Storage space allocation to maximize inter-replenishment times

Given a set of storage spaces and a set of products, with specific space requirements and demand rates, we find the optimal product assignment that will lead to the longest time before any product is depleted. When demand rates are known with certainty, the assignment is found through the solution of a max–min integer program. When demand rates are stochastic with a common law, the assignment is found by solving an integer programme the objective of which is a non-homogeneous partial difference equation of first order. Unlike what common rules of thumb would dictate, our results show that the proportion of spaces assigned to a product is not necessarily equal to its demand frequency. Numerical computations show that employing the latter policy would result in inter-replenishment times that are about 24% shorter than the optimal solution.