Exact algorithms for the bin packing problem with fragile objects |
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Authors: | Manuel A. Alba Martínez François Clautiaux Mauro Dell’Amico Manuel Iori |
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Affiliation: | 1. University of Modena and Reggio Emilia, Via Amendola 2, 42122 Reggio Emilia, Italy;2. Université de Lille 1, LIFL, UMR CNRS 8022, INRIA Lille Nord Europe, Parc de la Haute Borne, 59655 Villeneuve d’Ascq, France |
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Abstract: | We are given a set of objects, each characterized by a weight and a fragility, and a large number of uncapacitated bins. Our aim is to find the minimum number of bins needed to pack all objects, in such a way that in each bin the sum of the object weights is less than or equal to the smallest fragility of an object in the bin. The problem is known in the literature as the Bin Packing Problem with Fragile Objects, and appears in the telecommunication field, when one has to assign cellular calls to available channels by ensuring that the total noise in a channel does not exceed the noise acceptance limit of a call.We propose a branch-and-bound and several branch-and-price algorithms for the exact solution of the problem, and improve their performance by the use of lower bounds and tailored optimization techniques. In addition we also develop algorithms for the optimal solution of the related knapsack problem with fragile objects. We conduct an extensive computational evaluation on the benchmark set of instances, and show that the proposed algorithms perform very well. |
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Keywords: | Bin packing Fragile objects Branch-and-bound Branch-and-price |
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