Lexicographic α-Robust Knapsack Problem : Complexity Results

The knapsack problem is a classical combinatorial problem used to model many industrial situations. Faced with uncertainty on the model parameters, robustness analysis is an appropriate approach to find reliable solutions. The robust knapsack problem was studied in the literature using a max-min criterion. In this paper, we show the drawbacks of this criterion and propose a new robustness approach, called lexicographic α-robustness. We show that the complexity of the lexicographic α-robust problem does not increase compared with the max-min version and present a pseudo-polynomial algorithm in the case of a bounded number of scenarios.