# An Event-Based Supply Chain Partnership Integration Using a Hybrid Particle Swarm Optimization and Ant Colony Optimization Approach

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## Abstract

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## Featured Application

**Supply chain management, online business management, smart manufacturing.**

## Abstract

## 1. Introduction

- This is a work regarding the design of an event-based framework in a supply chain partnership integration problem, which is based on a clear understanding of key events in a dynamic supply chain process and focuses on how events can be used to reveal factors that influence partnership in supply chain operations.
- The hybrid algorithm, PSACO, which utilizes the functions of PSO and ACO, is proposed. In the algorithm, a linear decreasing inertia weight schema is introduced to achieve relatively high performance for PSO, and a new pheromone strategy is used for ACO.
- In order to improve the precision of experiment solutions, experimental analyses are carried out to select the optimal parameters of ACO.
- Experimental results demonstrate that PSACO can obtain better performance than traditional PSO and ACO.

## 2. Related Work

#### 2.1. Supply Chain Partnership Integration

#### 2.2. The Analytical Value and Identification of Event

## 3. Model

#### 3.1. Supply Chain Network Structures

#### 3.2. Event-Based Supply Chain Partnership Integration Model

- (1)
- The enterprise collects orders from its customers;
- (2)
- The enterprise evaluates the degree of trustworthiness the upstream suppliers have;
- (3)
- The enterprise submits the orders to the upper suppliers;
- (4)
- The enterprise receives materials or semi-finished products from suppliers;
- (5)
- The enterprise starts producing according productivity and the material received, then sends the finished products to customers.
- (6)
- The enterprise calculates its operating cost;
- (7)
- The enterprise updates the performance of its suppliers and decides its cooperation plan.

#### 3.2.1. Orders

#### 3.2.2. Trustworthiness

#### 3.2.3. Supplier Service

#### 3.2.4. Production and Products Delivery

#### 3.2.5. Cost

#### 3.2.6. Supplier Performance Updating and Partnership Integration

## 4. Concepts of Integrating the Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO)

#### 4.1. The Concepts of PSO and ACO

#### 4.2. The Idea of Integrating PSO and ACO

## 5. Supply Chain Partnership Integration Algorithm Based on the Hybrid Algorithm

#### 5.1. Updating Particles’ Positions and Velocities

#### 5.2. Ant Movement

#### 5.3. Pheromone Updating

## 6. Numerical Experiments

#### 6.1. Parameters Optimization

#### 6.2. Results and Discussion

^{th}iteration with its optimal solution of 1.6588. This states that ACO has the worst result for lacking available feedback information. As for the hybrid algorithm, PSACO rapidly achieves the optimal stable result 1.4432 at the 10th iteration. The curve of PSACO has the best solution value. It conquers the flaw of redundant iterations that PSO generates, especially where the problem is on a large scale. It utilizes the optimal solutions generated by PSO to update initial pheromone and the searching speed brought by ACO. Hence, Hence, compared with PSO and ACO, PSACO has lower time cost and better performance.

## 7. Conclusions and Further Research

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Optimization of parameters of ACO. (

**a**) ant number; (

**b**) pheromone coefficient; (

**c**) heuristic coefficient; (

**d**) pheromone volatilization coefficient.

**Table 1.**Advantages and disadvantages of particle swarm optimization (PSO), ant colony optimization (ACO), and the proposed hybrid algorithms.

Characteristics | PSO | ACO | The Hybrid Algorithm |
---|---|---|---|

Evolutionary strategies | Yes | Yes | Yes |

The quick convergence speed | Yes | No | Yes |

The lack of information pheromone in the initial stage | No | Yes | No |

The strong local searching capability | No | Yes | Yes |

Positive feedback and distributed computation | No | Yes | Yes |

Guarantee of good capability to search global optima or any specific approximation | No | Yes | Yes |

Source | Degree of Freedom (DF) | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

Factor | 2 | 0.6324 | 0.316205 | 117.61 | 0.000 |

Error | 147 | 0.4759 | 0.002689 | ||

Total | 149 | 1.1083 |

Algorithm | Supply Chain | Cooperated Suppliers | Objective Function Values |
---|---|---|---|

PSO | 1 | ${s}_{1,13}{s}_{2,6}{s}_{3,14}{s}_{4,4}{s}_{5,6}{s}_{6,1}{s}_{7,14}{s}_{8,5}{s}_{9,10}{s}_{10,2}$ | 1.4844 |

2 | ${s}_{1,13}{s}_{2,6}{s}_{3,14}{s}_{4,4}{s}_{5,6}{s}_{6,12}{s}_{7,4}{s}_{8,5}{s}_{9,10}{s}_{10,2}$ | 1.4872 | |

