A new interval-valued fuzzy optimization model for truck scheduling in a multi-door cross-docking system by considering transshipment and flexible dock doors extra cost

In a cross-docking system, doors can be used exclusively for receiving or sending operations, or they can be flexible enough to be used for both. Flexible doors have recently attracted a lot of attention as a way to improve cross-docking systems' performance. Despite the advantages of flexible doors, applying them is usually associated with additional costs due to the need for dual-function equipment to receive and send. Moreover, the distance that goods move within cross-docking facilities, from receiving to sending dock doors, significantly affects how well these facilities work. This paper presents a new bi-objective mixed-integer linear programming model for scheduling the inbound and outbound trucks in a cross-docking facility. The model objectives are to minimize total system costs, including additional costs of applying flexible doors and transshipment (maximize efficiency) and to minimize outbound trucks' tardiness from predetermined due dates (maximize responsiveness). As a result of the uncertainties in cross-dock truck scheduling problems, the parameters are considered triangular interval-valued fuzzy (IVF) numbers. Moreover, a new IVF-uncertain solution approach based on max-min operator and compromise programming concepts is proposed to solve multi-objective mathematical programming problems with triangular IVF numbers. The proposed model and IVF-solution approach are used for cross-docking operations planning at a well-known food manufacturing group. The results are also analyzed according to their sensitivity to changes in key parameters of the cross-docking problem. The comparison of the proposed approach and some fuzzy known methods for solving multi-objective models demonstrates the superior performance of the proposed approach in the real case study.