Scheduling Unit Tasks with Collective Preferences: Computational Social Choice Meets Scheduling

Core Concepts

Given a set of tasks and a set of voters with preferences over the order of task execution, the goal is to compute a consensus schedule that minimizes the average dissatisfaction of the voters.

Abstract

The content discusses the collective schedules problem, which involves scheduling a set of tasks shared by a set of voters (individuals) who have preferences over the order of task execution. Two models are considered: Order Preferences, where each voter provides a preferred order (permutation) of the tasks, and Interval Preferences, where each voter specifies a release date and deadline for each task.
The key highlights and insights are:

The problem can be solved optimally in polynomial time as an assignment problem, both for the binary criterion (whether a task is scheduled within the desired interval) and the distance criterion (how far a task is scheduled from the desired interval).

An analysis of the EMD (Earliest Median Date) rule shows that it is a 2-approximation for the total tardiness and total earliness criteria.

The paper studies the extent to which the rules (Distance Criterion, Binary Criterion, EMD) satisfy desirable properties like release date consistency, deadline consistency, and temporal unanimity when time constraints are inferred from the voters' preferences.

The paper also shows that the rules do not necessarily satisfy these properties, and provides examples to illustrate the cases where they fail to do so.

The problem is further studied under precedence constraints between tasks, showing that the previously studied rules can still be used with an additional polynomial-time step when the constraints are inferred from the voters' preferences, but become NP-hard when the constraints are not fulfilled by the voters' preferred schedules.

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Key Insights Distilled From

Ordering Collective Unit Tasks

by Martin Duran... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19197.pdf

Deeper Inquiries

How can the proposed rules be extended to handle tasks with different processing times

The proposed rules can be extended to handle tasks with different processing times by incorporating the processing times into the criteria used for scheduling. For tasks with varying processing times, the rules can be modified to consider the duration of each task in addition to the preferences of the voters. This adjustment would involve adjusting the cost calculations in the assignment problem to account for the processing times of the tasks. By incorporating the task durations into the criteria, the rules can be adapted to optimize the scheduling of tasks with different processing times while still considering the preferences of the voters.

What are the implications of the failure to satisfy release date and deadline consistency properties, and how can the rules be modified to address this issue

The failure to satisfy release date and deadline consistency properties can have significant implications for the effectiveness of the scheduling rules. When the rules do not adhere to these properties, it can lead to schedules that do not align with the time constraints specified by the voters. This can result in suboptimal schedules that do not meet the requirements or expectations of the voters. To address this issue, the rules can be modified to incorporate constraints that ensure tasks are scheduled within the specified release dates and deadlines. By adjusting the rules to prioritize schedules that adhere to these constraints, the scheduling process can be improved to better meet the needs and preferences of the voters.

What are the potential applications of the collective schedules problem beyond scheduling, and how can the insights from this work be leveraged in those domains

The collective schedules problem has potential applications beyond traditional scheduling scenarios. The insights gained from this work can be leveraged in various domains such as project management, event planning, and resource allocation. In project management, the collective schedules problem can help in optimizing task assignments and timelines based on the preferences of team members. For event planning, the problem can assist in organizing and scheduling activities to maximize attendee satisfaction. In resource allocation, the insights from this work can be used to efficiently allocate resources based on user preferences and constraints. By applying the principles and algorithms developed for the collective schedules problem, organizations can improve decision-making processes and enhance overall efficiency in various domains.