Solving probabilistic multi-facility Weber problem by vector quantization

The multi-facility Weber problem is concerned with locating in the plane m facilities having unlimited capacities and allocating them to n customers at minimum total cost. The deterministic version is a non-convex optimization problem and difficult to solve exactly. In this work we focus on a probabilistic extension and consider the situation where the customer locations are randomly distributed. For this problem, we propose new heuristics based on the principle of vector quantization which are capable of computing good quality solutions for general distance functions and customer location distributions.