Optimizing a bi-objective inventory model of a three-echelon supply chain using a tuned hybrid bat algorithm

•A bi-objective VMI model is developed regarding redundancy allocation problem (RAP).•A tuned hybrid bat algorithm is presented to find a near-optimum solution.•A GA is presented to solve the problem as well.

This paper presents a bi-objective VMI problem in a single manufacturer-single vendor multi-retailer (SM-SV-MR) supply chain, which a redundancy allocation problem is incorporated. In the hybridized problem, a manufacturer produces a single item using several machines that work in series, and stores it in a warehouse to replenish one vendor who delivers it to several retailers using the shortest possible route. A novel meta-heuristic, called hybrid bat algorithm (HBA), with calibrated parameters is utilized to find a near-optimum solution. To show the efficiency of HBA, the results are compared to the ones using the traditional BA and a genetic algorithm.