The capacitated multi‐facility Weber problem is concerned with locating I capacitated facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost of a single commodity. This is a nonconvex optimization problem and difficult to solve. In this work, we focus on a multi‐commodity extension and consider the situation where K distinct commodities are shipped subject to capacity constraints between each customer and facility pair. Customer locations, demands and capacities for each commodity, and bundle restrictions are known a priori. The transportation costs, which are proportional to the distance between customers and facilities, depend on the commodity type. We address several location–allocation and discrete approximation heuristics using different strategies. Based on the obtained computational results we can say that the alternate solution of location and allocation problems is a very efficient strategy; but the discrete approximation has excellent accuracy.
