A risk-based green location-inventory-routing problem for hazardous materials: NSGA II, MOSA, and multi-objective black widow optimization

The increasing importance and growth of the transportation of the industrial/nonindustrial hazardous materials and wastes in recent decades have been brought to the attention of the governments. Not paying attention to this issue has the different consequences, including the socially destructive effects leading to transportation incidents, storage and disposal of such materials and the risk of harm to the humans. On the other hand, due to the direct association of these materials with the industry, the supply chain members need to pay attention to this issue which can play a very important role in the economic development of the country. Special attention should be paid to negative environmental impacts from the greenhouse gas emissions due to the widespread transportation of these materials in the supply chain network as well as the disposal of industrial waste in the environment. The importance of the research problem in the social, economic and environmental fields have resulted in developing a mathematical model of a location-inventory-routing problem (LIRP) for hazardous materials and waste management at two levels of the supply chain with considering a heterogeneous vehicle fleet seeking to mitigate the supply chain risk, minimize the supply chain costs and reduce greenhouse gas emissions. Given that the proposed model is NP-hard, a meta-heuristic algorithm to solve the multi-objective optimization problems called multi-objective black widow optimization (MOBWO) algorithm is presented. The performance of the proposed meta-heuristic algorithm has been compared with multi-objective smulated annealing algorithm (MOSA) and non-dominated sorting genetic algorithm II (NSGA II). A new Minkowski-based approach is presented to choose a single solution from a set of non-dominated solutions of the first front as the final optimal solution for the proposed problem. The results of the present study demonstrated that the NSGA II algorithm in small- and medium-scale test problems gives better accuracy, but the MOBWO has better performance in the large-scale test problems in comparison with the other two algorithms.