# Repositioning and Optimal Re-Allocation of Empty Containers: A Review of Methods, Models, and Applications

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## Abstract

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## 1. Introduction

## 2. Research Methodology

## 3. Empty-Container Management

#### 3.1. Organizational Logistics Perspective

#### 3.1.1. Internal Solutions

- Container leasing has seen more attention in the past few years, as an approach for managing empty-container traffic. According to Theofanis and Boile [7], leasing arrangements come into three major types: master lease, long-term lease, and short-term lease. The master lease is the type that is most related to the repositioning issue, by hiring containers at places with a shortage and to off-hire containers at surplus points. On the contrary, long- and short-term leases aim to invest their equipment, without any management services provided to the lessee. However, the opportunity for shipping lines to save costs by leasing containers remains linked to the terms and conditions of leasing contracts [12].
- Container substitution is the second internal approach to deal with container fleet imbalance [13]. Due to containers having different types and sizes, the demand for a particular container can be fulfilled by supplying another one [14]. Regarding the size substitution, the demand for two 20 ft empty containers may be replaced by supplying a 40 ft empty container [15]. Additionally, shipping lines can apply type substitution, by exchanging the demand for dry containers by providing a reefer container, without operating the refrigerator. Braekers et al. [16] explained that this strategy is challenging and cannot be a common practice, especially if the customer demand is subjected to some rules and conditions.

#### 3.1.2. External Solutions

- Intra-channel solutions focus on vertical coordination among the different players in the container-transport chain. There are two proposed strategies for allocating empty containers: depot-direct and street-turn [17]. The idea of depot-direct is to establish a neutral supply point for empty containers to be stored, instead of moving them back to the port. Furthermore, the exporter can get the empty container faster, and the travel time and the repositioning cost will decrease [18]. Street-turn means that shipping companies can use imported containers directly for exporting purposes at the consignee’s location [17,19]. Although a street-turn strategy can reduce the total cost and congestion, it needs changing regarding some contract regulations with customers to deal with such reuse, tracking, and tracing of the empties’s interchange [20].
- Inter-channel solutions depends on horizontal cooperation [21]. Shipping lines can cooperate in several formats, such as slot exchange, alliances, and resource pooling, while competing in providing shipping services [22,23]. Pool-sharing containers is one of the critical strategies discussed by Theofanis and Boile [7]. They refer to the box-pool attempt, called Grey-Boxes, also known as free-label containers, which aims to reduce shareholders’s expenses by cooperating in providing empty containers without possession consideration. Vojdani et al. [24] ensured that such a strategy could decrease the movements of the empty container, store operations and subsequently, the total costs. This strategy did not receive the expected commercial acceptance due to competitiveness and confidentiality.

#### 3.2. Technological Innovation

#### 3.3. Modelling Approaches

## 4. Review on the Optimization of Empty-Container-Repositioning Techniques

#### 4.1. Repositioning by Network Flow Model

#### 4.2. Repositioning by Network Design

**u**denotes the vector of all the decision variables, namely;

#### 4.3. Repositioning under Resource Constraints

#### 4.4. The Use of Metaheuristic Algorithms

#### 4.4.1. Genetic Algorithm

#### 4.4.2. Tabu Search

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Transpacific | Europe to Asia | Transatlantic | ||||
---|---|---|---|---|---|---|

Year | Asia–North America | North America–Asia | Europe–Asia | Asia–Europe | North America–Europe | Europe–America |

2019 | 19.9 | 6.8 | 7.2 | 17.5 | 2.9 | 4.9 |

2020 | 20.6 | 6.9 | 7.2 | 16.9 | 2.8 | 4.8 |

2021 | 24.1 | 7.1 | 7.8 | 18.5 | 2.8 | 5.2 |

Percentage change 2020–2021 | 17.1 | 2.7 | 8.0 | 9.5 | 1.4 | 9.0 |

Selection Criteria | Scientific Database | |
---|---|---|

Inclusion | Peer-reviewed research articles, conference proceedings papers, books, book chapters, review papers, short surveys, and serials mainly discuss the models and methods to solve the empty-container-movements problem. | |

