Dataset on a problem of assigning activities to children, with various optimization constraints

Varone, Sacha; Beffa, Corentin

doi:10.1016/j.dib.2019.104168

Cited by 2 publications

(1 citation statement)

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“…We consider resource allocation problems that arise in practical applications such as hot desking or shared work spaces (Varone and Beffa 2019;Cai and Khan 2010), classroom scheduling (Phillips et al 2015), matching customers with taxicabs (Karamanis, Anastasiadis, and Angeloudis 2021;Kucharski and Cats 2020), and matching agricultural equipment with farms (Gilbert 2018;Rakhra and Singh 2020). In such scenarios, many agents (individuals, cohorts, farms, or in general, entities) are competing for a limited number of time-shared resources.…”

Section: Introductionmentioning

confidence: 99%

Resource Sharing through Multi-Round Matchings

Trabelsi

Adiga

Kraus

et al. 2023

AAAI

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Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which they want to be matched. Viewing such an application as a multi-round matching problem on a bipartite compatibility graph between agents and resources, we show that a solution (i.e., a set of matchings, with one matching per round) can be found efficiently if one exists. To cope with situations where a solution does not exist, we consider two extensions. In the first extension, a benefit function is defined for each agent and the objective is to find a multi-round matching to maximize the total benefit. For a general class of benefit functions satisfying certain properties (including diminishing returns), we show that this multi-round matching problem is efficiently solvable. This class includes utilitarian and Rawlsian welfare functions. For another benefit function, we show that the maximization problem is NP-hard. In the second extension, the objective is to generate advice to each agent (i.e., a subset of requirements to be relaxed) subject to a budget constraint so that the agent can be matched. We show that this budget-constrained advice generation problem is NP-hard. For this problem, we develop an integer linear programming formulation as well as a heuristic based on local search. We experimentally evaluate our algorithms on synthetic networks and apply them to two real-world situations: shared office spaces and matching courses to classrooms.

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