Robust cross-dock assignment problem with uncertain cost parameters

Amna Altaf, Adnen El Amraoui, Francois Delmotte and Christophe Lecoutre

International Journal of Production Research, 2025, vol. 63, issue 16, 6108-6133

Abstract: Amidst the unprecedented macroeconomic uncertainty following the pandemic, stakeholders in global supply chains face significant disruptions, necessitating robust decision-making frameworks. In this study, we present an enhanced solution approach to the Truck Dock Assignment with Temporary Storage (TDATS) problem, addressing critical uncertainties in supply chain and logistics operations. This deterministic model, TDATS, integrates operational, penalty, and storage costs, accounting for complex scenarios such as varying arrival times and temporary storage requirements. Additionally, we introduce a robust optimisation framework: Robust Truck Dock Assignment with Temporary Storage (R-TDATS), to effectively handle uncertainties in cost coefficients. Using polyhedral representations of uncertainty sets and the Bertsimas and Sim optimisation approach, the proposed solution provides decision-makers with conservative yet realistic solutions. Numerical experiments demonstrate the effectiveness of this method, showcasing its applicability to real-world instances of the problem. Moreover, the study also analyses the system's performance under higher levels of uncertainty by increasing the deviation of input variables to 25% and 50%. The results show a significantly increased Price of Robustness(PR) up to 39%, a Relative Increase (RI) in cost up to 88%, and Risk values up to 71%, particularly notable for the combined variation in all three cost coefficients (Co, Cp, Cs). Despite this, the magnitude of the cost increase remains relatively small, underscoring the importance of carefully adjusting and optimising input variables, such as demand forecasts and transportation schedules, to mitigate the impacts of uncertainty. An extensive sensitivity analysis using Monte Carlo simulations identifies a threshold point where increasing operational and storage costs reach a saturation level. Beyond this point, further increase in these costs have minimal impact, prompting a strategic shift towards penalty cost management. This includes nuanced trade-off analysis between operational/storage costs and penalty costs, guiding resource allocation and cost management strategies. Additionally, the analysis reveals a linear relationship between penalty costs and the unit penalty cost coefficient, facilitating the development of optimised penalty cost management strategies. The study offers valuable insights for decision-makers in the cross-docking sector, empowering them to make informed decisions that enhance the efficiency and resilience of supply chain networks amidst uncertainty.

Date: 2025
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DOI: 10.1080/00207543.2025.2469164

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