Cost-time trade-off in bi-criteria multi-index bulk transportation problem: A numerical approach

In this study, a bi-criteria multi-index bulk transportation problem is explored. The bulk transportation problem refers to a logistics scenario where the demand of each destination must be met exclusively by one source, although a single source can cater to multiple destinations. This problem balances two critical criteria: cost and time, focusing on achieving an optimal trade-off between them. A numerical example is used to illustrate the methodology for deriving the cost-time trade-off pairs in the multi-index bulk transportation problem. The least-cost solution is identified first, along with its corresponding time. Once this optimal solution is obtained, subsequent efficient trade-off pairs are determined. These trade-offs reveal how small compromises in cost can potentially reduce transportation time or vice-versa. The approach emphasizes achieving efficient transportation planning by minimizing costs while ensuring reasonable delivery times. This type of problem has real-world applications in logistics and supply chain management, where it is critical to optimize operations by balancing multiple objectives. The study provides practical insights into multi-index systems, showing how systematic methods can yield a sequence of cost-effective and time-efficient solutions to support better decision-making.