The manufacture of each type of furniture requires lumber and two types of skilled labour. Linear programming, or lp, is a method of allocating resources in an optimal way. The given lp whose dual we wish to find is called the primal lp. The computed rate provides a direct link between the model input resources and its output. Strong duality and sensitivity analysis in semiinfinite. As described further in the next chapter, sensitivity analysis basically involves investigating the effect on the optimal solution if changes occur in the values of the model pa rameters aij, bi, and cj. Contents 1 make it dual 2 2 be sensitive 4 3 public water system 7 4. Duality provides many in sights into the nature of linear programming, gives us the useful concept of shadow prices, and helps us understand sensitivity analysis.
Duality lagrange dual problem weak and strong duality geometric interpretation optimality conditions perturbation and sensitivity analysis examples generalized inequalities 51. There are a number of questions that could be asked concerning the sensitivity of an optimal solution to changes in the data. Sensitivity analysis in operation research pdf chap6 duality theory and sensitivity analysis. Duality, warm starting and sensitivity analysis in mixed. In 6 the authors study the sensitivity with respect to parameters driving the considered price model. Linear programming notes vii sensitivity analysis 1 introduction when you use a mathematical model to describe reality you must make approximations.
Linear progamming simplexbased sensitivity analysis and. Pdf in this paper the authors consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective. Ch 06 sensitivity analysis and duality free download as powerpoint presentation. Sensitivity analysis suppose that you have just completed a linear programming solution which will have a major impact on your company, such as determining how much to increase the overall production capacity, and are about to present the results to.
Chapter 4 duality given any linear program, there is another related linear program called the dual. First, these shadow prices give us directly the marginal worth of an additional unit of any of the resources. Request pdf duality and sensitivity analysis formulation of the dual problem primaldual relationships economic interpretation of the. Dualitysensitivity general procedure for sensitivity analysis. Sensitivity analysis in linear programming presented by kiran c jadhav government college of engineering, aurangabad an autonomous institute of government of maharashtra department of civil engineering 14172017 2. Duality, warm starting, and sensitivity analysis for milp. In this paper the authors consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective function is the ratio of two realvalued functions. The sensitivity analysis applies to linear fractional problems, even when they solve at an extreme ray, and includes a primaldual algorithm for parametric righthandside analysis. Duality and sensitivity analysis linear programming and network. This discovery revealed that every linear programming problem has associated with it another linear programming problem called the dual. Further, as is the case with lp, the existence of such sensitivity analysis is largely based upon the existence and exploitation of the dual of the lexicographic lgp. Lecture 10 local sensitivity theorem assume that the primal problem has. Content introduction basic parameter in sensitivity analysis duality and sensitivity analysis example of duality and sensitivity analysis references 24172017. Using duality and sensitivity analysis to interpret linear.
Duality and sensitivity analysis linear programming and. Revise the model calculate changes to the original final tableau covert to the proper form using gaussian elimination feasibility test. Second, you will get practice performing sensitivity analysis. Stochastic optimization, sensitivity analysis, sddp, dual sddp, relatively complete recourse. Using duality and sensitivity analysis to interpret linear programming solutions. Introduction formally, sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system numerical or otherwise can be apportioned to different sources of uncertainty. Using duality and sensitivity analysis to interpret linear programming solutions j. In this chapter, we will develop an understanding of the dual linear program. Lecture 10 duality and sensitivity university of illinois. Sensitivity analysisexample the rate of change in optimum z resulting from changing machine 1 capacity from 8 hours to 9 hours can be computed as follows. In this chapter, we will develop an understanding of the dual linear. Duality and sensitivity analysis for fractional programs.
The amount of each resource needed to make each type of furniture is given in the table. Introduction to operations research answers duality and sensitivity analysis prof. In this chapter we will address those that can be answered most easily. Sanjeeb dash garth isaak jeff linderoth ted ralphs department of industrial and systems engineering. Pdf 1st lecture of operation research 2 duality and. In what range of the lp model data is an optimal solution robust.
