Advanced queueing and location-allocation strategies for sustainable food supply chain

Background: This study presents an integrated multi-product, multi-period queuing location-allocation model for a sustainable, three-level food supply chain involving farmlands, facilities, and markets. The model employs M/M/C/K queuing systems to optimize the transportation of goods, enhancing efficiency and sustainability. A mixed-integer nonlinear programming (MINLP) approach is used to identify optimal facility locations while maximizing profitability, minimizing driver waiting times, and reducing environmental impact. Methods: The grasshopper optimization algorithm (GOA), a meta-heuristic algorithm inspired by the behavior of grasshopper swarms, is utilized to solve the model on a large scale. Numerical experiments demonstrate the effectiveness of the proposed model, particularly in solving large-scale problems where traditional methods like GAMS fall short. Results: The results indicate that the proposed model, utilizing the grasshopper optimization algorithm (GOA), effectively addresses complex and large-scale food supply chain problems. Compared to GAMS, GOA achieved similar outcomes with minimal differences in key metrics such as profitability (with a gap ranging from 0.097% to 1.11%), environmental impact (0.172% to 1.83%), and waiting time (less than 0.027%). In large-scale scenarios, GOA significantly reduced processing times, ranging from 20.45 to 64.78 s. The optimization of processing facility locations within the supply chain, based on this model, led to improved balance between cost (up to $74.2 million), environmental impact (122,112 hazardous units), and waiting time (down to 11.75 h). Sensitivity analysis further demonstrated that increases in truck arrival rates and product value had a significant impact on improving supply chain performance.