The economic lot-sizing problem with remanufacturing and heterogeneous returns: formulations, analysis and algorithms

Abstract

We address an extension of the economic lot-sizing problem with remanufacturing, in which the returns are assumed of heterogeneous quality. Costs for remanufacturing and holding inventory depend on the quality of the returns. For the problem with general cost functions, we provide a network flows formulation and a dynamic programming algorithm of pseudopolynomial time. Then, we consider the problem under stationary costs and different set-up schemes for manufacturing and remanufacturing. For the case of a joint set-up scheme, we derive certain properties related to the form of the optimal solutions. Based on these theoretical results, a polynomial-time algorithm is presented for the particular case of a large quantity of low-cost returns. For the case of separate set-up scheme, we show that the problem is NP-hard and present several lot-sizing rules specially designed for the problem. An extensive numerical experimentation was conducted to evaluate the suggested rules under different combinations of inventory and set-up costs. From the results obtained, we can extract several managerial insights, such as in general it is profitable to remanufacture all the available returns of the same quality in certain periods, but not necessarily those of the highest quality.

KEYWORDS:

• Lot-sizing problem
• remanufacturing
• heterogeneous returns
• network flows
• dynamic programming
• heuristics

Acknowledgements

We would like to thank the three anonymous reviewers for their valuable comments on previous versions of this manuscript. This work was supported in part by CSIC and PEDECIBA, Uruguay.

Disclosure statement

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

Additional information

Notes on contributors

Pedro Piñeyro

Pedro Piñeyro is an Assistant Professor at the Operations Research Department in the Computer Science Institute of the Engineering School of the Universidad de la República (Uruguay). He got his PhD in Computer Science at the National Program for the Development of Basic Sciences (PEDECIBA) of Uruguay in 2013, and the Computer Systems Engineer degree at the Universidad de la República, Uruguay, in 2002. He is a member of the Sistema Nacional de Investigadores (National Researchers System) of Uruguay and he is also a member of the teaching body of the MSc program in Operations Research in his university. His main research interests are related to lot-sizing problems, scheduling problems, reverse logistics, humanitarian logistics and Industry 4.0.

Omar Viera

Omar Viera is a MSc in Engineering in Physics from the Royal Institute of Technology (KTH), Stockholm Sweden. He is a Full Professor at the Operations Research Department in the Computer Science Institute of the Engineering School of the Universidad de la República (Uruguay). His main research areas are Logistics, Humanitarian Logistics, Vehicle Routing and Natural Disaster Management.