Catalog segmentation with the objective of satisfying customer requirements in minimum number of catalog

This work is concerned with customer-oriented catalog segmentation that each catalog consists of specific number of products. In this problem, requirements of a specific ratio of customers should be satisfied. According to the definition, when a customer is satisfied that at least t required products exist in his/her catalog. The objective of this problem is to minimize the number of catalogs, regarding to minimum number of customers constraint that was comply. In this paper, we present a mixed-integer programming model for this clustering problem. This problem is NP-hard in large scales and the optimum solution is almost impossible to reach. Hence, a solution procedure is developed based on genetic algorithm. Then, the results of computational experiments are reported, in which the GA solution is compared with exact solution of mixed-integer programming model.