# A MILP model for an extended version of the Flexible Job Shop Problem

arXiv: https://arxiv.org/abs/1401.3654 · HTML: https://mlsanity.com/paper/1401.3654/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2014.

## Built on by (most cited first, 5 of 5)

- [Job Shop Scheduling Benchmark: Environments and Instances for Learning and Non-learning Methods](https://mlsanity.com/paper/2308.12794/) (2023)
- [Scalability of Reinforcement Learning Methods for Dispatching in Semiconductor Frontend Fabs: A Comparison of Open-Source Models with Real Industry Datasets](https://mlsanity.com/paper/2505.11135/) (2025)
- [A heuristic method for data allocation and task scheduling on heterogeneous multiprocessor systems under memory constraints](https://mlsanity.com/paper/2206.05268/) (2022)
- [Graph-Supported Dynamic Algorithm Configuration for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2505.16471/) (2025)
- [Constrained Reinforcement Learning Using Successor Representations](https://mlsanity.com/paper/2607.24057/) (2026)

## Abstract (arXiv)

A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by "Ozg"uven, "Ozbakir, and Yavuz (Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Applied Mathematical Modelling, 34:1539--1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.