How Quantum Particle Swarm Optimizes Cold-Chain Logistics Networks

Research Paper

Abstract

Targeting the layout and transportation problems of cold-chain logistics networks, a nonlinear mixed-integer programming model is proposed with construction and operating costs as objectives. The model incorporates maximum distance, production volume, and capacity constraints and is solved using a quantum-behaved particle swarm optimization (QPSO) algorithm. The case study yields a minimum total cost of 26.7 million yuan for one operating cycle, demonstrating the model’s applicability to other logistics networks.

1 Background

Fresh agricultural products such as vegetables, fruits, meat, and seafood require temperature-controlled transport to preserve freshness. After harvest, they must be pre-cooled within a limited time before being dispatched to distribution centers for nationwide or export delivery. Various organizational modes exist, but all face the common challenge of optimizing the cold-chain network, including the placement of pre-cooling stations, selection of distribution centers, and transportation planning.

2 Problem Description

The optimization includes two parts: determining the number and locations of pre-cooling stations based on production sites, and planning the transportation of products from production sites to pre-cooling stations and then to distribution centers, aiming to minimize total logistics cost.

3 Model Formulation

3.1 Assumptions

Construction cost of each new pre-cooling station or distribution center is assumed fixed; minimizing the number of facilities reduces total construction cost.

All harvested products are first sent to a pre-cooling station before being transported to a distribution center.

3.2 Nonlinear Mixed-Integer Programming Model

Variables and parameters include the number of production sites, candidate pre-cooling stations, distance matrix, selection matrix, distribution matrix, maximum allowable distance, transportation cost matrix, daily supply quantities, and station capacity. The objective combines construction cost and transportation cost subject to distance, supply, and capacity constraints, forming a nonlinear mixed-integer program.

4 Quantum Particle Swarm Optimization

The QPSO algorithm initializes a population of particles representing decision variables (real and integer components). Particles are divided into feasible and infeasible groups, sorted by objective value or constraint violation, and updated using quantum-behaved formulas with random perturbations. The process iterates until the best solution remains unchanged for two consecutive generations.

5 Case Study

The case considers eight major production sites in Guangdong Province and six candidate pre-cooling stations. Distance, supply, capacity, and unit transportation cost data are used to build the matrices. Assuming a construction cost of 200 tons per pre-cooling station, the QPSO solution selects three stations (I, III, V) and two distribution centers (A, B), achieving a total cost of approximately 25.7 million yuan for one year.

6 Conclusion

The QPSO-solved nonlinear mixed-integer model effectively determines optimal locations for pre-cooling stations and distribution centers and generates transportation schedules, reducing both construction and operating costs. The approach is adaptable to other logistics networks and demonstrates strong applicability for network layout and transport management problems.

Afterword

This paper is suitable for students learning mathematical modeling, especially those interested in optimization models.