A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity

As an effective solution to the first- and last-mile logistics of door-to-door intermodal container transportation, inland container transportation involves transporting containers by truck between terminals, depots, and customers within a local area. This paper is the first to focus specifically on...

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Main Authors: Yujian Song, Yuting Zhang
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Applied Sciences
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Online Access:https://www.mdpi.com/2076-3417/14/24/11958
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author Yujian Song
Yuting Zhang
author_facet Yujian Song
Yuting Zhang
author_sort Yujian Song
collection DOAJ
description As an effective solution to the first- and last-mile logistics of door-to-door intermodal container transportation, inland container transportation involves transporting containers by truck between terminals, depots, and customers within a local area. This paper is the first to focus specifically on the inland container transportation problem with limited depot capacity, where the storage of empty containers is constrained by physical space limitations. To reflect a more realistic scenario, we also consider the initial stock levels of empty containers at the depot. The objective of this problem is to schedule trucks to fulfill inland container transportation orders such that the overall cost is minimum and the depot is neither out of stock or over stocked at any time. A novel graphical representation is introduced to model the constraints of empty containers and depot capacity in a linear form. This problem is then mathematically modeled as a mixed-integer linear programming formulation. To avoid discretizing the time horizon and effectively achieve the optimal solution, we design a tailored branch-and-price-and-cut algorithm where violated empty container constraints for critical times are dynamically integrated into the restricted master problem. The efficiency of the proposed algorithm is enhanced through the implementation of several techniques, such as a heuristic label-setting method, decremental state-space relaxation, and the utilization of high-quality upper bounds. Extensive computational studies are performed to assess the performance of the proposed algorithm and justify the introduction of enhancement strategies. Sensitivity analysis is additionally conducted to investigate the implications of significant influential factors, offering meaningful managerial guidance for decision-makers.
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spelling doaj-art-c9d516df9cff49848dd7f782411c4f192024-12-27T14:08:54ZengMDPI AGApplied Sciences2076-34172024-12-0114241195810.3390/app142411958A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot CapacityYujian Song0Yuting Zhang1School of Business Administration, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, ChinaSchool of Economic and Management, Tongji University, Shanghai 200092, ChinaAs an effective solution to the first- and last-mile logistics of door-to-door intermodal container transportation, inland container transportation involves transporting containers by truck between terminals, depots, and customers within a local area. This paper is the first to focus specifically on the inland container transportation problem with limited depot capacity, where the storage of empty containers is constrained by physical space limitations. To reflect a more realistic scenario, we also consider the initial stock levels of empty containers at the depot. The objective of this problem is to schedule trucks to fulfill inland container transportation orders such that the overall cost is minimum and the depot is neither out of stock or over stocked at any time. A novel graphical representation is introduced to model the constraints of empty containers and depot capacity in a linear form. This problem is then mathematically modeled as a mixed-integer linear programming formulation. To avoid discretizing the time horizon and effectively achieve the optimal solution, we design a tailored branch-and-price-and-cut algorithm where violated empty container constraints for critical times are dynamically integrated into the restricted master problem. The efficiency of the proposed algorithm is enhanced through the implementation of several techniques, such as a heuristic label-setting method, decremental state-space relaxation, and the utilization of high-quality upper bounds. Extensive computational studies are performed to assess the performance of the proposed algorithm and justify the introduction of enhancement strategies. Sensitivity analysis is additionally conducted to investigate the implications of significant influential factors, offering meaningful managerial guidance for decision-makers.https://www.mdpi.com/2076-3417/14/24/11958inland container transportationlimited depot capacityempty containerbranch-and-price-and-cut algorithm
spellingShingle Yujian Song
Yuting Zhang
A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
Applied Sciences
inland container transportation
limited depot capacity
empty container
branch-and-price-and-cut algorithm
title A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
title_full A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
title_fullStr A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
title_full_unstemmed A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
title_short A Branch-and-Price-and-Cut Algorithm for the Inland Container Transportation Problem with Limited Depot Capacity
title_sort branch and price and cut algorithm for the inland container transportation problem with limited depot capacity
topic inland container transportation
limited depot capacity
empty container
branch-and-price-and-cut algorithm
url https://www.mdpi.com/2076-3417/14/24/11958
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