Annals of Operations Research· 2026Q1
Balanced assignments of periodic tasks
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- 2026year
Short summary
A necessary and sufficient condition for balanced periodic task assignment to workers, ensuring equal task frequency per worker long-term, is established and verifiable in polynomial time.
AI-generated from the title and abstract; the full text is not read.
Key points
- Establishes a necessary and sufficient condition for balanced periodic task assignment.
- The condition ensures each worker performs tasks with equal long-term frequency.
- The condition can be verified in polynomial time.
- Proves that a periodic balanced assignment exists if any balanced assignment exists, even with added constraints.
AI-generated from the title and abstract; the full text is not read.
Abstract
This work addresses the problem of assigning periodic tasks to workers in a balanced way, i.e., so that each worker performs every task with the same frequency over the long term. The input consists of a list of tasks to be repeated weekly at fixed times and a number of indistinguishable workers. In the basic version, the sole constraint is that no worker performs two tasks simultaneously. In the extended version, additional constraints can be introduced, such as limits on the total number of working hours per week. Regarding the basic version, a necessary and sufficient condition for the existence of a balanced assignment is established. This condition can be verified in polynomial time. For the extended version, it is demonstrated that whenever a balanced assignment exists, a periodic balanced assignment exists as well, with a tighter bound on the period for the basic version.
The authors' abstract, as published at the source. Annals of Operations Research, 2026 · DOI ↗
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Field: Management Science and Operations Research
Management Science and Operations ResearchDecision Sciences