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A new optimal multi-product (Q, R, SS) policy with multivariate Markov stochastic demand forecasting model

Multi-product inventory control is a challenging problem. Since its complexity in computation, many prior studies simplify the modelling conditions to assume that the demands are independent. In this paper, we consider a multi-product inventory system with stochastic demands which have multivariate Markov transition characteristics. We first study the demand transition process based on multivariate Markov theory, and construct a multivariate Markov demand model to forecast the stochastic demands of multiple products. Then, we propose a new optimisation model of inventory decision for multi-product under the multivariate Markov demand transition pattern. By solving the optimal solution of the model, we propose an optimal (Q, R, SS) policy to decide the ordering quantity Q, ordering point R, and safety stock SS. At last, we use a numerical example to demonstrate the application feasibility and efficiency of the proposed method.