On 27 June 2015, flammable starch-based powder exploded at Formosa Fun Coast, a recreational water park in Bali, New Taipei, Taiwan, injuring 508 people, with 199 in critical condition. During the emergency medical distribution, two processes, casualty transportation and relief distribution, are poorly coordinated and performed. The medical relief distribution process can be described as vehicle routing problems with pickup and delivery under time-windows (VRPPDTW). Under Intelligent Transportation Systems (ITS), information can be gathered from roadside surveillance systems to design efficient and effective routes for medical relief distribution. In this study, a time-dependent VRPPDTW formulation is constructed based on the concept of step function and a solution algorithm is proposed to solve the VRPPDTW problem. Numerical experiments based on a city network with three hospitals are used to illustrate the proposed algorithms under different levels of traffic conditions.