Optimizing Supply Chain Management for Differentia Aluminum and Steel Company Using a Three-Dimensional Branch and Bound Transportation Model

Abstract

: Supply chain planning is important for manufacturing companies that handle several products across different supply and distribution locations. For aluminum and steel companies, transportation decisions are affected by product requirements, available quantities, destination demand, transportation rates, vehicle capacity, and other logistics costs. This study develops a three-dimensional transportation model for the supply chain network of Differentia Aluminum and Steel Company. The model considers source locations, destination locations, and product types as its three dimensions, allowing the distribution of individual products to be represented within the same transportation framework. The model is formulated as an integer programming problem with the objective of minimizing total transportation and distribution costs subject to supply, demand, product availability, transportation capacity, and non-negativity constraints. A branch-and-bound algorithm is used to determine the optimal allocation of products across the available source and destination locations. The analysis uses data on supply capacities at three warehouses, product demand at seven distribution depots, fuel costs, truck transportation rates, and driver dispatch expenses. The model was solved using R software. The resulting transportation plan satisfies all destination demands without shortages and gives a minimum total supply chain cost of ₦2,166,250. Sensitivity analysis indicates that an increase in fixed truck movement cost increases the total transportation logistics cost. The results provide a quantitative basis for planning product distribution and allocating transportation resources within the company.