# Implementing Cumulative Functions with Generalized Cumulative Constraints

arXiv: https://arxiv.org/abs/2508.01751 · HTML: https://mlsanity.com/paper/2508.01751/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 43 references that are in the map.
- First posted on arXiv 3 Aug 2025.

## Builds on (most cited first, 1 of 1)

- [Constraint and Mathematical Programming Models for Integrated Port Container Terminal Operations](https://mlsanity.com/paper/1712.05302/) (2017)

## Built on by (most cited first, 1 of 1)

- [CP or DP? Why Not Both: A Case Study in the Partial Shop Scheduling Problem](https://mlsanity.com/paper/2605.23569/) (2026)

## Abstract (arXiv)

Modeling scheduling problems with conditional time intervals and cumulative functions has become a common approach when using modern commercial constraint programming solvers. This paradigm enables the modeling of a wide range of scheduling problems, including those involving producers and consumers. However, it is unavailable in existing open-source solvers and practical implementation details remain undocumented. In this work, we present an implementation of this modeling approach using a single, generic global constraint called the Generalized Cumulative. We also introduce a novel timetabling filtering algorithm specifically designed to handle tasks defined on conditional time-intervals. Experimental results demonstrate that this approach, combined with the new filtering algorithm, performs competitively with existing solvers enabling the modeling of producer and consumer scheduling problems and effectively scales to large-scale problems.