A multi-objective mathematical model for virtual water allocation in the food industry of Khuzestan province using meta-heuristic algorithms

The purpose of this research is to optimize the use of water resources in dams in Khuzestan province. For this purpose, in this research, we seek to optimize the cost and time of sending water to each of the cities from the total dams in Khuzestan province. The model is solved using the deterministic epsilon constraint method and NSGA-II and MOPSO algorithms meta-heuristically. According to the results presented in this research, the water supply from the Balaroud dam to the cities of Ahvaz, Izeh, Abadan, Baghmolk, and Bandar Imam Khomeini has not been determined to be optimal. The same dam sends a certain amount of water to the cities of Andimeshk, Dezful, Shush, Shushtar and Gotvand. The results showed that NSGA-II has a more acceptable performance than the MOPSO algorithm from the point of view of three criteria, and the MOPSO algorithm has a better condition than the NSGA-II algorithm only in terms of the distance to the ideal point. In addition, according to the sensitivity analysis, it has been determined that the increase in water demand can increase the shipping time by 1.9% and the shipping cost by 60%. Therefore, the effect of water demand is more on time and not on cost. Increasing the budget can have an effect on cost and time, which of course has more effect on time than cost.