The Decomposition Algorithm for Linear Programs

Econometrica ◽  
1961 ◽  
Vol 29 (4) ◽  
pp. 767 ◽  
Author(s):  
George B. Dantzig ◽  
Philip Wolfe
Author(s):  
Haridas Kumar Das ◽  
Abir Sutra Dhar

This paper studies some decomposition methods, including Dantzig-Wolfe decomposition (DWD), decomposition-based pricing (DBP), Benders decomposition (BD), and a recently proposed improved decomposition (ID) method for solving linear programs (LPs). The authors then develop a new decomposition algorithm for solving LPs in a general form, allowing authors to combine the concept of Benders decomposition and decomposition-based pricing methods. The authors generate conditions for solving problems that have either infeasible or unbounded solutions. As an illustration, the authors give the corresponding models and numerical results for two standard mathematical programs: the two-person zero-sum game and the transportation problem. The authors compare several procedures and identify which one produces the best solution by giving the authors the smallest iteration number. This study reveals that the algorithm along with Benders decomposition produce the most efficient computational solutions of LPs.


2013 ◽  
Vol 33 (7) ◽  
pp. 1908-1911
Author(s):  
Bo LI ◽  
Shi WANG ◽  
Songxin SHI ◽  
Junyong HU

Sign in / Sign up

Export Citation Format

Share Document