min C’BV max same same Z+( CBV)XBV C’Bv out of range change change change min C’NBV max same same same C’NBv out of range XNBV ->X’BV change change min b’b max same change Z+SPb( bb) b’b out of range change change change min b’n max same same same b’n out of range change 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