A hybrid simulated annealing algorithm to estimate a better upper bound of the minimal total cost of a transportation problem with varying demands and supplies

Minimizing the total cost of transportation of a homogeneous product from multiple sources to multiple destinations when demand at each source and supply at each destination are deterministic and constant is commonly addressed in the literature. However, in practice, demand and supply may fluctuate within a certain range due to variations of the global economy. Subsequently, finding the upper bound of the minimal total cost of this transportation problem with varying demands and supplies (TPVDS) is NP hard. Yet, bounding the minimal total cost is of prime importance for financial sustainability. Although the lower bound of the minimal total cost can be methodologically attained, determining the exact upper bound is challenging. Herein, we demonstrate that existing methods may underestimate this upper minimal total cost bound. We therefore propose an alternative efficient and robust method that is based on the hybridization of simulated annealing and steepest descent. We provide theoretical evidence of its good performance in terms of solution quality and prove its superiority in comparison to existing techniques. We further validate its performance on benchmark and newly generated instances. Finally, we exemplify its utility on a real-world TPVDS