Branch-and-price algorithm for an auto-carrier transportation problem
  Original equipment manufacturers (OEMs) manufacture, inventory and transport new vehicles to franchised dealers. These franchised dealers inventory and sell new vehicles to end users. OEMs rely on logistics companies with a special type of truck called an auto-carrier to transport the vehicles to the dealers. The process of vehicle distribution has a common challenge. This challenge involves determining routes, and the way to load the vehicles onto each auto-carrier.In this paper, we present a heuristic to determine the route for each auto-carrier based on the dealers' locations, and subsequently, a branch-and-price algorithm to obtain optimal solutions to the loading problem based on the generated route. The loading problem considers the actual dimensions of the vehicles, and the restrictions imposed by vehicle manufacturers and governmental agencies on the loading process. We perform extensive computational experiments for the loading problem using real-world instances, and our results are benchmarked with a holistic model to corroborate the effectiveness of the proposed method. For the largest instance comprising of 600 vehicles, the proposed method computes an optimal solution for the loading problem within a stipulated runtime. 
Saravanan Venkatachalam, Kaarthik Sundar
math.OC