This paper introduces a multi-period, two-dimensional vehicle loading and dispatching problem, called Two-Dimensional Vehicle Loading and Dispatching Problem with Incompatibility Constraints (VLDP). The problem concerns preparing a single-origin single-destination transportation plan of loading required orders to vehicles at the origin and dispatching the vehicles to deliver the orders to the destination within their due dates. The decision maker uses their own fleet of vehicles, with each vehicle having a fixed transportation cost per trip, and may outsource additional vehicles at a higher cost. VLDP involves constraints regarding the due dates of the orders, pairwise incompatibility of orders packed in the same vehicle, incompatibility of orders and vehicles, as well as area and weight capacity of the vehicles. An order can be delivered earlier than its due date, incurring an earliness penalty due to storage requirements at the destination. The objective is to minimize the total vehicle usage and earliness penalty costs. A Mixed-Integer Linear Programming model (MILP) is provided, as well as an Adaptive Large Neighbourhood Search (ALNS) algorithm. Results of computational experiments on instances derived from real-world data show the effectiveness of the ALNS algorithm. © 2022 Elsevier B.V.