Scheduling double-track gantry cranes to minimize the overall loading/ unloading time

Jie Wang (), Guangting Chen, Xinle Xuan (), An Zhang, Yong Chen (), Yuehuan Wang () and Hecheng Zhang ()
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Jie Wang: School of Electronics and Information Engineering, Taizhou University, Linhai 317000, P. R. China
Guangting Chen: Zhejiang University of Water Resources and Electric Power, Zhejiang, Hangzhou 310018, P. R. China
Xinle Xuan: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
An Zhang: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Yong Chen: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Yuehuan Wang: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, P. R. China
Hecheng Zhang: Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 05, 1-26

Abstract: In this paper, we consider the gantry crane scheduling problem at a single storage block where a total of m gantry cranes are mounted on double tracks so that cranes on different tracks can pass each other while those on the same track cannot. Containers at the storage block are divided into bays and each bay of containers has to be loaded/unloaded together due to the same shipping destination or the same customer. To minimize the overall loading/ unloading time of containers, we first formulate the problem to a mixed integer linear programming (MILP) model, and compute the optimal solutions of small instances by the Gurobi solver. Then we design several heuristic algorithms and test their efficiency and performance by a series of large instances. In particular, we present a polynomial time approximation algorithm for the case where all but one gantry crane is mounted on the same track. We show that the algorithm has a worst case ratio of 2 − 2 m, outperforming the partition-based algorithms in the single-track scenario.

Keywords: Gantry cranes; non-crossing constraint; MILP model; approximation algorithm; worst case analysis; computational experiments (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595923400213

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