Exercise 1 items a, c, h exercise 1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30. Duality and sensitivity analysis sage research methods. Sensitivity analysis example the rate of change in optimum z resulting from changing machine 1 capacity from 8 hours to 9 hours can be computed as follows. Duality, sensitivity analysis and the simples tableau. Duality theory and sensitivity analysis one of the most important discoveries in the early development of linear programming was the concept of duality and its many important ramifications. Sensitivity analysis 1 is the study of the variation of the output of a model as the input of the model changes. It is a necessary basis for students planning to take advanced topics in linear and nonlinear programming. Chapter 18 simplexbased sensitivity analysis and duality. Then, you will apply your knowledge of duality and sensitivity by serving the public sector. Local sensitivity analysis suppose strong duality holds for unperturbed problem u 0,v 0, and. When we study the correlation between a target response variable y and a set of.
The duality correspondences that are developed do not require either differentiability or the existence of optimal solution. Duality, warm starting, and sensitivity analysis for milp ted ralphs and menal guzelsoy industrial and systems engineering lehigh university informs annual conference, denver, co, tuesday, october 26, 2004. Using duality and sensitivity analysis to interpret linear programming solutions public deposited. When we solve a modelwhatever type of model and with whatever algorithmwe are typically only roughly midphase in our overall process. How does the optimal solution value change in response to modi. Introduces and explains how to use duality theory and sensitivity analysis to interpret linear programming solutions. Finitedimensional linear programs satisfy strong duality sd and have the dual pricing dp property.
Finally, you will practice with complementary slackness and the dual simplex method by helping out a local farmer. In this paper we investigate the dual of a multistage stochastic linear program mslp to study two related. In the preceding chapter on sensitivity analysis, we saw that the shadowprice interpretation of the optimal simplex multipliers is a very useful concept. A geometric standpoint on linear programming part ii simplex algorithm, duality, sensitivity analysis created date. Sensitivity analysis, duality analysis, linear programming, optimal water treatment cost model, interiorpoint method. Duality and sensitivity analysis when we solve a modelwhatever type of model and with whatever algorithmwe are typically only roughly midphase in our overall process of analysis. Duality, warm starting, and sensitivity analysis for milp ted ralphs and menal guzelsoy industrial and systems engineering lehigh university sas institute, cary, nc, friday, august 19, 2005. Duality and sensitivity analysis of multistage linear.
This understanding translates to important insights about many optimization problems and algorithms. Duality in linear programming 4 in the preceding chapter on sensitivity analysis, we saw that the shadowprice interpretation of the optimal simplex multipliers is a very useful concept. Sensitivity analysis sensitivity is a postoptimality analysis of a linear program in which, some components of a, b, c may change after obtaining an optimalsolution with an optimal basis and an optimal objective value. Duality and sensitivity analysis of multistage linear stochastic. Part of the performance excellence in the wood products industry publication series. A geometric standpoint on linear programming part ii. Sensitivity analysis sensitivity analysis is the study of how the changes in the coefficients of a linear program affect the optimal solution in this chapter we discuss how sensitivity analysis information can be obtained from the final simplex tableau ranges for the objective function coefficients dual prices, ranges for the righthandside values. Pdf using duality and sensitivity analysis to interpret. Duality, warm starting, and sensitivity analysis for milp ted ralphs and menal guzelsoy industrial and systems engineering lehigh university informs annual. You do not have access to any existing collections.
Sensitivity analysis can also indicate which parameter values are. Mathematical sensitivity analysis duality exercises limpopo furniture company the limpopo furniture company manufactures desks, tables, and chairs. More recently, the sensitivity analysis of multistage stochastic programs was discussed in 6 and 27. Sensitivity analysis suppose that you have just completed a linear programming solution which will have a major impact on your company, such as determining how much to increase the overall production capacity, and are about to present the results to the board of directors. Linear progammingsimplexbased sensitivity analysis and duality. Linear programming and network flows, third edition. Sensitivity analysis provides an invaluable tool for addressing such issues. Pdf duality and sensitivity analysis for fractional programs. Sensitivity analysis is a powerful method for discovering the significant factors that contribute to understanding the interaction between variables in multivariate datasets.
Linearity assumptions usually are signi cant approximations. Sensitivity analysis question after solving a lp problem. Sensitivity analysis allows him to determine what level of accuracy is necessary for a parameter to make the model sufficiently useful and valid. Linear programmingduality and sensitivity analysis. Duality sensitivity general procedure for sensitivity analysis. Apr 17, 2017 sensitivity analysis linear programming copy 1. Further, the dual variable constraint for a primal.
1216 653 1330 361 702 1457 845 1521 1259 1302 560 370 478 364 1099 15 639 380 1636 62 1659 287 2 1321 866 630 1602 967 980 130 185 1102 1357 1135 1259 846 1220 1241 943 72 985