Applying queuing theory for a reliable integrated location inventory problem under facility disruption risks

This study considers a reliable location – inventory problem for a supply chain system comprising one supplier, multiple distribution centers (DCs), and multiple retailers in which we determine DCs location, inventory replenishment decisions and assignment retailers to DCs, simultaneously. Each DC is managed through a continuous review (S, Q) inventory policy. For tackling real world conditions, we consider the risk of probabilistic distribution center disruptions, and also uncertain demand and lead times, which follow Poisson and Exponential distributions, respectively. A new mathematical formulation is proposed and we model the proposed problem in two steps, in the first step, a queuing system is applied to calculate mean inventory and mean reorder rate of steady-state condition for each DC. Next, regarding the results obtained from the first step, we formulate a mixed integer nonlinear programming model which minimizes the total expected cost of inventory, location and transportation and can be solved efficiently by means of LINGO software. Finally, several test problems and sensitivity analysis of key parameters are conducted in order to illustrate the effectiveness of the proposed model.