The modal-shift transportation planning problem and its fast steepest descent algorithm

The modal-shift transportation planning problem (MSTPP) is the problem that finds a feasible schedule for carriers with the minimum total cost when sets of facilities, delivery orders, and carriers are given. We propose a fast steepest descent algorithm to solve the MSTPP. Our solution generates a set of candidate routes for each delivery order as a preprocess. Then, it finds a schedule by iteratively updating selections of the candidate routes in descent directions, while computing a configuration of carrier movements at each iteration by a greedy algorithm. Intensive numerical study using artificial data modeled from the manufacturing industry in Japan is also presented.