A continuous review inventory model with complex correlations among components

Under a flexible mass-production system, a manufacturer may need to provide highly customized products to meet customer satisfaction. It is likely that components in a customized product are correlated in such a way that the demands of some components depend on those of others. In order to cope with dependence in the demands, we proposed a continuous review multi-item inventory (Q, r) model that included a general form of correlation and dependence in demands among components. We represented the proposed model by using a probabilistic graphical model under the assumption that the demands of all components and their correlations were represented by a multivariate Gaussian probability distribution. By taking an advantage of a directed acyclic graph and its topological order, we demonstrated that the correlated demands among components in the proposed model could be solved without any approximation and assumption. As an illustration of the proposed method, we solved an inventory (Q, r) model of eight correlated components and discussed the experimental results in terms of correlation and dependence in demand.