Optimal allocation of storage space

Two versions of a product are to be stored in a facility of given capacity. The (complementary) probabilities with which the two products are demanded are known. It will be demonstrated how storage space is to be allocated to make the supply (of both versions) last through a maximum number of consecutive orders by developing an algorithm for maximizing the solution of a non-homogeneous linear partial difference equation of second order with homogeneous boundary conditions. It is shown that for small storage facilities, the ratio of the optimal numbers of assigned storage spaces for the two versions can deviate considerably from the ratio of the corresponding demand probabilities. However, this ratio will approach the ratio of demand probabilities as the number of available storage spaces tends to infinity.