# Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method

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## Abstract

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## 1. Introduction

## 2. Previous Review Papers

## 3. Research Methodology

#### 3.1. Data Collection Methods

- What is the classification of LIRP based on the type of problem and the characteristics of variables?
- What are the model-based solutions for LIRP?
- What are the current trends of LIRP?
- What are the challenges and future work directions of LIRP in real-world applications?

- Papers retrieved must be published in proceedings of peer-reviewed international journals or international conferences in the English language.
- The topic must include (but is not limited to) at least one paper on location inventory path, covering logistics location, inventory decision, and route optimization decision.
- The article must have at least one essential attribute related to the title, keywords, abstract, and body content mentioned previously.

#### 3.2. Descriptive Statistics

#### 3.3. Category Classification

## 4. Review of Literature

#### 4.1. Classification based on Problem Characteristics

#### 4.1.1. LIRP Classification Based on Inventory Periodicity and Quantity of Productions

#### Single-Period Single-Product Problem (SPSPP)

#### Single-Period Multi-Product Problem (SPMPP)

#### Multi-Period Single-Product Problem (MPSPP)

#### Multi-Period Multi-Product Problem (MPMPP)

#### 4.1.2. LIRP Classification Based on Echelons and Links

#### Single-Echelon Single-Link Problem (SESLP)

#### Multi-Echelon Single-Link Problem (MESLP)

#### Multi-Echelon Multi-Link Problem (MEMLP)

#### 4.1.3. LIRP Classification Based on Number of Depots and Retailers

#### Single-Depot Multi-Retailer Problem (SDMRP)

#### Multi-Depot Multi-Retailer Problem (MDMRP)

#### 4.2. Classification Based on Demand Data Types

#### 4.3. Classification Based on Models and Solutions

- Solution Methods of MIP Model

- Solution Methods of MILP Model

- Solution Methods of MINLP Model

#### 4.4. Classification Based on Applications

## 5. Current Trends

#### 5.1. Descriptive Analysis

#### 5.2. Overall Observations

## 6. Challenges and Future Work

#### 6.1. LIRP with Multi-Period and Multi-Stage

#### 6.2. LIRP with Multi-Echelon Multi-Link

#### 6.3. LIRP with Green Closed-Loop Supply Chain

#### 6.4. LIRP with Time Window and Shortage Allowance

#### 6.5. LIRP with Out of Stock Inventory and Transport Disruption during COVID-19

#### 6.6. LIRP in an Uncertain Environment

#### 6.7. LIRP with Modern Heuristic Algorithms

#### 6.8. LIRP in Healthcare Logistics

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

IRP | Inventory-routing problem |

LIP | Location-inventory problem |

LRP | Location-routing problem |

LIRP | Location-inventory-routing problem |

MIP | Mixed integer programming |

MILP | Mixed integer linear programming |

MINLP | Mixed integer nonlinear programming |

PRISMA | Preferred Reporting Items for Systematic Reviews and Meta-Analysis |

CLSC | Closed-loop supply chain |

GSCM | Green supply-chain management |

TSCC | Total supply-chain cost |

ECLS | E-commerce logistics system |

HSC | Hazmat supply chain |

PPLN | Perishable-products logistics network |

CCLN | Cold-chain logistics network |

ESSC | Environmentally sustainable supply chain |

HUSC | Humanitarian supply chain |

HEL | Healthcare logistics |

MOP | Multi-objective programming |

CP | Capacity planning |

CS | Customer satisfaction |

DC | Distribution center |

RL | Reverse logistics |

MS | Multi-stages |

SC | Shortage cost |

TC | Transportation cost |

TP | Total profit |

TW | Time window |

CEEI | CO_{2} emission and environmental impacts |

HOFV | Homogeneous fleet of vehicles |

HEFV | Heterogeneous fleet of vehicles |

ICRP | Inventory control replenishment policy |

PSI | Positive social impacts |

SCR | Supply-chain risks |

TTD | Total traversed distance |

SPSPP | Single-period single-product problem |

SPMPP | Single-period multi-product problem |

MPSPP | Multi-period single-product problem |

MPMPP | Multi-period multi-product problem |

SESLP | Single-echelon single-link problem |

MESLP | Multi-echelon single-link problem |

MEMLP | Multi-echelon multi-link problem |

SDMRP | Single-depot multi-retailer problem |

MDMRP | Multi-depot multi-retailer problem |

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**Figure 4.**LIRP in cold-chain logistics system (two-echelon single-link) (source: [61]).

