A rounding strategy-based algorithm for the k-clustering minimum biclique completion problem

In logistics, completion problems can arise in batching a group of distribution warehouses. It is often preferable to group orders from different customers into a pick batch (cluster), where all requested orders must be collected. This problem occurs when combining multiple orders from a single customer into a single pick order. Therefore, this study aims to investigate a variant of this problem: the k-clustering minimum bi-clique completion problem. For this purpose, a hybrid algorithm is designed to solve it, where both rounding strategy and augmented local search cooperate for highlighting the quality of the solutions achieved. The performance of the proposed method is evaluated on a set of benchmark instances taken from the literature, where its provided results (bounds) are compared to those achieved by the best method available in the literature. New bounds are obtained.