Stockpiling under price uncertainty and storage capacity constraints

A model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period. This is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level.An important feature of the model is that the price of the commodity is described by a stochastic process. This reflects the volatility of prices of oil products. Furthermore, the model takes storage capacity constraints explicitly into account, and thus can help to assess the optimal level of storage capacity expansion.The relevant stochastic dynamic programming equations are derived and solved for the least cost function, which turns out to be piecewise linear in the inventory level. The storage capacity enters only in the computation of the constant term of the value function. The solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy: in the model, an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity.