A two-level closed-loop supply chain under the constract Of vendor managed inventory with learning: a novel hybrid algorithm

Abstract

ABSTRACT This paper studies a two-level closed-loop supply chain under vendor managed inventory contract and learning effects. The proposed problem is formulated by a mixed-integer non-linear programming model. The main supposition of the proposed problem is to assume a known probability density function for the defective products rate, then the mean standard deviation utility function is used to minimize the mean cost of the system while taking the standard deviation costs. This paper deals with a multi-product model which is NP-hard and very difficult to solve. Hence, another main contribution of this work is to develop a hybrid metaheuristic with regards to three well-known and recent efficient metaheuristics. The results confirm the applicability and efficiency of the proposed hybrid algorithm in comparison with individual ones in this context and encourage the development and application of this approach more broadly.