Robust Multicovers with Budgeted Uncertainty
Sven O. Krumke, Eva Schmidt, Manuel Streicher
TL;DR
This paper introduces a robust version of the Min-q-Multiset Multicover problem, addressing demand uncertainty with budget constraints, and proposes solution methods with computational testing on synthetic and real-world instances.
Contribution
It formulates the robust Min-q-Multiset Multicover problem, analyzes its complexity, and develops solution approaches with computational experiments.
Findings
Robust version is strongly NP-hard for all q.
Non-robust version is NP-complete for q > 2.
Solution methods effectively handle real-world emergency doctor location instances.
Abstract
The Min--Multiset Multicover problem presented in this paper is a special version of the Multiset Multicover problem. For a fixed positive integer , we are given a finite ground set , an integral demand for each element in and a collection of subsets of . The task is to choose sets of the collection (multiple choices are allowed) such that each element in is covered at least as many times as specified by the demand of the element. In contrast to Multiset Multicover, in Min--Multiset Multicover each of the chosen subsets may only cover up to of its elements with multiple choices being allowed. Our main focus is a robust version of Min--Multiset Multicover, called Robust Min--Multiset Multicover, in which the demand of each element in may vary in a given interval with an additional budget constraint bounding the sum of the demands. Again, the task is…
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