An optimization algorithm for a penalized knapsack problem

Authors:
Alberto Ceselli;Giovanni Righini
Affiliations:
Dipartimento di Tecnologie dell'Informazione, Universití degli Studi di Milano, via Bramante 65, 26013 Crema (CR), Italy;Dipartimento di Tecnologie dell'Informazione, Universití degli Studi di Milano, via Bramante 65, 26013 Crema (CR), Italy
Venue:
Operations Research Letters
Year:
2006

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Abstract

We study a variation of the knapsack problem in which each item has a profit, a weight and a penalty; the sum of profits of the selected items minus the largest penalty associated with the selected items must be maximized. We present an ILP formulation and an exact optimization algorithm.