We give an upper bound for the number of different basic feasible solutions generated by Dantzig's simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bounded variables. We apply our bound to the minimum cost flow problem and the maximum flow problem, and we obtain new results of bounds for Dantzig's simplex method.
|Number of pages||9|
|Journal||Pacific Journal of Optimization|
|Publication status||Published - Jul 2012|
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Computational Mathematics
- Applied Mathematics