New heuristic methods for the capacitated multi-facility Weber problem

In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, squared Euclidean, and 𝓁p-distances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient.