Iranian Journal of Operations Research

other Computing maximum proportion and most violated sets Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original In Fisher's and Arrow-Debreu's market equilibrium models with linear utilities, a set <m:omath><m:r>B</m:r></m:omath> of buyers and a set<m:omath><m:r> </m:r><m:r>G</m:r><m:r> </m:r></m:omath>of divisible goods, suppose that there are some buyers with surplus money w.r.t current prices of goods. If there does not exists an equilibrium, then, there are some buyers with surplus money w.r.t the given prices. A set of buyers with surplus money called a violated set. Computing this set helps to find the set of buyers with maximum surplus money w.r.t the given prices.  In this paper, two new kinds of violated sets are defined, which called maximum proportion and most violated sets. We present an algorithm to compute a maximum proportion set, which runs in at most <m:omath><m:r>|</m:r><m:r>B</m:r><m:r>|</m:r></m:omath> maximum flow computations. Also, we show that the set of all buyers <m:omath><m:r>B</m:r></m:omath> is a most violated set.   The market equilibrium problem, Fisher's and Arrow-Debreu's models, Violated sets 123 134 http://iors.ir/journal/browse.php?a_code=A-10-1422-61&slc_lang=other&sid=1 Mehdi Ghiyasvand Mehdi Ghiyasvand mghiyasvand@basu.ac.ir 1111111111 1111111111 Yes Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran