Supply Chain Management Analysis Using a Linear Programming Model to Minimize Product Distribution Costs

Abstract

Supply chain distribution decisions in many firms remain shaped by managerial experience and established routing habits rather than systematic quantitative optimization, generating unnecessary logistics expenditure in multi-source and multi-destination networks. This study develops and applies a Transportation Linear Programming model to minimize product distribution costs based on actual operational data, evaluating the model against the company existing distribution practice rather than a hypothetical benchmark. Using a case study design, the network comprised four supply sources, two production facilities and two regional warehouses, serving six distributor destinations, with parameters derived from documentation, direct observation, and interviews. The model minimized total distribution cost subject to supply, demand, and route capacity constraints. Results show the baseline arrangement incurred a total cost of Rp139,356 thousand, whereas the optimal allocation reduced this to Rp117,238 thousand, yielding a cost saving of Rp22,118 thousand, or 15.87 percent, achieved by reallocating shipments toward underutilized, lower-cost routes without altering supply, demand, or network structure. Validation confirmed that the optimal solution satisfied all supply, demand, and capacity constraints with full demand fulfilment. Sensitivity analysis indicated that total cost responded most steeply to variation in customer demand and distribution cost, while remaining robust to changes in supply capacity, and became infeasible under a twenty percent reduction in supply or increase in demand. These findings demonstrate that Transportation Linear Programming provides firms with an evidence-based tool for improving distribution efficiency and cost-conscious logistics planning.