OPERATIONS RESEARCH 1
OPERATIONS RESEARCH 1 ESI 4312
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Ms. Dorian Wiegand
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This 2 page Class Notes was uploaded by Ms. Dorian Wiegand on Friday September 18, 2015. The Class Notes belongs to ESI 4312 at University of Florida taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/206806/esi-4312-university-of-florida in Industrial Engineering at University of Florida.
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Date Created: 09/18/15
Finding a dual to a general linear program Primal or Dual Dual or Primal unrestricted max min Constraints Variables non negative 2 non positive unrestricted Variables non negative Constraints non positive H M l Tableau Formulas max or min 2 c stAz b m 2 0 Tm B submatrix of A Whose columns correspond to basic variables N submatrix of A Whose columns correspond to non basic variables CB entries of 0 corresponding to basic variables 0N entries of 0 corresponding to non basic variables m m by m identity matrix 0 4c ich lN CgBilb Tableau The tableau is optimal for a maximization problem if 7 problem if 40 7 ch lN 0 Assumes we have an LP and an optimal basis We then make a change to a parameter of the LP and wish to investigate if the current basis remains optimal We now outline the types of B lN T Sensitivity Analysis CN CB B lb B lN 2 0 and for a minimization changes and the resulting effect on the tableau of the optimal basis 1 Change Objective function coefficient of a non basic variable j E ect in the tableau reduced cost of the variable j 2 Change Objective function coefficient of a basic variable j nonbasic variables 3 Change Right hand side of constraint 2 E ect The values on the right hand side of the tableau7 ie7 the values of the basic variables E ect reduced cost of all 4 Change The column7 Aj of a non basic variable j E ect The reduced cost of variable j and the column in the tableau corresponding to variable j 01 Change Adding in a new activityvariable E ect We must add in a column in the tableau for the new variable and see if it is eligible for entry into the basis a Change Adding in a new constraint E ect If the current solution satis es the constraint7 then it remains optimal Otherwise7 we take the current basis plus the slackexcess variable of the new constraint as the starting basis to the new problem If the current basis is no longer optimal to our new problem7 then we will apply the primal simplex method for changes 17 27 4 and 5 and the dual simplex method for changes 3 and 6 Def The shadow price of constraint i is the amount the optimal objective function value improves if we increase bl by 17 assuming the current basis remains optimal Def The 100 rule states that if we set where Aj is the change in 07 A1 is the maximum allowable increase in 0739 and AD is the maximum allowable decrease inc 0739 A 7777 ifAjZO 739 77 A luglt0 Di then if 21 rj 17 then the current basis remains optimal to the new linear program