Optimal Inventory Policies under a Hierarchy of Setup Costs

This paper considers multi-product inventory problems which are subject to an order cost or setup cost hierarchy of the following form: all replenishment orders issued in any given scheduling period are filled in the next period, with the total setup cost of replenishing N different products in one period being S + s N . The values of N observed in the various periods, and therefore the expected setup cost per job, depend on the unknown lot sizes. This type of setup cost dependence can arise in simple inventory problems but is more commonly found in production environments in which the setup cost for a given job depends on the job immediately preceding it in the production schedule. Assuming demands to be random with known probability distributions, an iterative algorithm is presented for computing optimal lot sizes and reorder points for a set of heterogeneous products.