**Figure 5.**LIRP in cold-chain logistics system (source: [34]).

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[14] | An extensive review of the existing literature on the LIP model. Provided significant insights and identified potential research topics for future research. | 1976–2013 | 142 |

[15] | A classification of problem variants and extension of LRP. Conveyed the main ideas of each paper. | 2006–2014 | 154 |

[16] | Proposed a new taxonomy to capture some recently emerging issues in LRP. Provided analysis of publication intensity, problem characteristics, solution methods, and applications. | 2014–2019 | 222 |

[17] | Categorized IRPs with respect to their structural variants and with respect to availability. | 1987–2012 | 130 |

[18] | Proposed information management of IRP. Provided the relationship between inventory policy and demand information. Summarized requirement modeling and used optimization methods to find suitable solutions. | 2006–2014 | 41 |

[19] | Presented an overview of the conceptual framework of marine IRP. | 2010–2017 | 60 |

[20] | Reviewed IRP studying random demand and random lead times with a focus on their multi-warehouse aspects. Reviewed some characteristics and solutions of multi-warehouse IRP. | 2003–2017 | 66 |

[21] | Reviewed research on IRP that considered a novel classification for sustainable development. Introduced practical aspects and incorporate sustainability into the model. Emphasized scarcity and the direction of future study. | 2010–2018 | 75 |

[22] | First literature review of alternative IRP. Pointed out that the existing literature is not helpful enough for the decision-making process of legislators. | 1984–2018 | 329 |

[23] | Classified according to the models and the algorithms of IRP. Classified according to time horizon and structure. | 1983–2013 | 41 |

[24] | Summarized the comparison of three algorithms for solving a certain IRP. | 1997–2014 | 26 |

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Type of Publication | Year | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | Total | |

Journal | 1 | 1 | 2 | 4 | 5 | 3 | 11 | 8 | 9 | 11 | 12 | 30 | 97 |

Conference Proceedings | 4 | 2 | 0 | 1 | 2 | 1 | 2 | 1 | 2 | 0 | 0 | 0 | 15 |

Total | 5 | 3 | 2 | 5 | 7 | 4 | 13 | 9 | 11 | 11 | 12 | 30 | 112 |

Publisher | Number of Papers | Year | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | ||

Elsevier | 42 | 2 | 0 | 0 | 1 | 3 | 1 | 5 | 3 | 6 | 6 | 4 | 11 |

Springer | 15 | 1 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | 6 |

Hindawi | 8 | 0 | 0 | 0 | 1 | 0 | 1 | 2 | 0 | 2 | 0 | 0 | 2 |

IEEE Xplore | 7 | 2 | 1 | 0 | 1 | 1 | 0 | 2 | 0 | 0 | 0 | 0 | 0 |

Emerald Insight | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |

Taylor & Francis | 2 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Growing Science | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |

Wiley Online | 2 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |

IOS Press | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |

MDPI | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |

EDP Sciences | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |

Others | 25 | 0 | 1 | 0 | 0 | 2 | 1 | 2 | 4 | 3 | 2 | 4 | 6 |

Total | 112 | 5 | 3 | 2 | 5 | 7 | 4 | 13 | 9 | 11 | 11 | 12 | 30 |

Country | Year | Total | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | ||

China | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 2 | 0 | 3 | 0 | 7 | 16 |

