Joint location-inventory problem with differentiated service levels using critical level policy

•We design a distribution network able to provide two service levels (high and low).•We formulate the location-inventory model as an MINLP.•We obtain a good quality bound by solving a one-level service relaxation.•For the instances solved, we find solutions within 2.7% from the optimal solution.

This paper analyzes the design of a distribution network for fast-moving items able to provide differentiated service levels in terms of product availability for two demand classes (high and low priority) using a critical level policy. The model is formulated as a MINLP with chance constraints for which we propose a heuristic to solve it. Although the heuristic does not guarantee an optimal solution, our computational experiments have shown that it provides good-quality solutions that are on average 0.8% and at worst 2.7% from the optimal solution.