Synchromodal transport planning with flexible services: Mathematical model and heuristic algorithm

Modeling a Carbon-Efficient Road–Rail Intermodal Routing Problem with Soft Time Windows in a Time-Dependent and Fuzzy Environment by Chance-Constrained Programming

“…Currently, time-dependent intermodal routing studies primarily focus on time-dependent travel times. Zhang et al [9] modeled the time dependency of truck travel times as a piecewise linear function and investigated a carbon-efficient intermodal routing problem with soft pickup and delivery time windows and road service flexibility. Sun et al [32] and Guo et al [33] considered the same modeling of time dependency as Zhang et al [9] and presented an intermodal routing problem in a dynamic environment and a multimodal routing problem with traffic congestion and capacity uncertainty, respectively.…”

“…Zhang et al [9] modeled the time dependency of truck travel times as a piecewise linear function and investigated a carbon-efficient intermodal routing problem with soft pickup and delivery time windows and road service flexibility. Sun et al [32] and Guo et al [33] considered the same modeling of time dependency as Zhang et al [9] and presented an intermodal routing problem in a dynamic environment and a multimodal routing problem with traffic congestion and capacity uncertainty, respectively. In these studies, the formulation of time-dependent travel times contributes to optimizing the efficiency of intermodal transfer and timeliness regarding time windows or due dates.…”

“…Besides the single-objective setting, many articles on deterministic intermodal routing discussed multi-objective optimization problems considering at least two goals oriented on the economy (as the primary goal), timeliness (e.g., [42,43]), risk (e.g., [44,45]), and sustainability (e.g., [46,47]), etc., and obtained the Pareto solutions to balance the objectives conflicting with each other. Modeling transportation modes is also concerned by deterministic intermodal routing studies, in which some transportation modes are modeled with fixed departure times (e.g., [48,49]), fixed service time windows (e.g., [42,50,51]), or fixed timetables/schedules covering the above parameters (e.g., [52]); meanwhile, the flexibility of some transportation modes starts to receive consideration [9]. To formulate the deterministic intermodal routing problems, researchers proposed optimization models using pure 0-1 integer programming (e.g., [53]), mixed 0-1 integer programming (e.g., [50,52]), linear programming (e.g., [17]), and nonlinear programming (e.g., [44,52]).…”

“…Furthermore, the RRIRP should be studied in a real-world transportation scenario to ensure that the coordination of road and rail can be realized by RRIRP in the actual transportation. In real-world transportation, the operations of rail services (specifically, in this study, container block trains) follow fixed timetables [8], while road services (specifically, in this study, container trucks) are flexible [9]. Coordinating road and rail by RRIRP to enhance intermodality and accomplish transportation orders should fully model the above differences.…”

Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints

“…However, the majority of relevant studies focus more on the delivery than the pickup when modeling the time window and assume that containers are released at a fixed time [13,16] or there is the earliest release time [17]. Currently, quite a few works simultaneously model the two types of time windows, in which Sun et al [2] and Zhang et al [18] use the soft time window. Although these studies discuss the pickup and delivery time windows, their modeling still has the disadvantage of the soft time windows indicated above.…”