Language Models for Business Optimisation with a Real World Case Study in Production Scheduling

TL;DR

The paper addresses the challenge of automatically formulating optimization problems from natural-language descriptions, a task traditionally demanding substantial domain expertise. It proposes a framework that fine-tunes cost-efficient LLMs (notably CodeRL) using modular prompts and a dataset of problem descriptions and formulations, then validates generated formulations by solving them with OR-Tools. Across conventional Job Shop Scheduling and a real-world embroidery scheduling case, the method yields accurate formulations and competitive performance relative to state-of-the-art prompt-based approaches, with an additional LP dataset showing 72% success. The work demonstrates a scalable path to automate problem formulation, reducing dependence on optimization specialists while enabling broader access to sophisticated scheduling solutions, and provides open datasets to support future research.

Abstract

Business optimisation has been used extensively to determine optimal solutions for challenging business operations. Problem formulation is an important part of business optimisation as it influences both the validity of solutions and the efficiency of the optimisation process. While different optimisation modelling languages have been developed, problem formulation is still not a trivial task and usually requires optimisation expertise and problem-domain knowledge. Recently, Large Language Models (LLMs) have demonstrated outstanding performance across different language-related tasks. Since problem formulation can be viewed as a translation task, there is a potential to leverage LLMs to automate problem formulation. However, developing an LLM for problem formulation is challenging, due to limited training data, and the complexity of real-world optimisation problems. Several prompt engineering methods have been proposed in the literature to automate problem formulation with LLMs. While the initial results are encouraging, the accuracy of formulations generated by these methods can still be significantly improved. In this paper, we present an LLM-based framework for automating problem formulation in business optimization. Our approach introduces a method for fine-tuning cost-efficient LLMs specifically tailored to specialized business optimization challenges. The experiment results demonstrate that our framework can generate accurate formulations for conventional and real-world business optimisation problems in production scheduling. Extensive analyses show the effectiveness and the convergence of the proposed fine-tuning method. The proposed method also shows very competitive performance when compared with the state-of-the-art prompt engineering methods in the literature when tested on general linear programming problems.

Figures (11)

• Figure 1: Layout of a Melbourne embroidery factory. In the diagram, the arrows indicate the sequence of machines used to process an actual job.
• Figure 2: Overview of the proposed framework. In the framework, a pre-trained LLM is fine-tuned using problem descriptions and relevant problem formulations. The fine-tuned LLM is capable of constructing a problem formulation for a given problem description.
• Figure 3: An overview of dataset development. Problem descriptions and problem formulations are created based on objectives and constraints. The problem descriptions are regenerated using ChatGPT in different styles. Finally, problem formulations are reorganised into code modules.
• Figure 4: Testing Results - Conventional Job Shop Scheduling
• Figure 5: A sample problem formulation generated by our framework and the output of the executed problem formulation.