Given a set of items, each characterized by a profit and a weight, we study the problem of maximizing the product of the profits of the selected items, while respecting a given capacity. To the best of our knowledge this is the first manuscript that studies this variant of the knapsack problem which we call Product Knapsack Problem (PKP). We show that PKP is weakly NP-hard. We propose and implement a Dynamic Programming algorithm and different Mixed Integer Linear and Nonlinear Programming formulations for the PKP. Finally, we present an extensive computational study on a large set of benchmark instances derived from the literature.
On the Product Knapsack Problem / D'Ambrosio, C.; Furini, F.; Monaci, M.; Traversi, E.. - In: OPTIMIZATION LETTERS. - ISSN 1862-4472. - 12:4(2018), pp. 691-712. [10.1007/s11590-017-1227-5]
On the Product Knapsack Problem
Furini F.
;
2018
Abstract
Given a set of items, each characterized by a profit and a weight, we study the problem of maximizing the product of the profits of the selected items, while respecting a given capacity. To the best of our knowledge this is the first manuscript that studies this variant of the knapsack problem which we call Product Knapsack Problem (PKP). We show that PKP is weakly NP-hard. We propose and implement a Dynamic Programming algorithm and different Mixed Integer Linear and Nonlinear Programming formulations for the PKP. Finally, we present an extensive computational study on a large set of benchmark instances derived from the literature.| File | Dimensione | Formato | |
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