Exclusion | Before importation to a bibliographic manager | Non-English publications, articles with missing abstracts, notes, editorials |

During title screening | Generic articles about empty-container movements are used as examples and/or future recommendations. | |

During abstract screening | -Not related to the transportation field, e.g., safety management. -Articles address the new technologies of reusing empty containers. -Industry publications where outcomes are not relevant for analysis. | |

During full-text screening | -Articles related to the environmental responsibilities and emissions measurement of empty-container movements. -Articles discussed the empty-container repositioning without describing specific applications. |

Year | Authors | Model | Solution Approach | Description |
---|---|---|---|---|

1998 | Cheung and Chen [28] | A two-stage stochastic network | Quasi-gradient method | Evaluating the model over a rolling horizon environment |

2002 | Choong et al. [29] | Integer programming | Deterministic Dynamic Optimization | A case study of potential container-on-barge operations within the Mississippi River |

2005 | Olivo et al. [30] | Integer programming | A minimum cost flow problem | A Mediterranean region was examined as a case study by different modes of transportation. |

2007 | Shintani et al. [31] | Knapsack problem, then network flow problem | Genetic algorithm | Both port and ship-related cost factors were used in a non-linear cost function |

2007 | Lam et al. [32] | Dynamic stochastic programming | Approximate Dynamic Programming | The cost function is based on multi-port and multi-service system |

2007 | Wang and Wang [33] | Integer linear programming | LINGO | Inland transportation considers the container shortage and leasing costs |

2008 | Chang et al. [13] | Container substitution flow problem | Rounding LP-solution, branch and bound and CPLEX | Container substitution allows street turns |

2009 | Bandeira et al. [34] | Decision support system | LINDO | Mathematical programming techniques, stochastic models, simulation, and heuristic technique was integrated |

2009 | Di Francesco et al. [35] | Multi-commodity flow problems | Time-extended multi-scenario optimization model | A shipping company located in the Mediterranean region was examined |

2009 | Dong and Song [36] | Simulation-based Optimization | Genetic Algorithms and Evolutionary Strategies | The model includes multi-vessel, multi-port and multi-voyage shipping systems |

2010 | Shintani et al. [37] | An integer linear programming model | container flow mode | Foldable containers were considered |

2011 | Brouer et al. [38] | Relaxed linear multi-commodity flow model | Column generation algorithm | Real-life data from the largest liner shipping company, Maersk |

2011 | Meng and Wang [39] | Network design problem: mixed-integer linear programming model | CPLEX | Hub and spoke and multi-port-calling operations based on Asia–Europe–Oceania shipping network |

2011 | Choi et al. [40] | linear programming model | Time-expanded minimum-cost flow problem | Global shipping company in Korea used as a case study |

2012 | Long et al. [41] | A two-stage stochastic programming model | Sample Average Approximation | Scenario decomposition as considered |

2012 | Dang et al. [42] | Inventory control problem by the simulation model | Heuristics with genetic algorithm | The perspective of a container depot |

2012 | Dong and Song [11] | Cargo routing problem: Integer programming | Two-stage of shortest path and heuristics for an integer programming | An Asian shipping company with multiple service routes was examined as a case study |

2012 | Epstein et al. [8] | An inventory model and a multi-commodity network flow model | CPLEX | Consider multiple container types |

2013 | Moon et al. [25] | Three mathematical models and Two heuristics | A heuristic for an initial solution of small instances by using Lingo and using local search for improvement | Comparing standard and foldable containers based on costs |

2013 | Di Francesco et al. [43] | A stochastic programming approach | Time-extended multi-scenario/CPLEX | Non-anticipatively conditions were used to link scenarios |

2013 | Lai [44] | Time-space network | Integrating Branch and Bound with CPLEX for the multiple-scenarios situation | Data uncertainties for empty containers were used, such as capacity, handling, storage and transport |

