Component commonality is an efficient mechanism to mitigate the negative impact of a highly diversified product line. In this paper, we address the optimal commonality problem in a real multidimensional space, developing a novel algorithmic approach aimed at transforming a continuous multidimensional decision problem into a discrete decision problem. Moreover, we show that our formulation is equivalent to the k-median facility location problem. It is well known that when several dimensions are included and components’ features are defined in the real line, the number of potential locations grows exponentially, hindering the application of standard integer programming techniques for solving the problem. However, as formulated, the multidimensional component commonality problem is a supermodular minimization problem, a family of problems for which greedy-type heuristics show very good performance. Based on this observation, we provide a collection of descent-greedy algorithms which benefits from certain structural properties of the problem and can handle substantially large instances. Additionally, a MathHeuristic is developed to improve the performance of the algorithms. Finally, results of a number of computational experiments, which testify for the good performance of our heuristics, are presented. 
The component commonality problem in a real multidimensional space: An algorithmic approach