On the Product Knapsack Problem

D’Ambrosio, Claudia; Furini, Fabio; Monaci, Michele; Traversi, Emiliano

D’Ambrosio, Claudia; Furini, Fabio; Monaci, Michele; Traversi, Emiliano (2018), On the Product Knapsack Problem, Optimization Letters, 12, 4, p. 691-712. 10.1007/s11590-017-1227-5

Type

Article accepté pour publication ou publié

Date

2018

Journal name

Optimization Letters

Volume

Number

Pages

691-712

Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Furini, Fabio
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Monaci, Michele

Traversi, Emiliano
Laboratoire d'Informatique de Paris-Nord [LIPN]

Abstract (EN)

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.

Subjects / Keywords

Knapsack problem; Dynamic programming; Complexity; Mixed integer (non)linear programming