Deterministic hierarchical substitution inventory models

In this paper, we consider a deterministic nested substitution problem where there are multiple products which can be substituted one for the other, if necessary, at a certain cost. We consider the case when there are n products, and product jcan substitute products j + 1,…, n at certain costs. The trade-off is the cost of storing products (for example, customised products) at a higher inventory holding stage versus the cost of transferring downwards from a lower inventory holding cost (generic product) stage. The standard approach to solving the problem yields an intractableformulation, but by reformulating the problem to determine the optimal run-out times, we are able to determine theoptimal order and substitution quantities. Numerical examples showing the effect of various system parameters on theoptimal order and substitution policy are also presented.