Mathematical Optimisation of 3D Container Loading Using Simulated Annealing and Ant Colony Algorithms

The surge in online purchasing has intensified price competition, compelling businesses to reduce product costs and shipping fees to remain competitive in a rapidly expanding digital marketplace. For logistics service providers, an effective strategy for reducing shipping costs is to maximize the use of container storage capacity while minimizing wasted space, an approach referred to as the container loading problem. This classic optimisation challenge has wide applications in delivery companies, particularly due to the limited number of containers suitable for box packaging. As a result, manufacturers and postal delivery services have faced challenges in transporting and dispatching parcels efficiently. This highlights the need for an effective solution to the packing problem in rectangular containers. The proposed approach aims to reduce storage and shipping costs while minimizing processing and delivery times. To accomplish this, metaheuristic algorithms, particularly Simulated Annealing (SA) and Ant Colony Optimisation (ACO), were used in combination with the Axis Order Test (AOT) and Corner Point Placing (CPP). The performances of SA-AOT, SA-CPP, ACO-AOT, and ACO-CPP in terms of space utilisation and processing time were then compared. The results indicated that the ACO-CPP model was more effective than the others, achieving a maximum space utilisation of up to 98.19 per cent and having the fastest processing time (under 0.2 hours). The ACO-CPP model reduced packaging time and operational costs, offering a sustainable solution for logistics providers in the new era of e-commerce.