# A lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem

Yi Min Fu, Ali Diabat

Research output: Contribution to journalArticle

### Abstract

Decisions on the quay crane assignment problem and the quay crane scheduling problem are typically made independently. However, the efficiency of container terminals can be increased when these decisions are made simultaneously due to the interrelation between quay crane assignment and scheduling. A mathematical formulation for the integrated quay crane assignment and scheduling problem (QCASP) is developed in this paper. Practical considerations are incorporated in the model, such as quay crane (QC) interference. A Lagrangian relaxation is proposed for the model. Feasible solutions are then obtained from the proposed heuristic. Computational results are provided for the proposed Lagrangian relaxation.

Original language English (US) 1194-1201 8 Applied Mathematical Modelling 39 3-4 https://doi.org/10.1016/j.apm.2014.07.006 Published - Jan 1 2015

### Fingerprint

Lagrangian Relaxation
Cranes
Assignment Problem
Scheduling Problem
Scheduling
Container Terminal
Computational Results
Assignment
Interference
Heuristics
Formulation
Model
Containers

### Keywords

• Integer programming
• Integrated models
• Lagrangian relaxation
• Quay crane assignment
• Quay crane scheduling

### ASJC Scopus subject areas

• Modeling and Simulation
• Applied Mathematics

### Cite this

In: Applied Mathematical Modelling, Vol. 39, No. 3-4, 01.01.2015, p. 1194-1201.

Research output: Contribution to journalArticle

title = "A lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem",
abstract = "Decisions on the quay crane assignment problem and the quay crane scheduling problem are typically made independently. However, the efficiency of container terminals can be increased when these decisions are made simultaneously due to the interrelation between quay crane assignment and scheduling. A mathematical formulation for the integrated quay crane assignment and scheduling problem (QCASP) is developed in this paper. Practical considerations are incorporated in the model, such as quay crane (QC) interference. A Lagrangian relaxation is proposed for the model. Feasible solutions are then obtained from the proposed heuristic. Computational results are provided for the proposed Lagrangian relaxation.",
keywords = "Integer programming, Integrated models, Lagrangian relaxation, Quay crane assignment, Quay crane scheduling",
author = "Fu, {Yi Min} and Ali Diabat",
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doi = "10.1016/j.apm.2014.07.006",
language = "English (US)",
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journal = "Applied Mathematical Modelling",
issn = "0307-904X",
publisher = "Elsevier Inc.",
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TY - JOUR

T1 - A lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem

AU - Fu, Yi Min

AU - Diabat, Ali

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Decisions on the quay crane assignment problem and the quay crane scheduling problem are typically made independently. However, the efficiency of container terminals can be increased when these decisions are made simultaneously due to the interrelation between quay crane assignment and scheduling. A mathematical formulation for the integrated quay crane assignment and scheduling problem (QCASP) is developed in this paper. Practical considerations are incorporated in the model, such as quay crane (QC) interference. A Lagrangian relaxation is proposed for the model. Feasible solutions are then obtained from the proposed heuristic. Computational results are provided for the proposed Lagrangian relaxation.

AB - Decisions on the quay crane assignment problem and the quay crane scheduling problem are typically made independently. However, the efficiency of container terminals can be increased when these decisions are made simultaneously due to the interrelation between quay crane assignment and scheduling. A mathematical formulation for the integrated quay crane assignment and scheduling problem (QCASP) is developed in this paper. Practical considerations are incorporated in the model, such as quay crane (QC) interference. A Lagrangian relaxation is proposed for the model. Feasible solutions are then obtained from the proposed heuristic. Computational results are provided for the proposed Lagrangian relaxation.

KW - Integer programming

KW - Integrated models

KW - Lagrangian relaxation

KW - Quay crane assignment

KW - Quay crane scheduling

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JF - Applied Mathematical Modelling

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