بررسي و مقايسه روش هاي تحليل مدل هاي رياضي نا شدني خطي

چكيده انگليسي :

Comparison of the infeasibility resolution methods in linear mathematical models Abozar Soltani Soltanitabar@yahoo com 2009 07 12 Department of Industrial System Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Naser Mollaverdi PhD naserm@cc iut ac ir Abstract In nowadays world human beings face a lot of problems with greater complexities than the past Engineers urban designers and economists use modeling to solve and predict problems in their respected fields of study Linear modeling is one of the simplest mathematical models In considering the linear models there are instances which the created model does not reach the solution In the other word the feasible solution set is empty These models are called infeasibility Models Infeasibility results from the lack of intersection between constraints This can result from the errors occurred during the modeling or from wrong information and data used In addition to the errors of modeling and wrong information the constraints of the model may not be compatible and change into an infeasible problem The infeasibility Studies have been done in two fields of diagnosis infeasibility and resolution the infeasibility Resolution infeasibility is possible in two cases The other method is altering some of the constraints to reach a feasible model In this paper some of the resolution infeasibility algorithms have been introduced and at the end three algorithms Goal programming Least Squares and Roodman have been chosen for the sake of the comparison The reason why these three algorithms have been chosen is novelty and their application in the recent papers and research The algorithms have been realized in MATLAB software Not having access to the real world problems made the researcher to use the artificial problems by applying the simulation model as a result some generators were designed and used to produce the infeasible linear programming In this study two kinds of the linear programming problems are intended to be applied one as the variables are free in the sign and the other as the variables are positive For the comparison several factors such as the time needed to reach the solution the required memory the value of the objective function the amount of infeasibility the number of the altering constraints the number of iterations and the number of zero and non zero variables were taken into solution Factors such as time the value of the objective function the amount of infeasibility and the average percentage of the altering constraints were considered more important than the other factors Regarding different factors and indices applied to compare the different methods one can not say for sure which method the best is considering all the other indices since the structure of the problem plays a great role in here In practice some of these indices might be deemed appropriate by some users and the other indices might not By comparing the four important indices and considering the sample generated problems the researcher found out that Roodman method was better than the other two methods In comparing the two other methods one can say that none outweighs the other and in this situation one can choose the better one based on the user s viewpoints and the indices which are suitable for the user Key words Infeasibility resolution infeasibility irreducible infeasible set IIS altering constraints Goal programming Least Squares Roodman pdfMachine Is a pdf writer that produces quality PDF files with ease Produce quality PDF files in seconds and preserve the integrity of your original documents Compatible across nearly all Windows platforms if you can print from a windows application you can use pdfMachine Get yours now

سلطاني شورباخورلو، ابوذر

بررسي و مقايسه روش هاي تحليل مدل هاي رياضي نا شدني خطي

تحليل نا شدني , سيستم ناسازگار ساده ناپذير , دستكاري محدوديت , برنامه ريزي ارماني , حداقل مربعات , رودمن