Efficient Solution Procedure to Develop Maximal Covering Location ProblemUnder Uncertainty (Using GA and Simulation)

In this paper, we present the stochastic version of Maximal Covering Location Problem which optimizes both location and allocation decisions, concurrently. It’s assumed that traveling time between customers and distribution centers (DCs) is uncertain and described by normal distribution function and if this time is less than coverage time, the customer can be allocated to DC. In classical models, traveling time between customers and facilities is assumed to be in a deterministic way and a customer is assumed to be covered completely if located within the critical coverage of the facility and not covered at all outside of the critical coverage. Indeed, solutions obtained are so sensitive to the determined traveling time. Therefore, we consider covering or not covering for customers in a probabilistic way and not certain which yields more flexibility and practicability for results and model. Considering this assumption, we maximize the total expected demand which is covered. To solve such a stochastic nonlinear model efficiently, simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

Keywords:

maximal covering , location , genetic algorithm , simulation , uncertainty modeling