A new modified randomly iterated search and statistical competency (RISC) approach for solving a nonlinear controlling model in three-level supply chain

Abstract

This paper proposes a nonlinear controlling model in three-level supply chain. The proposed model consists of a manufacturer, a warehouse and two retailers. As nonlinear multi level programming problems are much more difficult to solve, the proposed model was converted to two nonlinear bilevel programming problems in order to make the model easier both to solve and to describe. The first model consists of warehouse's objective function at its first level and the manufacturer at the second level. In the second model, retailers are the leader and warehouse is the follower. Bilevel programming has been investigated to be NP-hard problem. Numerous algorithms have been developed so far for solving bilevel programming problem; however, algorithm proposed in this paper is easier than other algorithms for solving this type of problems. In this paper, we proposed a modified randomly iterated search and statistical competency approach in genetic algorithm to provide precise and reliable optimal solutions for manufacturer, warehouse and retailers' value in situations with no empirical observations and we presented confidence interval as solution.