We address the Green Vehicle Routing Problem with two -dimensionalloadingconstraints and Split Delivery (G2L-SDVRP), which extends the split delivery vehicle routing problem to include customer demands represented b...
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We address the Green Vehicle Routing Problem with two -dimensionalloadingconstraints and Split Delivery (G2L-SDVRP), which extends the split delivery vehicle routing problem to include customer demands represented by two-dimensional, rectangular items. We aim to minimize carbon dioxide (CO 2 ) emissions instead of travel distance, a critical issue in contemporary logistics activities. The CO 2 emission rate is proportional to fuel consumption and measured in terms of the vehicle's total weight and traveled distance. We propose the first metaheuristic for the G2L-SDVRP, based on a variable neighborhood search approach that designs effective routes and guarantees the feasibility of loadingconstraints using various strategies, such as lower bound procedures, the open space heuristic, and a constraint programming model. We evaluate the performance of our approach through computational experiments using benchmark and newly created instances. The results indicate that the proposed approach is effective. It achieves improved solutions for 21 out of 60 instances in relatively short computing times when compared to existing methods for the G2L-SDVRP. Furthermore, our approach is competitive on benchmark instances of a related variant, namely the Capacitated Vehicle Routing Problem with two -dimensionalloadingconstraints, improving the best-known solutions for 50 out of 180 instances.
In this study, we develop a branch-and-cut algorithm for the vehicle routing problem with twodimensionalloadingconstraints. A separation algorithm is proposed to simultaneously identify infeasible set inequalities a...
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In this study, we develop a branch-and-cut algorithm for the vehicle routing problem with twodimensionalloadingconstraints. A separation algorithm is proposed to simultaneously identify infeasible set inequalities and weak capacity inequalities for fractional solutions. Classic capacitated vehicle routing problem (CVRP) inequalities are adopted as well. A branch-and-cut (B&C) algorithm is built to solve the problem. Experimental results illustrate that the algorithm is competitive. In particular, we solve 6 instances to optimality for the first time. Extensive computational analysis is also conducted to reveal the impact of infeasible set inequalities, the branching strategy, and the packing algorithms on the B&C algorithm. (c) 2022 Elsevier B.V. All rights reserved.
This paper presents a study about the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L-CVRP) and its three variants: allowing split delivery (2L-SDVRP), with green requirements (G2L-CVR...
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This paper presents a study about the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L-CVRP) and its three variants: allowing split delivery (2L-SDVRP), with green requirements (G2L-CVRP), and integrating split delivery with green requirements (G2L-SDVRP). When considering split delivery, a customer can be served by more than one vehicle. The green variant takes into consideration the CO2 emission. Our objective is to analyze the cost benefits obtained with the aggregation of split delivery and the reduction of CO2 emission. Mathematical models are presented for each variant, and instances are solved with a branch-andcut approach. We develop a tailored procedure to address the packing subproblem, including the computation of lower bounds, a constructive-based heuristic, and a constraint programming formulation. Computational experiments performed on literature instances and newly created ones show that the proposed approach can outperform previous results. Besides that, the green variant has solutions with low emissions of CO2. The variant with split delivery has solutions with lower cost but at the expense of higher computing time.
This study defines grey time windows as periods during which customers expect deliveries at a specific time, with an allowance for a certain amount of advance or delay. For model solving, the grey time window is first...
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This study defines grey time windows as periods during which customers expect deliveries at a specific time, with an allowance for a certain amount of advance or delay. For model solving, the grey time window is first whitened using the whitening triangle function based on different satisfaction thresholds and corresponding delivery costs. A tightness function is then designed for two-dimensionalloading, which measures the effectiveness of different key points and loading postures. Finally, the Iori dataset was utilised to verify the effectiveness of the proposed solution algorithm. To the best of our knowledge, this is the first time the joint design concept of grey time windows and the whitening method have been introduced. Additionally, a grey opportunity-constrained programming model was constructed, with the model transformation and solution methods provided. Simulation results demonstrate that the proposed two-dimensionalloading algorithm is both simple and efficient, and that the constructed grey chance-constrained programming model is solvable and has practical application value. Ultimately, this study provides insights for logistics companies on optimising delivery plans under various time window concepts.
The postal sector plays a crucial role in enhancing and advancing services for businesses and citizens through its diverse services. Hence, optimizing the routing system collecting and transporting letters and parcels...
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The postal sector plays a crucial role in enhancing and advancing services for businesses and citizens through its diverse services. Hence, optimizing the routing system collecting and transporting letters and parcels is a vital element within a well-rounded delivery management system. We model the problem as a Capacitated vehicle routing problem (CVRP) with two-dimensional loading constraints (2L-CVRP). This involves designing a set of routes that start and end at a central depot. Moreover, items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. The main objective is to optimize the total transportation costs using a homogeneous vehicle fleet. Due to the NP-hardness of the 2L-CVRP, we proposed an adaptive chemical reaction optimization (ACRO) metaheuristic to generate potential solutions. The algorithm adjusts its parameters and is intelligent search strategies during the optimization process based on the characteristics of the problem. Consequently, the algorithm can exploit and explore new regions of the search space. We compared our results with state-of-the-art meta-heuristics using 2L-CVRP benchmark instances from the literature. The results showed competitive solutions regarding the optimal ones. The empirical results, derived from benchmark datasets comprising a total of 180 instancesrove the high competitiveness of the proposed ACRO. It achieves a 67% success rate out of 36 instances for class 1 and a 59% success rate out of 144 instances for class 2-5 in terms of obtained solutions. In addition to benchmarking, we considered a real-world case study from the Tunisian Post Office. The ACRO results outperform the scenario adopted by the post office.
Oil exploration in Brazil is done mainly by offshore oil platforms located far from the coast and ships transport all supplies for them. This paper proposes a method based on a Hybrid Simulated Annealing with Ship'...
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Oil exploration in Brazil is done mainly by offshore oil platforms located far from the coast and ships transport all supplies for them. This paper proposes a method based on a Hybrid Simulated Annealing with Ship's Balance (HSA-SB) metaheuristic to plan the transport of loads to offshore platforms considering the arrangement of the loads on the ship's deck and the ship's balance about its keel. The main objective of HSA-SB is to minimize the ships affreightment costs by reducing the number of ships used and the distance sailed. It also arranges the loads on the deck, aiming to reduce ship's imbalance. HSA-SB was tested on real instances from a major Brazilian oil company and the results showed possible financial benefits.
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