A sample average approximation approach for a green closed-loop supply chain for water supply

Now, attention to drought, design of water and wastewater system network is very important, Avoiding high costs and environmental impacts in water supply chain is important. In this paper, leads to using the two-stage stochastic multi-objective optimization model for the water supply chain. In the following, the sample average approximation approach is used for the provided multi-objective problem. Also, a combined method with a sample averages approximation with compromise programming method. Using this combination method, we determine the appropriate size of scenarios. Finally, considering three problems, we will examine the results.

Keywords:

sample average approximation , multi-objective optimization model , Stochastic programming model , Compromise programming , water supply