# Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines

arXiv: https://arxiv.org/abs/1808.10661 · HTML: https://mlsanity.com/paper/1808.10661/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2018.

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

- [Single and Parallel Machine Scheduling with Variable Release Dates](https://mlsanity.com/paper/2103.01785/) (2021)

## Abstract (arXiv)

We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobs.