The vendor-managed inventory (VMI) is a common policy in supply chain management (SCM) to reduce bullwhip effects. Although different applications of VMI have been proposed in the literature, the multi-vendor multi-retailer single-warehouse (MV-MR-SW) case has not been investigated yet. This paper develops a constrained MV-MR-SW supply chain, in which both the space and the annual number of orders of the central warehouse are limited. The goal is to find the order quantities along with the number of shipments received by retailers and vendors such that the total inventory cost of the chain is minimized. Since the problem is formulated into an integer nonlinear programming model, the meta-heuristic algorithm of particle swarm optimization (PSO) is presented to find an approximate optimum solution of the problem. In the proposed PSO algorithm, a genetic algorithm (GA) with an improved operator, namely the boundary operator, is employed as a local searcher to turn it to a hybrid PSO. In addition, since no benchmark is available in the literature, the GA with the boundary operator is proposed as well to solve the problem and to verify the solution. After employing the Taguchi method to calibrate the parameters of both algorithms, their performances in solving some test problems are compared in terms of the solution quality. 
Optimizing a multi-vendor multi-retailer vendor managed inventory problem: Two tuned meta-heuristic algorithms