Exact Optimization Framework for Storage Space of Hazardous Materials

Hazardous materials (HAZMAT) storage facilities are indispensable across various industrial sectors, including mining operations, defense manufacturing, research facilities, and construction. Ensuring safe storage of these materials, to prevent accidents and ensure public safety, presents a complex optimization challenge, constrained by geometric, regulatory and safety constraints. Current practices predominantly rely on human judgment and historical trends, resulting in inefficiencies, delays, frequent re-adjustments, and elevated safety risks in high-consequence environments. This study enhances the safety and efficiency of HAZMAT storage by conceptualizing the problem as a multi-container loading problem. The objective is to minimize the wasted space while satisfying a comprehensive array of explicit HAZMAT constraints. To achieve this, a Mixed-Integer Linear Programming (MILP) model is developed that employs preprocessing techniques to address the stacking constraints, thereby streamlining the optimization process. The model is progressively refined by incorporating constraints and is solved using an exact solver to boost computational efficiency. The MILP model is evaluated on specially designed synthetic instances. Extensive computational experiments demonstrate that the model significantly improves storage efficiency and safety for small size problems.