Pesquisa Operacional (2015) 35(3): 439-464 © 2015 Brazilian Operations Research Society Printed version ISSN 0101-7438 / Online version ISSN 1678-5142 www.scielo.br/pope doi: 10.1590/0101-7438.2015.035.03.0439 INDUSTRIAL INSIGHTS INTO LOT SIZING AND SCHEDULING MODELING* Bernardo Almada-Lobo 1** , Alistair Clark 2 , Lu´ ıs Guimar˜ aes 1 , Gonc ¸alo Figueira 1 and Pedro Amorim 1 Received October 12, 2015 / Accepted November 30, 2015 ABSTRACT. Lot sizing and scheduling by mixed integer programming has been a hot research topic in the last 20 years. Researchers have been trying to develop stronger formulations, as well as to incorporate real-world requirements from different applications. This paper illustrates some of these requirements and demonstrates how small- and big-bucket models have been adapted and extended. Motivation comes from different industries, especially from process and fast-moving consumer goods industries. Keywords: lot sizing and scheduling, mixed integer programming, industrial applications, real-world features. 1 INTRODUCTION Production planning and scheduling seeks to efficiently allocate resources while fulfilling cus- tomer requirements and market demand, often by trading-off conflicting objectives. Lot sizing and scheduling (L&S) is one of the most important and challenging processes within the produc- tion planning of an industrial company, which is done under a hierarchical process with several stages, each containing different aims and planning horizons. According to the Supply Chain Planning (SCP) matrix (e.g. Fleischmann & Meyr, 2003), L&S is of short/medium-term scope and is placed between Master Production Scheduling and Operational Scheduling. Integrating lot sizing and scheduling is crucial for many companies (Clark et al., 2011). Lot sizing determines the timing and level of production to meet product demand over a finite plan- ning horizon. Sequencing establishes the order in which lots are executed within a time period, accounting for the sequence dependent setup times and costs. The motivation for integrating these two problems may come from: *Invited paper. **Corresponding author. 1 INESC TEC and Faculdade de Engenharia, Universidade do Porto, Porto, Portugal. – E-mails: almada.lobo@fe.up.pt; guimaraes.luis@fe.up.pt; goncalo.figueira@fe.up.pt; amorim.pedro@fe.up.pt 2 University of the West of England, Department of Engineering Design and Mathematics, Bristol, UK. – E-mail: alistair.clark@uwe.ac.uk