3 | ${s}_{1,13}{s}_{2,3}{s}_{3,4}{s}_{4,4}{s}_{5,8}{s}_{6,6}{s}_{7,11}{s}_{8,5}{s}_{9,5}{s}_{10,2}$ | 1.4882 | |

4 | ${s}_{1,13}{s}_{2,6}{s}_{3,14}{s}_{4,4}{s}_{5,14}{s}_{6,1}{s}_{7,14}{s}_{8,5}{s}_{9,10}{s}_{10,2}$ | 1.4931 | |

5 | ${s}_{1,13}{s}_{2,6}{s}_{3,4}{s}_{4,4}{s}_{5,6}{s}_{6,1}{s}_{7,4}{s}_{8,5}{s}_{9,10}{s}_{10,13}$ | 1.5063 | |

ACO | 1 | ${s}_{1,10}{s}_{2,12}{s}_{3,4}{s}_{4,4}{s}_{5,1}{s}_{6,1}{s}_{7,15}{s}_{8,5}{s}_{9,11}{s}_{10,2}$ | 1.6588 |

2 | ${s}_{1,13}{s}_{2,3}{s}_{3,15}{s}_{4,6}{s}_{5,6}{s}_{6,12}{s}_{7,8}{s}_{8,5}{s}_{9,8}{s}_{10,2}$ | 1.6597 | |

3 | ${s}_{1,14}{s}_{2,12}{s}_{3,1}{s}_{4,4}{s}_{5,14}{s}_{6,2}{s}_{7,13}{s}_{8,5}{s}_{9,1}{s}_{10,3}$ | 1.6599 | |

4 | ${s}_{1,13}{s}_{2,6}{s}_{3,7}{s}_{4,4}{s}_{5,6}{s}_{6,1}{s}_{7,4}{s}_{8,15}{s}_{9,10}{s}_{10,2}$ | 1.6646 | |

5 | ${s}_{1,13}{s}_{2,7}{s}_{3,13}{s}_{4,7}{s}_{5,14}{s}_{6,8}{s}_{7,1}{s}_{8,15}{s}_{9,11}{s}_{10,2}$ | 1.6673 | |

PSACO | 1 | ${s}_{1,13}{s}_{2,6}{s}_{3,14}{s}_{4,4}{s}_{5,1}{s}_{6,1}{s}_{7,14}{s}_{8,5}{s}_{9,10}{s}_{10,3}$ | 1.4432 |

2 | ${s}_{1,13}{s}_{2,6}{s}_{3,14}{s}_{4,4}{s}_{5,14}{s}_{6,6}{s}_{7,14}{s}_{8,5}{s}_{9,10}{s}_{10,2}$ | 1.4454 | |

3 | $\begin{array}{cccc}{s}_{1,13}& {s}_{2,12}& {s}_{3,10}& \begin{array}{cccc}{s}_{4,4}& {s}_{5,6}& {s}_{6,1}& \begin{array}{cccc}{s}_{7,14}& {s}_{8,5}& {s}_{9,10}& {s}_{10,2}\end{array}\end{array}\end{array}$ | 1.4526 | |

4 | $\begin{array}{cccc}{s}_{1,13}& {s}_{2,3}& {s}_{3,14}& \begin{array}{cccc}{s}_{4,4}& {s}_{5,6}& {s}_{6,12}& \begin{array}{cccc}{s}_{7,4}& {s}_{8,5}& {s}_{9,10}& {s}_{10,2}\end{array}\end{array}\end{array}$ | 1.4538 | |

5 | ${s}_{1,13}{s}_{2,6}{s}_{3,10}{s}_{4,4}{s}_{5,6}{s}_{6,1}{s}_{7,14}{s}_{8,5}{s}_{9,10}{s}_{10,2}$ | 1.4558 |

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**MDPI and ACS Style**

Lu, Z.; Wang, H.
An Event-Based Supply Chain Partnership Integration Using a Hybrid Particle Swarm Optimization and Ant Colony Optimization Approach. *Appl. Sci.* **2020**, *10*, 190.
https://doi.org/10.3390/app10010190

**AMA Style**

Lu Z, Wang H.
An Event-Based Supply Chain Partnership Integration Using a Hybrid Particle Swarm Optimization and Ant Colony Optimization Approach. *Applied Sciences*. 2020; 10(1):190.
https://doi.org/10.3390/app10010190

**Chicago/Turabian Style**

Lu, Zhigang, and Hui Wang.
2020. "An Event-Based Supply Chain Partnership Integration Using a Hybrid Particle Swarm Optimization and Ant Colony Optimization Approach" *Applied Sciences* 10, no. 1: 190.
https://doi.org/10.3390/app10010190