Optimizing logistics warehouse space utilization with minimum total transportation

Logistics warehouses are integral to supply chain management, enabling the efficient storage and movement of goods. However, the dynamic operational nature of these facilities, characterized by high product turnover, often results in suboptimal space utilization. This study addresses the inefficiency caused by partially filled pallets and the honeycombing effect, which leads to substantial storage capacity loss. Focusing on a third-party logistics warehouse managing apparel boxes, the uniqueness of each box introduces specific challenges in space optimization. To mitigate these issues, two integer linear programming models were developed. The first model is utilized for emptying and reallocating products from the predetermined low-capacity shelf cells to new locations. The second model simultaneously identifies both the shelf cells to be vacated and the optimal relocation destinations. Both models aim to minimize the total transportation costs. The first model is suited for rapid reallocation and efficient short-term solutions, whereas the second model offers a more holistic approach to long-term space optimization. These models provide a systematic, data-driven solution for enhancing warehouse space management. The problem is also considered bi-objective, with the objectives of maximizing the number of empty shelf cells and minimizing the total transportation costs. The bi-objective mathematical model was scalarized using the epsilon-constraint method and solved for different epsilon values. This process yielded 39 Pareto-optimal solutions. The results indicate that as more cells are emptied, both the total cost and cost per cell increase. Considering the problem in a bi-objective form has also been advantageous for offering the decision-maker not just one solution but a solution set with different numbers of cells to be emptied and different transportation costs.