A Lagrangian relaxation algorithm and hybrid genetic algorithm-black widow optimization for perishable products supply chain with sustainable development goals consideration

In this study, a location-inventory-routing problem (LIRP) for perishable products with a many-to-many network and a heterogeneous vehicle fleet is considered. Retailer demand changed in the different time periods, and decreased as a function of the lifetime of the perishable product. A lost sale due to quality loss is considered. Taking the necessary actions to limit climate change and efficient use of natural resources are some of the Sustainable Development Goals (SDGs) in the supply chain management environment (Number 12 and 13 of SDGs). The carbon dioxide (CO₂) cap-and-trade mechanism is considered due to its significant contribution to the control of global warming. In this study, LIRP sought to minimize the fixed and variable transportation costs, inventory holding costs, facility opening costs, lost sales costs, and the amount of CO₂ emissions. A mixed integer non-linear programming (MINLP) model is proposed and validated in general algebraic modeling system (GAMS). A Lagrangian relaxation algorithm and hybrid genetic algorithm-black widow optimization (HGABWO) are considered to solve the different problems and specify the best lower and upper bounds. Our findings showed that results of the solutions obtained from the HGABWO algorithm are better than those of the genetic algorithm (GA) and black widow optimization (BWO) algorithm. On the other hand, the time to solve the large-scale problems, using the proposed algorithms compared to the GAMS is significantly reduced. Finally, the sensitivity analysis is performed for the effect of the CO₂ cap-and-trade mechanism on the problem. The sensitivity analysis results indicated that considering the CO₂ cap-and-trade mechanism in the problem could reduce the transportation costs and CO₂ emissions.