Optimal policies of stage construction for transportation facilities under uncertainty

In this paper we present a method for finding optimal policies of stage construction for transportation facilities under uncertainty. Under policies of stage construction, the transportation facility is brought to its ultimate standard in stages, and is improved at each stage. The main feature which distinguishes the analysis for the case where certainty exists from the case where uncertainty prevails is the following. Under certainty, the decision maker may decide in advance (i.e. at the origin) the optimal periods at which the transportation facility should be upgraded. He will not subsequently change his decision. However, when uncertainty prevails, the decision maker should not commit himself at the origin to upgrade the transportation facility at any specific time in the future. Thus, at any period of time the decision maker will review the relevant information. Based on this information, he will decide whether to upgrade the transportation facility, or further postpone this decision. We show how the optimal upgrading policy may be obtained, and how changes in uncertainty affect the optimal policy. We use, then, the model to find under uncertainty the optimal stage construction policy for an existing road. We compare our solution to the one obtained under certainty.