The bi-objective multi-depot split delivery location routing problems under uncertain conditions

Abstract

This research focuses on addressing the multi-depot location-routing problem with split delivery and multiple objectives under uncertain conditions. A mathematical model is proposed to effectively tackle this problem by considering various constraints and considerations. The paper emphasises the use of split delivery as an effective approach for reducing transportation costs. Furthermore, the study explores bi-objective optimisation, specifically cost minimisation and distance balancing. To assess the robustness of the proposed model under different scenarios, sensitivity analysis tools are employed. Numerical examples are presented to demonstrate the effectiveness of the model. Bi-objective optimisation is conducted using the augmented ε-constraint method, enabling decision-makers to analyse trade-offs between cost minimisation and distance balancing objectives. The findings of the study reveal that an increase in demand leads to higher cost minimisation and lower distance balancing. Conversely, an increase in transportation costs results in higher distance balancing. The research also highlights the robustness of the model and its potential for cost reduction through split delivery compared to scenarios without uncertainty.

Keywords:

• Bi-objective
• multi-depot
• split delivery
• location-routing

Data availability statement

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

Disclosure statement

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