Network-Based Approximate Linear Programming for Discrete Optimization

2017 ◽  
Author(s):  
Selvaprabu Nadarajah ◽  
Andre Augusto Cire
2020 ◽  
Vol 68 (6) ◽  
pp. 1767-1786
Author(s):  
Selvaprabu Nadarajah ◽  
Andre A. Cire

Several prescriptive tasks in business and engineering as well as prediction in machine learning entail the solution of challenging discrete optimization problems. We recast the typical optimization formulation of these problems as high-dimensional dynamic programs and approach their approximation via linear programming. We develop tractable approximate linear programs with supporting theory by bringing together tools from state-space aggregations, networks, and perfect graphs (i.e., graph completions). We embed these models in a simple branch-and-bound scheme to solve applications in marketing analytics and the maintenance of energy or city-owned assets. We find that the resulting technique substantially outperforms a state-of-the-art commercial solver as well as aggregation-heuristics in terms of both solution quality and time. Our results motivate further consideration of networks and graph theory in approximate linear programming for solving deterministic and stochastic discrete optimization problems.


2013 ◽  
Vol 46 (13) ◽  
pp. 478-483
Author(s):  
Yan Zhaoyang ◽  
Ma Xin ◽  
Gao Dong ◽  
Liu Pingping ◽  
Zhang Beike

2020 ◽  
Vol 7 (3) ◽  
pp. 038-043
Author(s):  
A. N. Shingareva ◽  
◽  
M. N. Rasskazova ◽  

This article discusses a linear programming problem on the construction of rolling shift schedules for warehouse employees. A mathematical model of an integer linear programming problem has been developed. The target function can be either minimization of the total number of employees or minimization of wages. Experiments were carried out for various work schedules, which showed the effectiveness of the proposed approach.


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