Fuel Replenishment Problem of Heterogeneous Fleet in Initiative Distribution Mode

Petrol, a vital energy source for residents’ consumption and economically sustainable operation, generates substantial distribution demand. To reduce distribution costs, we propose a fuel replenishment problem using a heterogeneous fleet based on the initiative distribution mode. In this mode, the distribution center determines both the delivery orders of customers and the distribution plan. We develop a mathematical model with minimal operational costs, including transport, employment, and penalty costs. A Two-stage heuristic algorithm K-IBKA based on time-space clustering is proposed, which also combines the advantages of the butterfly optimization algorithm in quick convergence and hierarchical mutation strategy in population diversity. The results demonstrate that: (1) Heterogeneous truck distribution exhibits better cost advantages compared to homogeneous distribution, reducing total costs by 13.07%; (2) Compared to passive distribution mode, the total cost of the initiative distribution mode is reduced by 11.03% and 41.80%, respectively, through small and large-scale instances. (3) Compared with the unimproved BKA, ALNS, and GA, the total cost calculated by K-IBKA is reduced by 37.68%, 35.30%, and 27.26%, respectively, thus demonstrating the contribution of this work to reducing the cost of petrol distribution and achieving sustainable development of distribution.