Presenting a stochastic location-inventory-routing model for perishable products with shortage and shipping time

As the importance of supply chain management becomes more evident to the industry owners, the role of cooperation and integration of supply chain different components has become more vivid in creating competitive advantage. This paper proposes a comprehensive mathematical model for location-inventory-routing problem of perishable products given shortage, shipping time, and environmental considerations under uncertainty. To this purpose, an accurate solution was proposed by formulating the problem as non-linear programming of mixed integer using scenario-based stochastic approach. This approach simultaneously minimizes the sum of system costs (the cost of locating centers with certain level of capacity, operational cost of centers, transportation costs, maintaining inventory, and/or shortage of combined center of production/inspection), the sum of maximum time in the chain and emission of pollutants in the whole network. As the problem is NP-hard, a genetic algorithm approach has been proposed to solve the model. For validation, the results of the proposed algorithm in the small size examples were compared to the results of precise solution method. The obtained results revealed the capability of the proposed algorithm in reaching a solution with acceptable percentage difference and in a very shorter time compared to precise solution method. Additionally, the results from algorithm performance were investigated based on standard indicators. The computational results show the efficiency of the proposed model and solution method.