The Decomposition Algorithm for Linear Programs

Econometrica ◽  
1961 ◽  
Vol 29 (4) ◽  
pp. 767 ◽  
Author(s):  
George B. Dantzig ◽  
Philip Wolfe
Keyword(s):  
Decomposition Algorithm ◽  
Linear Programs

Analyzing Decomposition Procedures in LP and Unraveling for the Two Person Zero Sum Game and Transportation Problems

2020 ◽  
Vol 3 (1) ◽  
pp. 21-41
Author(s):  
Haridas Kumar Das ◽  
Abir Sutra Dhar
Keyword(s):  
Transportation Problem ◽  
Benders Decomposition ◽  
Decomposition Methods ◽  
Decomposition Algorithm ◽  
Linear Programs ◽  
Transportation Problems ◽  
Unbounded Solutions ◽  
Mathematical Programs ◽  
Iteration Number ◽  
Zero Sum

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.

Optimum packing of rectangles based on heuristic dynamic decomposition algorithm

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