A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road–Rail Multimodal Routing Problem with Time Windows

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.

Fuzzy Programming Approaches for Modeling a Customer-Centred Freight Routing Problem in the Road-Rail Intermodal Hub-and-Spoke Network with Fuzzy Soft Time Windows and Multiple Sources of Time Uncertainty

“…Therefore, it is not completely applicable to use the piecewise linear cost function to represent the economic objective function. Currently, the majority of the existing studies employ generalized costs to formulate the charges for accomplishing the transportation orders, e.g., Sun et al [1,18,25,30], Ayar and Yaman [31], Hrušovský et al [2] and Demir et al [3]. Generalized costs have a structure shown as Figure 2 [30,33,34] and thus cover all the payment created in the activities of the intermodal transportation.…”

“…Under this situation, soft time windows receive a lot of attention from the intermodal routing literature when discussing the formulation of due dates. Sun et al [1,18,30] and Fazayeli et al [46] explore the intermodal location-routing problem with due dates denoted by soft time windows. In Fazayeli et al's study, the penalty cost strategy that is the same as that of Hrušovský et al [2] and Demir et al [3] is used to optimize the timeliness of the intermodal transportation.…”

“…Among the diverse forms of transportation, road-rail intermodal transportation integrates the time-flexible road transportation implemented by container trucks and scheduled rail transportation. It therefore enjoys both the good mobility of trucks on short/medium-distance collection and delivery and the cost efficiency as well as large capacity of rail transportation on long-distance distribution [18,19]. Thus, the road-rail intermodal transportation is the most representative form of the diverse intermodal transportation modes and gets more and more popular in inland transportation.…”

“…With the road-rail intermodal transportation network becoming mature, how to optimally utilize the existing transportation facilities and equipment in the network to accomplish the transportation orders draws considerable attention from both transportation demanders (e.g., companies with transportation demands) and transportation managers (e.g., intermodal transportation operators) [20]. Consequently, the road-rail intermodal routing problem becomes the forefront in the intermodal transportation planning field [18].The road-rail intermodal routing problem aims at designing the best origin-to-destination routes that combine container trucks and container trains to enable customers to accomplish their transportation orders. It is much more complex than the famous vehicle routing problem, since two different transportation modes, i.e., road transportation (container trucks) and rail transportation (container trains), should be optimized in a combinatorial way in the same transportation network [21].…”

“…With the road-rail intermodal transportation network becoming mature, how to optimally utilize the existing transportation facilities and equipment in the network to accomplish the transportation orders draws considerable attention from both transportation demanders (e.g., companies with transportation demands) and transportation managers (e.g., intermodal transportation operators) [20]. Consequently, the road-rail intermodal routing problem becomes the forefront in the intermodal transportation planning field [18].…”