A vindication of centralized controls in inventory management

We study here a set of quasi-variational inequalities related to inventory/production stochastic problems. We mainly focus our attention on two subjects: (i) From a theoretical point of view, we compare the advantages of global controls versus a decentralized approach via a model of an inventory serial system wth Gaussian demand. (ii) We consider discretized systems, we solve the simple model of (i), and we apply a similar technique for solving a more complex system with Poissonian demand. The centralized approach naturally leads to large-scale problems; we solve them using a fast algorithm of resolution with very good performances. We conclude with some numerical results.