Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

Li, Xinya; Sun, Yan; Qi, Jinfeng; Wang, Danzhu

doi:10.3390/axioms13030200

Cited by 3 publications

(16 citation statements)

References 25 publications

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“…Consequently, the hard time window reduces the flexibility of the MRP. As a result, most MRP studies are interested in soft time windows that make the earliness and lateness allowable on condition that penalty or storage costs must be paid when the time window is violated, e.g., Zhang et al [10], Fazayeli et al [11], Yuan et al [12], and Li et al [13]. In this case, the penalty or storage period is calculated by the continuous piecewise linear function that introduces nonlinearity into the modeling of MRP.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, both pickup and delivery determine the time efficiency of the entire multimodal transportation process [15]. 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.…”

Section: Introductionmentioning

confidence: 99%

“…Uddin et al [23,24] utilize the scenario-based approach to model the uncertain capacities of rail transportation and terminals and build stochastic programming models for the MRP. Contrary to stochastic programming, based on the fuzzy set theory [25], Sun et al [8], Li et al [13], and Lu et al [26] use triangular fuzzy numbers to model capacity uncertainty and establish the fuzzy chance-constrained programming (FCCP) models to deal with their MRPs. A group of studies by Sun et al [2,16,27] model trapezoidal fuzzy capacities and propose FCCP models for specific MRPs.…”

Section: Introductionmentioning

confidence: 99%

“…Under the above situation, fuzzy programming based on the use of fuzzy numbers to model uncertainty [29,30] is an alternative for MRP under capacity uncertainty. However, References [2,8,13,16,26,27] use regular fuzzy numbers when modeling uncertain capacity and only analyze the influence of the confidence level introduced by fuzzy programming approaches on the MRP. In these studies, the influence of the uncertainty level of the fuzzy capacity on the MRP is not considered.…”

Section: Introductionmentioning

confidence: 99%

“…In these studies, the influence of the uncertainty level of the fuzzy capacity on the MRP is not considered. Additionally, apart from Li et al [13], the studies cited above only formulate the uncertainty of the travel capacity of rail transportation, while taking the travel capacities of other transportation modes to be deterministic, together with the node transfer capacities between different transportation modes.…”

Section: Introductionmentioning

confidence: 99%

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

Ge,

Sun

2024

Axioms

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This study models a container routing problem using multimodal transportation to improve its economy, timeliness, and reliability. Pickup and delivery time windows are simultaneously formulated in optimization to provide the shipper and the receiver with time-efficient services, in which early pickup and delayed delivery can be avoided, and nonlinear storage periods at the origin and the destination can be minimized. Furthermore, the capacity uncertainty of the multimodal network is incorporated into the advanced routing to enhance its reliability in practical transportation. The LR triangular fuzzy number is adopted to model the capacity uncertainty, in which its spread ratio is defined to measure the uncertainty level of the fuzzy capacity. Due to the nonlinearity introduced by the time windows and the fuzziness from the network capacity, this study establishes a fuzzy nonlinear optimization model for optimization problem. A chance-constrained linear reformulation equivalent to the proposed model is then generated based on the credibility measure, which makes the global optimum solution attainable by using Lingo software. A numerical case verification demonstrates that the proposed model can effectively solve the problem. The case analysis points out that the formulation of pickup and delivery time windows can improve the timeliness of the entire transportation process and help to achieve on-time transportation. Furthermore, improving the confidence level and the uncertainty level increases the total costs of the optimal route. Therefore, the shipper and the receiver must prepare more transportation budget to improve reliability and address the increasing uncertainty level. Further analysis draws some insights to help the shipper, receiver, and multimodal transport operator to organize a reliable and cost-efficient multimodal transportation under capacity uncertainty through confidence level balance and transportation service and transfer service selection.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Ge,

Sun

2024

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Optimization of Multimodal Paths for Oversize and Heavyweight Cargo under Different Carbon Pricing Policies

