# Stochastic Planning and Scheduling with Logic-Based Benders Decomposition

arXiv: https://arxiv.org/abs/2012.14074 · HTML: https://mlsanity.com/paper/2012.14074/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2020.

## Built on by (most cited first, 2 of 2)

- [Learning to control inexact Benders decomposition via reinforcement learning](https://mlsanity.com/paper/2508.06700/) (2025)
- [Resource-constrained Project Scheduling with Time-of-Use Energy Tariffs and Machine States: A Logic-based Benders Decomposition Approach](https://mlsanity.com/paper/2601.06542/) (2026)

## Abstract (arXiv)

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second-stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple nogood cuts as well as analytical logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method, with a branch-and-check variant of LBBD faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classical Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem, and the first comparison of LBBD with the integer mboxL-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse.