A Location Programming under Stochastic Travel Time through Genetic Algorithm

This paper considers a location-optimization problem where the classical facility location model is recast in a stochastic environment with several risk factors that make travel time from facility site to customer site probabilistic. We present a Stochastically Travel Time Location Problem (STTLP), a more general set covering problem than classical set covering location problem. Given a discrete network G(V,A), we formulate STTLP as an integer programming under the goal of minimizing the sum of set up cost of selected facilities and opportunity cost of the unserved customers, and then provide a mixed genetic algorithm strategies to solve the variety of size of the problem, the result was analyzed after computational experiment and compared with two greedy-based heuristic algorithms which have proven to be overall the best in solving set covering location problems. The computational experiment shows a good performance of our mixed genetic algorithm.