An analytical investigation of alternative batching policies for remanufacturing under stochastic demands and returns

Abstract

This article examines a fundamental lot-sizing problem which arises in the context of a make-to-order remanufacturing environment. The problem setting is characterized by a stochastic used-item return process along with a stochastic remanufactured-item demand process faced by a remanufacturer. We explicitly take into account for all relevant costs, including the fixed costs (associated with remanufacturing of used-items and dispatching of remanufactured-item orders in batches) and inventory-related cost (associated with used-item inventory holding costs and remanufactured-item order waiting costs). We propose five batching policies inspired by shipment consolidation practice (three periodic policies and two threshold policies). For the purpose of computing policy parameters, we develop analytical models that are aimed at minimizing the long-run average expected total cost of the remanufacturer. Since the underlying cost expressions are not analytically tractable, we propose easily computable approximations that lead to closed-form expressions for obtaining policy parameters. A careful numerical investigation demonstrates that the resulting policy parameters are highly effective approximations. Then, we extend the policies by considering disposal options when needed. For this extension, an effective parameter-based approximation approach is developed for computational purposes, and additional numerical experiments demonstrate the effectiveness of the proposed approach.

Keywords:

• Remanufacturing
• batch processing
• periodic policies
• threshold policies
• stochastic process
• disposal

Notes

1 Given that $X_1$ is a stopping time with respect to the process $\{N(t),t>0\},$ for every $t\ge 0$ and given $N(X_1),N(X_1+t)$ is independent of the events up to $X_1$ (Resnick, 2013, p. 162).

2 Notation — indicates a conditioning argument.

3 Observe that $E\left[\text{Fixed}\mathrm{ }\text{cost}\mathrm{ }\text{in}\mathrm{ }CL(·)\right]=K$ for all policies except for the $T_F$-policy. That is, under this policy, if an empty batch is not allowed then $E\left[\text{Fixed}\mathrm{ }\text{cost}\mathrm{ }\text{in}\mathrm{ }CL(·)\right]=K(1-e^{-a{T}_F}).$ One can argue that the treatment provided in this article, however, allows empty dispatches so that $E\left[\text{Fixed}\mathrm{ }\text{cost}\mathrm{ }\text{in}\mathrm{ }CL(·)\right]=K.$ Equivalently, one can argue that the demand rate a is large enough so that $a{T}_F$ is also sufficiently large. Hence, the probability that no demand is received in a cycle is nearly zero. This, in turn, implies that $K(1-e^{-a{T}_F})\approx K.$

Additional information

Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1530965. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Notes on contributors

Yi Zhang

Yi Zhang is a senior manager in data science in Maxim Integrated. She has a PhD in industrial engineering from Texas A&M University in College Station, Texas. She also has an MS in control theory from University of Science and Technology of China and a BS in automation from Harbin Institute Technology in China. Her research interests mainly focus on inventory control and capacity planning. At Maxim Integrated, she works on forecasting and pricing problems.

Elif Akçalı

Elif Akçalı is an associate professor and The Cottmeyer Family Innovative Frontiers Faculty Fellow in the Department of Industrial and Systems Engineering (ISE) in the Herbert Wertheim College of Engineering at the University of Florida (UF). She obtained her PhD in industrial engineering in 2001 from Purdue University in West Lafayette, Indiana. She received an MS in industrial engineering from Purdue University in West Lafayette, Indiana and a BS in industrial engineering from Middle East Technical University in Ankara, Turkey. Her research primarily focuses on manufacturing planning and control.

Sıla Çetinkaya

Sıla Çetinkaya is Cecil H. Green Professor of Engineering and Department Chair of Engineering Management, Information, and Systems (EMIS) Department at Lyle School of Engineering of Southern Methodist University (SMU). She obtained her PhD in management science and systems from McMaster University in Canada in 1996. She also holds an MS in industrial engineering (1991) from Bilkent University and a BS in industrial engineering (1989) from Istanbul Technical University in Turkey. Her research program focuses on supply chain operations with an emphasis on stochastic models and applied probability applications. Çetinkaya was named IISE Fellow in 2012, and she has been a department editor of IISE Transactions since 2005.