Wu,

Zhang,

Xiao

et al. 2024

Sustainability

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With the increasing global concern over climate change, reducing greenhouse gas emissions has become a universal goal for governments and enterprises. For oversize and heavyweight cargo (OHC) transportation, multimodal transportation has become widely adopted. However, this mode inevitably generates carbon emissions, making research into effective emission reduction strategies essential for achieving low-carbon economic development. This study investigates the optimization of multimodal transportation paths for OHC (OMTP-OHC), considering various direct carbon pricing policies and develops models for these paths under the ordinary scenario—defined as scenarios without any carbon pricing policies—and two carbon pricing policy scenarios, namely the emission trading scheme (ETS) policy and the carbon tax policy, to identify the most cost-effective solutions. An enhanced genetic algorithm incorporating elite strategy and catastrophe theory is employed to solve the models under the three scenarios. Subsequently, we examine the impact of ETS policy price fluctuations, carbon quota factors, and different carbon tax levels on decision-making through a case study, confirming the feasibility of the proposed model and algorithm. The findings indicate that the proposed algorithm effectively addresses this problem. Moreover, the algorithm demonstrates a small impact of ETS policy price fluctuations on outcomes and a slightly low sensitivity to carbon quota factors. This may be attributed to the relatively low ETS policy prices and the characteristics of OHC, where transportation and modification costs are significantly higher than carbon emission costs. Additionally, a comparative analysis of the two carbon pricing policies demonstrates the varying intensities of emission reductions in multimodal transportation, with the ranking of carbon emission reduction intensity as follows: upper-intermediate level of carbon tax > intermediate level of carbon tax > lower-intermediate level of carbon tax = ETS policy > the ordinary scenario. The emission reduction at the lower-intermediate carbon tax level (USD 8.40/t) matches that of the ETS policy at 30%, with a 49.59% greater reduction at the intermediate level (USD 50.48/t) compared to the ordinary scenario, and a 70.07% reduction at the upper-intermediate level (USD 91.14/t). The model and algorithm proposed in this study can provide scientific and technical support to realize the low-carbonization of the multimodal transportation for OHC. The findings of this study also provide scientific evidence for understanding the situation of multimodal transportation for OHC under China’s ETS policy and its performance under different carbon tax levels in China and other regions. This also contributes to achieving the goal of low-carbon economic development.

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Modeling a Multimodal Routing Problem with Flexible Time Window in a Multi-Uncertainty Environment

Ge,

Sun,

Zhang

2024

Systems

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In this study, we extend the research on the multimodal routing problem by considering flexible time window and multi-uncertainty environment. A multi-uncertainty environment includes uncertainty regarding the demand for goods, the travel speed of the transportation mode, and the transfer time between different transportation modes. This environment further results in uncertainty regarding the delivery time of goods at their destination and the earliness and lateness caused by time window violations. This study adopts triangular fuzzy numbers to model the uncertain parameters and the resulting uncertain variables. Then, a fuzzy mixed integer nonlinear programming model is established to formulate the specific problem, including both fuzzy parameters and fuzzy variables. To make the problem easily solvable, this study employs chance-constrained programming and linearization to process the proposed model to obtain an equivalent credibilistic chance-constrained linear programming reformulation with an attainable global optimum solution. A numerical case study based on a commonly used multimodal network structure is presented to demonstrate the feasibility of the proposed method. Compared to hard and soft time windows, the numerical case analysis reveals the advantages of the flexible time window in reducing the total costs, avoiding low reliability regarding timeliness, and providing confidence level-sensitive route schemes to achieve flexible routing decision-making under uncertainty. Furthermore, the numerical case analysis verifies that it is necessary to model the multi-uncertainty environment to satisfy the improved customer requirements for timeliness and enhance the flexibility of the routing, and multimodal transportation is better than unimodal transportation when routing goods in an uncertain environment. The sensitivity analysis in the numerical case study shows the conflicting relationship between the economic objective and the reliability regarding the timeliness of the routing, and the result provides a reference for the customer to find a balance between them.

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Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

Cited by 3 publications

References 25 publications

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

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

Optimization of Multimodal Paths for Oversize and Heavyweight Cargo under Different Carbon Pricing Policies

Modeling a Multimodal Routing Problem with Flexible Time Window in a Multi-Uncertainty Environment

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