Performance evaluation of a merge supply system with a distribution centre, two reliable suppliers, one buffer and Erlang lead times

In this work a two echelon merge supply chain is examined. Specifically, two non identical reliable suppliers feed a distribution centre with a shared buffer. The first echelon consists of the distribution centre and the shared buffer, the second echelon includes two non identical reliable suppliers. There is an unlimited supply of materials to suppliers and an unlimited capacity shipping area after the distribution centre. In other words, suppliers are never starved, and the distribution centre is never blocked. The materials are processed by suppliers with rates following the Erlang distribution. The distribution centre has a reliable machine that pushes material with service times following the Erlang distribution. Blocking appears when one or more suppliers finish their process and try to feed the buffer that is full. The supply network is modelled as a continuous time Markov process with discrete states. The structures of the transition matrices of those systems are explored and a computational algorithm is developed. Our aim is to generate stationary distributions for different values of system's parameters so as the various measures of the system can be estimated. Finally, for the mathematical programming model and the rest of the calculations the Matlab software is used.