Mathematical models and decomposition methods for the multiple knapsack problem

Dell’Amico, Mauro, Maxence Delorme, Manuel Iori and Silvano Martello

European Journal of Operational Research, 2019, vol. 274, issue 3, 886-899

Abstract: We consider the multiple knapsack problem, that calls for the optimal assignment of a set of items, each having a profit and a weight, to a set of knapsacks, each having a maximum capacity. The problem has relevant managerial implications and is known to be very difficult to solve in practice for instances of realistic size. We review the main results from the literature, including a classical mathematical model and a number of improvement techniques. We then present two new pseudo-polynomial formulations, together with specifically tailored decomposition algorithms to tackle the practical difficulty of the problem. Extensive computational experiments show the effectiveness of the proposed approaches.

Keywords: Combinatorial optimization; Multiple knapsack problem; Exact algorithms; Pseudo-polynomial formulations; Decomposition methods (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:274:y:2019:i:3:p:886-899

DOI: 10.1016/j.ejor.2018.10.043

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