Explicit solution of a two-dimensional quasi-variational inequality associated to the management of a two-product inventory system

We determine the optimal policy for an impulse control problem associated to the management of a two-product inventory system, in a deterministic situation; the coupling appears only in the fixed cost. Dynamic Programming leads to the study of a Quasi-Variational Inequality (Q.V.I.) in R2. This Q.V.I. is solved exactly and an explicit formula is given for the boundary of the continuation set.