Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model

When a price–demand relationship is needed in inventory/pricing models, very often a convenient (typically linear) function is arbitrarily chosen. The common-wisdom implication is that any downward-sloping demand curve would lead to similar conclusions. This paper applies different demand-curve functions to a simple inventory/pricing model, and shows that while the common-wisdom implication is valid for a single-echelon system, assuming different demand-curve functions can lead to very different results in a multi-echelon system. In some situations, a very small change in the demand-curve appearance leads to very large changes in the model's optimal solutions. Other significant but counter-intuitive effects of the demand-curve form are also revealed. This paper does not completely resolve the difficulties revealed by the counter-intuitive effects reported here, but establishing the existence of these effects represents a first step towards developing procedures to handle such effects; these procedures will be necessary to ensure the reliability of many multi-echelon models for products having price-sensitive demands.