Integrated supply chain management via randomized rounding

We consider the supply chain problem of minimizing ordering, distribution and inventory holding costs of a supply chain formed by a set of warehouses and retailers over a finite time horizon, that we call Production and Distribution Problem (PDP). This is a common generalization of the classical Metric Facility Location Problem and Joint Replenishment Problem, that coordinates the network design and inventory management decisions in an integrated manner. This coordination can represent significant economy for many applications, where network design and operational costs are normally considered separately. This problem is considered when the instances satisfy assumptions such as metric space of warehouse and retailer locations, and monotonic increasing inventory holding costs. In this work, we give a 2.77-approximation based on the randomized rounding of the natural mixed integer programming relaxation. Also, we give a 5-approximation for the case that objective function includes retailer ordering costs