Fix-and-Relax based heuristic approach for robust two-echelon vehicle routing problem for milk collection: A case study

Nowadays, several tons of milk in the collection network are being spoiled and discarded before reaching the collection centers or the milk factory due to a lack of proper planning. This issue incurs significant costs in the milk collection network, emphasizing the importance of efficient milk collection networks at various levels. This paper discusses the routing of milk collection vehicles from farms to factories. The study examines various levels, including milk production farms, milk collection centers, and factories. To address this, a bi-objective mixed integer programming model is proposed with the objective of minimizing transportation costs and earlinesstardiness times. The proposed model is validated using data from a real case study of the milk collection network in Torbat Jam, Iran. To solve the bi-objective model, the weighted-additive fuzzy goal programming (WFGP) approach is employed. Due to the NP-hardness of the research problem, a heuristic solution method based on the Fix-and-Relax approach is developed to solve large-size problems. Additionally, the Bertsymas and Sim approach is applied to address uncertainty in the travel time parameter. Furthermore, a sensitivity analysis is conducted on the important parameters of the proposed model. The results demonstrate that the heuristic solution method can provide optimal or near-optimal solutions within a reasonable time frame. Moreover, the robust bi-objective optimization model can effectively schedule milk collection with low costs.