Service-level-driven procurement and production lot-sizing problem with demand fulfilment

Abstract

This paper presents novel models for the Integrated Procurement and Lot-Sizing Problem with multiple customers and backlogging. Since allowing backlog in a traditional cost minimisation model involves dealing with intangible costs of not fulfilling the demand on time, we propose optimising service-levels while keeping the costs minimal using a budget constraint. The motivation of this study emanates from a manufacturing company that assembles commercial and industrial refrigeration equipment, using both purchased materials and in-house products. Instead of considering an aggregate demand, we consider the specific demand from various customers. This allows us to incorporate demand fulfilment decisions into the model in case of stock-outs by deciding which customers will have their orders backlogged. The fill-rate, or β service-level, is considered both globally and for customers and products individually. Computational experiments show that the service-level-driven models improve service when compared to the traditional cost model and also end up enforcing service equity among different customers at the expense of a deterioration in the global fill-rate.

Keywords:

• Production
• raw material procurement
• lot-sizing
• service-level
• backlog

Acknowledgements

The authors thank the two anonymous reviewers for their helpful feedback.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [grant number 2019/10824-7]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant number 307466/2021-3]; and was carried out using the computational resources of the Center for Mathematical Sciences Applied to Industry (CeMEAI) funded by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [grant number 2013/07375-0].

Notes on contributors

Caio Paziani Tomazella

Caio Paziani Tomazella is a Ph.D. candidate at ICMC, University of São Paulo, Brazil, and is currently a visiting student at HEC Montréal. He received the B.Sc. degree in Mechanical Production Engineering and the M.Sc. degree in Production Engineering, both from EESC, University of São Paulo, Brazil. His research interests include lot-sizing and scheduling problems, and he has published articles in journals such as Computers & Industrial Engineering and Expert Systems with Applications.

Maristela Oliveira Santos

Maristela Oliveira Santos is an associate professor at the Department of Applied Mathematics and Statistics at the University of São Paulo (USP), São Carlos, Brazil. She has an M.Sc. and Ph.D. in Computer Science and Computational Mathematics, all from the University of São Paulo, in 1996 and 2000, respectively. She has been working with production planning and integrated problems, focusing mainly on developing new solution methodologies and new mathematical models.

Douglas Alem

Douglas Alem received the B.Sc. degree in Production Engineering from the Federal University of Sao Carlos UFSCar (Brazil) in 2004 and the M.Sc. and Ph.D. degrees in Applied Mathematics and Computer Science from the University of Sao Paulo ICMC/USP (Brazil) in 2007 and 2011, respectively. He is currently working as an Associate Professor in Business Analytics of the University of Edinburgh Business School (Scotland), where he teaches operations research and mathematical programming. He is also serving as director of the MSc Data and Decision Analytics (online) in the same institution. Prior to joining the University of Edinburgh Business School, Dr Alem served as an Assistant Professor in Operations Research at the Federal University of Sao Carlos in Sorocaba. Dr Alem published over 30 papers in journals indexed by SCI/SSCI/SCI-E papers at reputable venues such as Taylor & Francis, Elsevier, Informs, Springer, and ACS. He has served as a reviewer for more than 15 journals. His research focuses on developing mathematical programming approaches to improve humanitarian supply chains and production planning settings.

Raf Jans

Raf Jans is a Professor of Operations Management at HEC Montréal, where he holds a Chair in Supply Chain Operations Planning. He obtained a Ph.D. in Applied Economics with a specialization in Operations Research from the University of Leuven (KUL) in Belgium. He also spent two years as a visiting PhD student at the Decision Sciences department of the London Business School. Previously, he held a tenured position at RSM Erasmus University in the Netherlands. His research interests are in optimization modeling and algorithms, applied mainly in the area of production and distribution planning. His research has appeared in academic journals such as Operations Research, INFORMS Journal on Computing, Transportation Science, Omega, Computers & Operations Research, International Journal of Production Research and the European Journal of Operational Research.