Effect of a secondary market on a system with random demand and uncertain costs

In this paper, we consider inventory and pricing decisions for a system where the customer demand can be partitioned into two segments: a primary and a secondary market. These kinds of systems are observed, for instance, in technology intensive products or services where the primary market, being more loyal, is generally not too sensitive to the pricing of the product or service. While the primary market customer demand occurs right after the introduction of the product, the secondary market customer demand typically occurs after the product matures, and these customers are much more sensitive to changes in the sales price. The purchasing costs of technology intensive products very much depend on the spot currency exchange rate, and hence can be modelled as a stochastic process. Consequently, the sales price for the primary market customers can be assumed to be a mark-up of the spot purchasing cost of the product. On the other hand, as the secondary market customers are more sensitive to the sales price, a demand model, where the customer demand explicitly depends on the selling price would be more appropriate. We try to accomplish three objectives: (1) to model the described system, (2) to find the optimal initial quantity to stock, and (3) to determine the optimal sales price for the secondary market customers.