Abstract
Demand uncertainty is an important issue that influences the strategic, tactical, and operational-level decision making in the transportation/logistics/supply chain planning. In this study, we explore the effect of demand uncertainty on the operational-level freight routing problem in the capacitated multimodal transportation network that consists of schedule-based rail transportation and time-flexible road transportation. Considering the imprecise characteristic of the demand, we adopt fuzzy set theory to model its uncertainty and use trapezoidal fuzzy numbers to represent the fuzzy demands. We set multiple transportation orders as the optimization object and employ soft time windows to reflect the customer requirement on on-time transportation. Under the above situation, we establish a fuzzy mixed integer nonlinear programming (FMINLP) model to formulate the capacitated road–rail multimodal routing problem with demand uncertainty and time windows. We first use the fuzzy expected value model and credibility measure based fuzzy chance-constrained programming to realize the defuzziness of the model and then adopt linearization technique to reformulate the crisp model to finally generate an equivalent mixed integer linear programming (MILP) model that can be solved by standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. Sensitivity analysis and fuzzy simulation are combined to quantify the effect of demand uncertainty on the routing problem and also reveal some helpful insights and managerial implications.
Highlights
As an effective alternative to the road transportation that is the most typical representative of traditional monomodal transportation, road–rail multimodal transportation combines the good mobility of road transportation in short- or medium-distance pickup and delivery and the mass capacity and outstanding reliability of rail transportation in long-distance transportation, which can provide the customers with seamless door-to-door services [1,2]
We mainly explore the effect of demand uncertainty on a capacitated road–rail multimodal routing problem with soft due date time windows
The case study combining sensitivity analysis and fuzzy simulation indicates that the demand uncertainty influence the planning on the best road–rail multimodal routes and considering fuzzy demands can help decision makers make better tradeoff among transportation economy, efficiency and reliability when optimizing the road–rail multimodal routes
Summary
As an effective alternative to the road transportation that is the most typical representative of traditional monomodal transportation, road–rail multimodal transportation combines the good mobility of road transportation in short- or medium-distance pickup and delivery and the mass capacity and outstanding reliability of rail transportation in long-distance transportation, which can provide the customers with seamless door-to-door services [1,2]. In this study, minimizing the generalized costs for accomplishing multiple transportation orders will be the optimization objective of our road–rail multimodal routing model. The setting of penalty costs has already been employed by Hrušovský [21] and Zhao et al [34] in improving the transportation efficiency of the multimodal routing that uses time points to represent the due dates These two studies only use penalty costs to avoid delayed accomplishment. As for the road–rail multimodal routing problem, there is still research potential to improve its efficiency and reliability by considering soft due date time windows and demand uncertainty, respectively.
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