Minimize shipping costs from multi-warehouse to multi-outlet with VAM and MODI - Fristi Riandari; Ruri Hartika Zain (Jurnal Mandiri IT, 2026)
Distribution costs are a dominant component in logistics operations, especially in multi-warehouse to multi-outlet delivery schemes involving variations in supply capacity, demand, and route costs. This study aims to minimize shipping costs by modeling the problem as a Transportation Problem (TP), generating an initial solution using Vogel's Approximation Method (VAM), and ensuring an optimal solution using the Modified Distribution Method (MODI). The case study was conducted in one planning period with input data in the form of a matrix of shipping costs per unit, supply capacity per warehouse, and demand per outlet (balanced condition). The results show that the baseline distribution cost is 4,898 (thousand IDR), while the initial VAM solution reduces the cost to 3,777 (thousand IDR). After optimality testing and improvements using MODI, the minimum cost is 3,605 (thousand IDR), with an additional improvement of 172 (thousand IDR) from the VAM solution. Compared to the baseline, the optimal solution provides savings of 1,293 (thousand IDR) or 26.40%, without violating the supply-demand constraint. These findings confirm that the VAM-MODI flow is effective as a fast, audit-friendly, and applicable end-to-end procedure for the preparation of minimum cost delivery plans in logistics companies.