An oracle-based algorithm for robust planning of production routing problems in closed-loop supply chains of beverage glass bottles

Ali Borumand (Corresponding author), Ahmadreza Marandi (Corresponding author), Ali Shahandeh Nookabadi (Corresponding author), Zümbül Atan (Corresponding author)

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The demand for glass bottles is exhibiting an upward trend over time. The manufacturing of glass bottles is costlier in terms of time and resources and is associated with a higher level of heat generation and environmental pollution compared to recycling processes. In response to the aforementioned challenges, companies that use glass bottles need to implement strategies to manage their reverse supply chains in conjunction with their traditional supply chains, as the economic and environmental benefits of returned products are unquestionable. Closed-loop supply chains (CLSCs) integrate forward and reverse flows of products and information. This integration helps companies to have a broader view of the whole chain. Despite these advantages, managing CLSCs can be challenging as they are exposed to many uncertainties regarding supply and demand processes, travel times, and quantity/quality of returned products.

In this study, we consider the production planning, inventory management, and vehicle routing decisions of a CLSC of beverage glass bottles. We propose an MILP model and rely on a multi-stage adjustable robust optimization (ARO) formulation to deal with the randomness in both the demand for filled bottles and the requests for pickups of empty bottles. We develop an exact oracle-based algorithm to solve the ARO problem and propose a heuristic search algorithm to reduce the solution time. Our numerical experiments not only show the incompetency of the customary method, namely the affine decision rule approach, but also illustrate how our algorithms can solve the small-size problems and significantly improve the quality of the obtained solution for large problems. Furthermore, our numerical results show that robust plans tend to be sparse, meaning the routes are chosen so that empty bottles are transported to production sites in such a way that fewer new bottles need to be ordered. Thus, robust planning makes the CLSCs more environmentally friendly.
Original languageEnglish
Article number102939
Number of pages17
JournalOmega : The International Journal of Management Science
Publication statusPublished - Jan 2024


This work made use of the Dutch national e-infrastructure with the support of the SURF Cooperative using grant no. EINF-2933 .

FundersFunder number


    • Adjustable robust optimization
    • Closed-loop supply chain
    • Oracle-based algorithm
    • Uncertain demand
    • Vehicle routing problem


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