Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

• This paper studies a three-level supply chain network.
• In order to make the problem more realistic, we consider uncertain demand and leadtime.
• A queueing approach is used to obtain some performance measures of the system in the steady-state.
• We propose a mixed integer nonlinear programming model (MINLP) for presented problem.

This paper studies a three-level supply chain network, which includes a single supplier, multiple potential distribution centers (DCs) and multiple retailers. The problem is to optimize the facility location, allocation retailers’ demands, and inventory replenishment decisions simultaneously such that the total expected cost of location, transportation and inventory are minimized. In order to make the problem more realistic, we consider uncertain demand and lead-time, which follow Poisson and Exponential distributions, respectively. Hence, a queueing approach is used to obtain the amount of annual ordering, purchase and shortage as well as the mean inventory in the steady-state condition. Then, according to the results of queuing analysis, we propose a mixed integer nonlinear programming model (MINLP) to address the location-inventory problem. Moreover, the expected mean inventory is calculated using two different methods and the results are also compared through different criteria.