Framework for characterising mathematical programming models for capacitated lot-sizing and scheduling problem

Abstract

The Capacitated Lot-Sizing and Scheduling Problem (CLSSP) integrates production planning and scheduling decisions under capacity constraints. It combines multiple complex subproblems, including lot-sizing, production assignment, sequencing, and timing (often subject to dependent setup times), as well as inventory management across periods. Although several mathematical programming models have been proposed to address this problem, the literature lacks a structured framework to systematically characterise and compare these formulations. To fill this gap, this paper presents a novel framework specifically designed for characterising mathematical programming models for the CLSSP. The framework consists of seven dimensions, each developed through a structured methodology combining a PRISMA-based systematic literature review of related works, an in-depth analysis of selected papers. It was validated both by applying it to existing optimisation models in the literature and through a real-world industrial case study. The validation results demonstrate the framework’s applicability in literature reviews, as it captured all modelled characteristics from the analysed selected studies, enabling the identification of emerging trends and research gaps in CLSSP modelling. As for its application in industry, the target users of the framework are described and its use is illustrated through a industrial case study based on a real problem. Therefore, the proposed framework offers three main functionalities: i) providing a structured basis to characterise the CLSSP, ii) enabling systematic analysis and comparison of existing mathematical programming models for the CLSSP, and iii) supporting the design of new optimisation models to effectively address the CLSSP in real-world industrial settings.