Vendor-managed inventory in the joint replenishment problem of a multi-product single-supplier multiple-retailer supply chain A teacher-learner-based optimization algorithm

Purpose - in this paper, the joint replenishment problem is modeled fora two-level supply chain consisting of a single supplier and multiple retailers that use the vendor-managed inventory (VMI) policy for several products. This paper aims to find the optimal number of products to order in both policies, the optimal times at which each retailer orders the products in the traditional policy and the optimal times at which the supplier orders the product in the VMI policy. Design/methodology/approach - The problem is first formulated into the framework of a constrained integer nonlinear programming model; then, the problem is solved using a teacher-learner based optimization algorithm. As there are no benchmarks available in the literature, a genetic algorithm is used as well to validate the results obtained. Findings - The solutions obtained using both the algorithms for several numerical examples are compared to the ones of a random starch procedure for further validation. A real case is solved at the end to demonstrate the applicability of the proposed methodology and to compare both the policies. Research limitations/implications - The paper does not have any special limitations. Practical implications - The study has significant practical implications for the sellers and for the suppliers who have to get the most profit. Also, satisfying the constraints make decision more complicated. Originality/value - This paper has two main originalities. The authors have developed the model of the joint replenishment problem and have contributed in the problem-solving process. They have used a new meta-heuristic and then compared it to a classic one.