Robust single-stage selection problems with budgeted interval uncertainty

TL;DR

This paper investigates robust single-stage selection problems under budgeted interval uncertainty, providing complexity classifications and algorithms for decision-making with uncertain costs and constraints.

Contribution

It offers a comprehensive computational complexity analysis and algorithms for robust selection problems with budgeted interval uncertainty, extending prior two-stage models.

Findings

Polynomial-time algorithms for specific cases.

NP-hardness results for general cases.

Complexity classifications including NP and Sigma p 2 completeness.

Abstract

We study single-stage decision problems in which a subset of items with minimum total cost has to be selected at once from a given set of items, subject to two costs of each item -fixed and uncertain -and cardinality constraints for each cost type. The worst-case budgeted interval uncertainty is considered. At the time of decision making, the fixed costs are known, but for each uncertain cost, only the range of its values is available. Similar but two-stage selection problems have been studied in the literature, in which first-and second-stage decisions are made before and after uncertain costs become known, respectively. The problems studied are distinguished by continuous or discrete uncertain costs, and by uncertainty budgets based on cardinality or volume. An almost complete computational complexity classification is provided, including fast polynomial-time algorithms, NP-and $\Sigma$ p 2 -completeness and hardness proofs. keyword robust optimization -budgeted uncertainty -selection problem -dynamic programming -computational complexity