Algorithmic Methods for Concave Optimization Problems

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.