2013 | Furio et al. [45] | Min-cost network flow optimization model | Decision Support System (DSS) | The model considered street-turn applications in the hinterland of Valencia |

2013 | Mittal et al. [46] | A two-stage stochastic programming model | Depot location problem in time horizon/CPLEX | New York/New Jersey port was selected as a case study for the model |

2013 | Dong et al. [47] | OD-based matrix solutions | Genetic algorithm | Experiments on three shipping service routes operated by three shipping companies |

2014 | Jansen [48] | Integer programming formulation/The flow network | CPLEX | Solving problems with planning horizons and forecast |

2015 | Huang et al. [49] | Mixed-integer programming model | CPLEX | A case study: Asia-Europe-Oceania shipping network |

2015 | Wong et al. [50] | Constrained linear programming | Shipment yield network driven-based model | A case study of service routes of Trans-Pacific trade operated in the G6 alliance |

2015 | Zheng et al. [51] | Two-stage optimization method | Centralised Optimization then Inverse Optimization | Experiments on an Asia–Europe–Oceania shipping service network |

2016 | Zheng et al. [52] | Network design: mixed-integer non-linear model | CPLEX | Considered perceived container and leasing prices |

2016 | Sainz Bernat et al. [53] | Simulation models with metaheuristic | Discrete-event simulation and genetic algorithm | Pollution, repair, and street turns are in the context of model |

2016 | Akyüz and Lee [54] | Mixed-integer linear programming model | b-column generation and ranch and bound algorithm | Simultaneous service type assignment and container routing problem were solved |

2017 | Monemi and Gelareh [55] | Integrated modelling framework: mixed-integer linear programming | Branch, Cut and Benders Algorithm (BCB) | The transhipment decision was considered |

2017 | Wang et al. [56] | A revised simplex algorithm | Network flow model | Foldable containers were included |

2017 | Xie at al. [57] | A game-theoretical: Inventory sharing game | Nash equilibrium | Intermodal transportation system consists of one rail firm and one-liner carrier |

2017 | Benadada and Razouk [58] | Optimization-simulation | Arena software | A real case study of the container terminal at Tanger Med port was applied |

2018 | Belayachi et al. [59] | A heuristic method by neighbourhood. | A decision-making/Taboo Search method. | Reverse logistics of containers |

2019 | Zhang et al. [60] | Two-layer collaborative optimization model | CPLEX and Genetic Algorithm | Combined tactical and operational levels based on business flow |

2019 | Xing et al. [61] | Simulation-based two-stage Optimization | Dynamic planning horizon and Genetic Algorithm | The quotation-booking process is included in operations decisions |

2019 | Hosseini and Sahlin [62] | A multi-period uncertainty optimization model | Chance constrained programming | A case study of European logistic service provider |

2019 | Gusah et al. [63] | Simulation modelling by agent-based modelling | AnyLogic | A case study of Melbourne, Australia |

2020 | Göçen et al. [64] | Two mathematical programming models | Mixed-integer linear programming and scenario-based stochastic programming | Real data taken from a liner carrier company include different types of containers |

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**MDPI and ACS Style**

Abdelshafie, A.; Salah, M.; Kramberger, T.; Dragan, D.
Repositioning and Optimal Re-Allocation of Empty Containers: A Review of Methods, Models, and Applications. *Sustainability* **2022**, *14*, 6655.
https://doi.org/10.3390/su14116655

**AMA Style**

Abdelshafie A, Salah M, Kramberger T, Dragan D.
Repositioning and Optimal Re-Allocation of Empty Containers: A Review of Methods, Models, and Applications. *Sustainability*. 2022; 14(11):6655.
https://doi.org/10.3390/su14116655

**Chicago/Turabian Style**

Abdelshafie, Alaa, May Salah, Tomaž Kramberger, and Dejan Dragan.
2022. "Repositioning and Optimal Re-Allocation of Empty Containers: A Review of Methods, Models, and Applications" *Sustainability* 14, no. 11: 6655.
https://doi.org/10.3390/su14116655