Performance evaluation of a multi-echelon production, transportation and distribution system: A matrix analytical approach

This study proposes an originative method to evaluate complex supply chains. A tentative multi-echelon production, transportation and distribution system with stochastic factors built-in is employed as a test bed for the proposed method. The supply subsystem formulated in this study is a two-stage production facility with constant probability of feedback and stochastic breakdowns. The transportation subsystem is a service facility with one server. The distribution subsystem under study is a single central warehouse with M retailers. All the participants of the supply chain use base-stock policies and single-server settings. We investigated both the make-to-order (MTO) and make-to-stock (MTS) policies for different base-stock levels, as adopted at different sites. Applying quasi-birth-and-death (QBD) processes as decomposed building blocks and then using the existing matrix analytical computing approach for the performance evaluation of a tandem queue constitutes the main procedure of this study. We also discuss the possibilities of extending the current model to account for other inventory control policies as well as for multi-server case. Numerical study shows our proposed analytical model is robust for practical use.