The Multiple Multidimensional Knapsack with Family-Split Penalties

The Multiple Multidimensional Knapsack Problem with Family-Split Penalties (MMdKFSP) is introduced as a new variant of both the more classical Multi-Knapsack and Multidimensional Knapsack Problems. It reckons with items categorized into families and where if an individual item is selected to maximize the profit, all the items of the same family must be selected as well. Items belonging to the same family can be assigned to different knapsacks; however, in this case, split penalties are incurred. This problem arises in resource management of distributed computing contexts and Service Oriented Architecture environments. An exact algorithm based on the exploitation of a specific combinatorial Benders’ cuts approach is proposed. Computational experiments on different sets of benchmark test problems show the effectiveness of the proposed algorithm. The comparison against a state-of-the-art commercial solver confirms the validity of the proposed approach considering also the scalability issue.