In this work, we investigate a new, yet practical, variant of the vehicle routing problem called the vehicle routing problem with time windows and link capacity constraints (VRPTWLC). The problem considers new constraints imposed on road links with regard to vehicle passing tonnage, which is motivated by a business project with a Hong Kong transportation company that transports hazardous materials (hazmats) across the city and between Hong Kong and mainland China. In order to solve this computationally challenging problem, we develop a tabu search heuristic with an adaptive penalty mechanism (TSAP) to help manage the company's vehicle fleet. A new data set and its generation scheme are also presented to help validate our solutions. Extensive computational experiments are conducted, showing the effectiveness of the proposed solution approach.
