Joint replenishment for two non-identical companies

We consider an inventory control problem of two companies facing Poisson demand with a different rate, that review their inventory continuously and replenish it by ordering different quantities. Our aim is to analytically identify conditions under which joint ordering is advantageous for both companies. Numerical experiments show that the optimal order quantities under joint ordering are lower than or equal to those under independent ordering and that joint ordering is preferred to independent ordering for two companies. In addition, we carry out a sensitivity analysis.