Iran | 0 | 1 | 0 | 0 | 1 | 0 | 2 | 0 | 2 | 1 | 3 | 7 | 17 |

France | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 2 | 3 |

Indonesia | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 2 |

Canada | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |

Denmark | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |

Malaysia | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

Morocco | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |

Taiwan | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

Turkey | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |

Total | 1 | 2 | 0 | 1 | 2 | 1 | 5 | 3 | 2 | 5 | 5 | 17 | 44 |

Problem Characteristics | Demand Data Types | Models/Solutions | Applied Fields | ||
---|---|---|---|---|---|

Period-Product | Echelons-Links | Depots-Retailers | |||

Single-Single | Single-Single | Single-Multi | Deterministic | MIP | ECLS |

Single-Multi | Multi-Single | Multi-Multi | Variable | MILP | HSC |

Multi-Single | Multi-Multi | Stochastic | MINLP | PPLN | |

Multi-Multi | Fuzzy | Exact Algorithm | CCLN | ||

Heuristic and Metaheuristic | ESSC | ||||

Mixed Exact and Heuristic and Metaheuristic | HUSC | ||||

Other Approaches | HEL | ||||

Others |

MPMPP | MESLP | MDMRP | Total |
---|---|---|---|

✓ | ✓ | ✓ | 23 |

✓ | ✓ | 6 | |

✓ | ✓ | 13 | |

✓ | ✓ | 12 | |

✓ | 9 | ||

✓ | 5 | ||

✓ | 37 |

Type of Problem | SPSPP | SPMPP | MPSPP | MPMPP | SESLP | MESLP | MEMLP | SDMRP | MDMRP |
---|---|---|---|---|---|---|---|---|---|

Single-objective | 6 | 2 | 19 | 28 | 3 | 21 | 4 | 3 | 46 |

Multi-objective | 2 | 1 | 5 | 23 | 1 | 25 | 2 | 1 | 39 |

Total | 8 | 3 | 24 | 51 | 4 | 46 | 6 | 4 | 85 |

Model Type | MIP | MILP | MINLP | Total |
---|---|---|---|---|

Single-objective | 22 | 22 | 20 | 64 |

Multi-objective | 12 | 18 | 18 | 48 |

Total | 34 | 40 | 38 | 112 |

Demand Data Type | Deterministic | Variable | Stochastic | Fuzzy | Total |
---|---|---|---|---|---|

Single-objective | 29 | 8 | 26 | 1 | 64 |

Multi-objective | 8 | 13 | 20 | 7 | 48 |

Total | 37 | 21 | 46 | 8 | 112 |

Demand Data Types | Year | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | Total | |

Deterministic | 1 | 2 | 1 | 3 | 3 | 2 | 7 | 3 | 4 | 1 | 4 | 6 | 37 |

Variable | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 3 | 4 | 2 | 9 | 21 |

Stochastic | 4 | 1 | 0 | 2 | 3 | 2 | 4 | 5 | 4 | 6 | 4 | 11 | 46 |

Fuzzy | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 2 | 4 | 8 |

Total | 5 | 3 | 2 | 5 | 7 | 4 | 13 | 9 | 11 | 11 | 12 | 30 | 112 |

Demand Data Types | MIP | MILP | MINLP | Total |
---|---|---|---|---|

Deterministic | 10 | 17 | 10 | 37 |

Variable | 8 | 7 | 6 | 21 |

Stochastic | 15 | 9 | 22 | 46 |

Fuzzy | 1 | 7 | 0 | 8 |

Total | 34 | 40 | 38 | 112 |

Type of Problem | SPSPP | SPMPP | MPSPP | MPMPP | SESLP | MESLP | MEMLP | SDMRP | MDMRP |
---|---|---|---|---|---|---|---|---|---|

