Hybrid branch-and-price-and-cut algorithm for the two-dimensional vector packing problem with time windows
•We investigate the two-dimensional vector packing problem with time windows.•A branch-price-and-cut method is proposed with exact and heuristic pricing.•The proposed algorithm significantly outperforms three exact algorithms. This paper introduces the two-dimensional vector packing problem with tim...
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| Vydané v: | Computers & operations research Ročník 157; s. 106267 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.09.2023
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| ISSN: | 0305-0548 |
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| Abstract | •We investigate the two-dimensional vector packing problem with time windows.•A branch-price-and-cut method is proposed with exact and heuristic pricing.•The proposed algorithm significantly outperforms three exact algorithms.
This paper introduces the two-dimensional vector packing problem with time windows (2DVPPTW). It packs all items into identical bins to minimize the number of used bins. Items are characterized by their weights, volumes, and time windows. Items have different time requirements for delivery in many practical settings. For example, items have their time windows for packing and delivery. The 2DVPPTW is subjected to three constraints: weight, volume, and time windows. We present an integer programming (IP) model for the proposed 2DVPPTW. The IP model is reformulated into the master problem and the subproblem (SP). A hybrid branch-and-price-and-cut (H-BPC) algorithm is developed to solve the 2DVPPTW. On the basis of extensive computational experiments, the proposed H-BPC is significantly effective in comparison with the commercial branch-and-bound/cut solvers, such as CPLEX, and two exact methods. The primary reason for the computational efficiency of the H-BPC is the development of a heuristic algorithm, namely, adaptive large neighborhood search (ALNS), to solve the SP, which is usually computationally expensive. Developing the heuristic algorithm extends the works on the solution to the SPs of bin packing problems and two-dimensional vector packing problems. Two dynamic programming (DP) algorithms are also proposed to solve the SP optimally, namely, the label-setting algorithm and the maximal clique-based DP (MC_DP) algorithm. Moreover, two cooperative schemes are proposed and compared. One is composed of the ALNS and label-setting algorithm, which has a shorter computational time, and the other is composed of the ALNS and MC_DP, which can obtain more optimal solutions. Furthermore, subset-row inequalities, rounded capacity inequalities, multidimensional dual-feasible function, and incompatibility preprocessing policy help to decrease the computational burden dramatically. |
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| AbstractList | •We investigate the two-dimensional vector packing problem with time windows.•A branch-price-and-cut method is proposed with exact and heuristic pricing.•The proposed algorithm significantly outperforms three exact algorithms.
This paper introduces the two-dimensional vector packing problem with time windows (2DVPPTW). It packs all items into identical bins to minimize the number of used bins. Items are characterized by their weights, volumes, and time windows. Items have different time requirements for delivery in many practical settings. For example, items have their time windows for packing and delivery. The 2DVPPTW is subjected to three constraints: weight, volume, and time windows. We present an integer programming (IP) model for the proposed 2DVPPTW. The IP model is reformulated into the master problem and the subproblem (SP). A hybrid branch-and-price-and-cut (H-BPC) algorithm is developed to solve the 2DVPPTW. On the basis of extensive computational experiments, the proposed H-BPC is significantly effective in comparison with the commercial branch-and-bound/cut solvers, such as CPLEX, and two exact methods. The primary reason for the computational efficiency of the H-BPC is the development of a heuristic algorithm, namely, adaptive large neighborhood search (ALNS), to solve the SP, which is usually computationally expensive. Developing the heuristic algorithm extends the works on the solution to the SPs of bin packing problems and two-dimensional vector packing problems. Two dynamic programming (DP) algorithms are also proposed to solve the SP optimally, namely, the label-setting algorithm and the maximal clique-based DP (MC_DP) algorithm. Moreover, two cooperative schemes are proposed and compared. One is composed of the ALNS and label-setting algorithm, which has a shorter computational time, and the other is composed of the ALNS and MC_DP, which can obtain more optimal solutions. Furthermore, subset-row inequalities, rounded capacity inequalities, multidimensional dual-feasible function, and incompatibility preprocessing policy help to decrease the computational burden dramatically. |
| ArticleNumber | 106267 |
| Author | Li, Junheng Wahab, M.I.M. Chen, Yanru Gao, Mujin |
| Author_xml | – sequence: 1 givenname: Mujin surname: Gao fullname: Gao, Mujin organization: School of Economics and Management, Southwest Jiaotong University, 111, 1st Section, Northern 2nd Ring Road, Chengdu, Sichuan 610031, China – sequence: 2 givenname: Yanru orcidid: 0000-0002-0162-5067 surname: Chen fullname: Chen, Yanru email: chenyanru@swjtu.cn organization: School of Economics and Management, Southwest Jiaotong University, 111, 1st Section, Northern 2nd Ring Road, Chengdu, Sichuan 610031, China – sequence: 3 givenname: Junheng surname: Li fullname: Li, Junheng organization: School of Economics and Management, Southwest Jiaotong University, 111, 1st Section, Northern 2nd Ring Road, Chengdu, Sichuan 610031, China – sequence: 4 givenname: M.I.M. orcidid: 0000-0002-5458-0886 surname: Wahab fullname: Wahab, M.I.M. organization: Department of Mechanical and Industrial Engineering, Toronto Metropolitan University, 350 Victoria Street, Toronto M5B2K3, Canada |
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| Keywords | Time windows Adaptive large neighborhood search Hybrid method Two-dimensional vector packing problem Branch-and-price-and-cut |
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| SubjectTerms | Adaptive large neighborhood search Branch-and-price-and-cut Hybrid method Time windows Two-dimensional vector packing problem |
| Title | Hybrid branch-and-price-and-cut algorithm for the two-dimensional vector packing problem with time windows |
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