The problem of production-distribution under uncertainty based on Vendor Managed Inventory

In this paper, a problem of managed inventory by the vendor in the production-distribution supply chain is presented based on the scenario. The main purpose of presenting the model of maximizing producer profit in a three-level supply chain network consisting of various strategic and tactical decisions under uncertainty. Due to the nonlinearity and NP-Hardness of the problem, meta-heuristic genetic algorithms, Whale optimization algorithm and league champions algorithm have been used. The results of problem solving show the high efficiency of meta-heuristic algorithms compared to accurate methods in solving the above model. So that the maximum percentage of relative differences between the methods mentioned with GAMS is less than 1%.Also, by solving the sample problems in larger sizes, it was observed that the league champions algorithm has the highest efficiency in terms of achieving the optimal value of the target function in a shorter time than the other algorithms used, with a useful weight of 0.998.