Abstract
In this study, we combine the fuzzy customer information problem with the multicommodity multimodal routing with schedule-based services which was explored in our previous study [1]. The fuzzy characteristics of the customer information are embodied in the demanded volumes of the multiple commodities and the time windows of their due dates. When the schedule-based services are considered in the routing, schedule constraints emerge because the operations of block container trains should follow their predetermined schedules. This will restrict the routes selection from space-time feasibility. To solve this combinatorial optimization problem, we first build a fuzzy chance-constrained nonlinear programming model based on fuzzy possibility theory. We then use a crisp equivalent method and a linearization method to transform the proposed model into the classical linear programming model that can be effectively solved by the standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. The sensitivity of the best solution with respect to the values of the confidence levels is also examined.
Highlights
The routing problem has always been a highlight in combinatorial optimizations
The schedule-constrained multicommodity multimodal routing problem aims to select the best time-feasible routes for all commodity flows through the multimodal service network
In order to explain the performance of the routing by comparing the planned costs, the actual minimal costs, and actual costs, we should first simulate the actual multimodal transportation case by randomly generating deterministic volumes of the commodity flows according to their triangular fuzzy volumes
Summary
The routing problem has always been a highlight in combinatorial optimizations. Great importance has been attached to it, in the transportation field, and in many other industries such as telecommunications, manufacturing and the Internet [2]. Cho et al [19] presented a weighted constrained shortest path model and a label setting algorithm to draw the optimal international intermodal routing They applied the proposed method to a real-world routing case from Busan to Rotterdam. Similar to the transportation scenario constructed in Reference [1], the rail service (the schedulebased service) in the multimodal service network refers to the “point-to-point” block container train service. This kind of service is operated directly and periodically from its loading organization station to its unloading organization station.
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