عنوان مقاله [English]
This research considers a tri-stage supply chain with multi vendors, multi retailers, and a warehouse entitled by vendor management inventory (VMI) to support the vendors. In the proposed model, the annual order and warehouse capacity are assumed to be limited. Also, the demand of retailers is considered as probabilistic, wherein it follows Normal probability density function. The main goal of the current paper is minimization of the total cost of supply chain, such as holding and ordering costs for retailers, vendors, and warehouse. The minimum cost is obtained by calculating the economic order quantity of the first retailer which is supplied by vendor i, and also the replenishment quantity of retailers and vendors based on the model and its constraints. First, a non-linear integer programming (NILP) is modeled, and then the mentioned model is considered with stochastic demand. The proposed models are solved by CPLEX software and analyzed by Taguchi method to determine the best demand for the abovementioned model. Finally, the method of analysis of variances (ANOVA) with significance level of is $alpha=0.05$ applied to demonstrate the independence of the mean of demands.