Deterministic | 1 | 1 | 10 | 11 | 1 | 11 | 1 | 1 | 29 |

Variable | 0 | 0 | 6 | 13 | 2 | 11 | 0 | 0 | 13 |

Stochastic | 6 | 1 | 8 | 21 | 1 | 19 | 5 | 3 | 35 |

Fuzzy | 1 | 1 | 0 | 6 | 0 | 5 | 0 | 0 | 8 |

Total | 8 | 3 | 24 | 51 | 4 | 46 | 6 | 4 | 85 |

Model Type of Problem | SPSPP | SPMPP | MPSPP | MPMPP | SESLP | MESLP | MEMLP | SDMRP | MDMRP |
---|---|---|---|---|---|---|---|---|---|

MIP | 4 | 0 | 8 | 11 | 2 | 8 | 1 | 3 | 24 |

MILP | 0 | 1 | 9 | 24 | 2 | 23 | 1 | 0 | 29 |

MINLP | 4 | 2 | 7 | 16 | 0 | 15 | 4 | 1 | 32 |

Total | 8 | 3 | 24 | 51 | 4 | 46 | 6 | 4 | 85 |

Solution Approach | Year | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | Total | |

Exact Algorithm only | 1 | 1 | 0 | 2 | 0 | 2 | 5 | 1 | 2 | 2 | 3 | 7 | 26 |

Heuristic and Metaheuristic | 4 | 2 | 1 | 3 | 6 | 1 | 8 | 6 | 8 | 9 | 7 | 17 | 72 |

Exact, Heuristic and Metaheuristic | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 4 | 10 |

Other Approaches | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 2 | 4 |

Total | 5 | 3 | 2 | 5 | 7 | 4 | 14 | 8 | 11 | 11 | 12 | 30 | 112 |

Solution Approach | SPSPP | SPMPP | MPSPP | MPMPP | SESLP | MESLP | MEMLP | SDMRP | MDMRP |
---|---|---|---|---|---|---|---|---|---|

Exact Algorithm only | 0 | 1 | 10 | 12 | 0 | 15 | 2 | 1 | 17 |

Heutistic and Metaheuristic | 7 | 1 | 11 | 31 | 3 | 27 | 3 | 3 | 56 |

Exact, Heuristic and Metaheuristic | 1 | 0 | 2 | 6 | 1 | 4 | 1 | 0 | 8 |

Others | 0 | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 4 |

Total | 8 | 3 | 24 | 51 | 4 | 46 | 6 | 4 | 85 |

Solution Approach | MIP | MILP | MINLP | Total |
---|---|---|---|---|

Exact Algorithm | 4 | 18 | 4 | 26 |

Heutistic and Metaheuristic | 27 | 18 | 27 | 72 |

Exact, Heuristic and Metaheuristic | 2 | 3 | 5 | 10 |

Other Approaches | 1 | 1 | 2 | 4 |

Total | 34 | 40 | 38 | 112 |

Type of Application | Year | Total | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | ||

ECLS | 0 | 0 | 1 | 3 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 7 |

HSC | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 2 | 2 | 2 | 4 | 15 |

PPLN | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 3 | 4 | 10 | 21 |

CCL | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 2 | 5 |

ESSC | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 1 | 1 | 2 | 6 | 13 |

HUSC | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 1 | 3 |

HEL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 5 |

Others | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 5 |

Total | 1 | 1 | 1 | 3 | 1 | 1 | 7 | 6 | 8 | 7 | 12 | 26 | 74 |

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**MDPI and ACS Style**

Liu, L.; Lee, L.S.; Seow, H.-V.; Chen, C.Y.
Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method. *Sustainability* **2022**, *14*, 15853.
https://doi.org/10.3390/su142315853

**AMA Style**

Liu L, Lee LS, Seow H-V, Chen CY.
Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method. *Sustainability*. 2022; 14(23):15853.
https://doi.org/10.3390/su142315853

**Chicago/Turabian Style**

Liu, Lihua, Lai Soon Lee, Hsin-Vonn Seow, and Chuei Yee Chen.
2022. "Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method" *Sustainability* 14, no. 23: 15853.
https://doi.org/10.3390/su142315853