TITLE:
Algorithmic Methods for Concave Optimization Problems
AUTHORS:
Xu Zhang, Xue Tian, Chen Wang, Tao Li
KEYWORDS:
LMRP, Lagrangian Method, Linearization Method
JOURNAL NAME:
American Journal of Industrial and Business Management,
Vol.7 No.7,
July
19,
2017
ABSTRACT: In this thesis, we reformulate
the original non-linear model for the LMRP. Firstly, we introduced a set of
parameters to represent the non-linear part of the cost increase for a facility
space allocated potential additional costs and new set of decision variables,
indicating how many customers each equipment distribution. The algorithms are
tested on problems with 5 to 500 potential facilities and randomly generated
locations. Then using actual data to validate this new method is better. Our work was motivated by the modeling approach
used in the Maximum Expected Covering Location Problem (MEXCLP). We compare new
method and Lagrangian relaxation method to solve LMRP with constant customer
demand rate and equal standard deviation of daily demand.