5. Conclusions and Discussion
In this study, our case studies are developed for multi-mode transfer operations. General models are developed for most combinations of modes (e.g. trucks to rail trains, trucks to airplanes, rail trains to ships, etc.), which can be described in terms of their vehicle capacities, unit operating costs, average speeds and travel time variances. The pre-planning model is developed for optimizing in advance system characteristics such as terminal capacities, vehicle sizes, routes, schedules and probabilistic reserve factors built into operating schedules.
The hybrid heuristic algorithm is developed for resolving the variability in optimal results in SQP and reducing the running time of the GA. It is found that SQP is very sensitive to different initial feasible solutions. Similarly, GA results may also be affected by different random seeds, resulting in different initial populations and local optimal solutions. Moreover, the convergence in final steps may be very slow in GA and additional stopping criteria or thresholds may be needed. Therefore, the hybrid GA-SQP
algorithm is proposed which uses a GA to find a reasonable initial estimate for SQP, and then uses SQP to solve the problem until no further improvement can be found. In this approach, a random feasible initial starting point applied in SQP can be an appropriate threshold (i.e. one stopping criterion) for the GA.
In addition, for freight transportation operations, users (e.g. shippers) and operators (e.g. carriers) may have some conflicting interests regarding service quality. Shippers may prefer to send cargos at the lowest prices while minimizing total shipping time; however, carriers may choose a route with multiple transfers to create economies. Moreover, competition may exist among service providers because each of them eventually pursues the maximization of its own total profit. Competitive behaviors may become unavoidable and require other models to capture their details. Our models are mainly usable by consortiums or “alliances” of private freight transportation companies. Leader – follower decision making models of consortiums or alliances require different formulations. Different decision makers from various agencies may have different control abilities, market share rates, information flow knowledge, and etc.