Abstract:
In this thesis, we consider the problem of purchasing a commodity with a uctuating market price so as to maximize its pro t from selling it over two selling season. Over the primary season, the market price evolution is described by the Geometric Brownian Motion and we describe the demand process as a Poisson Process. Moreover demand and price is independent during this season. Over the secondary selling season, demand depends on the price the rm assigns. Considering the salvage value in place of the secondary market, we develop a mathematical model and nd a closed form of solution. For the general model, we model the secondary market demand as a linear model and rst solve optimization problem of maximizing the revenue from the secondary market. Then, we combine two selling seasons and model the problem for maximizing the total expected pro t. In addition, we perform a numerical study to investigate how the optimal quantity and the optimal pro t values depend on the price process parameters. We also test the performance of the optimal policy against the policy that ignores the volatility of the price.
