Sample average approximation for a two-echelon inventory system with service-level constraints

We propose a sample-average-approximation-based simulation optimisation approach for solving a two-echelon inventory problem containing a total cost objective function and multiple service-level constraints. Some necessary parameter settings and conditions are provided to achieve the stopping condition in practice and the convergence to the optimal solution. The approach takes into account the stochastic nature of the objective and constraint performance measures, and allows the customer demands to occur with a random size and all events to occur at random points in time (including the stochastic lead times). Experimental studies are performed to evaluate the efficiency of the developed algorithms and other existing solution approaches.