A novel branch and bound algorithm for optimal development of gas fields under uncertainty in reserves

We consider the problem of optimal investment and operational planning for development of gas fields under uncertainty in gas reserves. Assuming uncertainties in the size and initial deliverabilities of the gas fields, the problem has been formulated as a multistage stochastic program by Goel and Grossmann (2004). In this paper, we present a set of theoretical properties satisfied by any feasible solution of this model. We also present a Lagrangean duality based branch and bound algorithm that is guaranteed to give the optimal solution of this model. It is shown that the properties presented here achieve significant reduction in the size of the model. In addition, the proposed algorithm generates significantly superior solutions than the deterministic approach and the heuristic proposed by Goel and Grossmann (2004). The optimality gaps are also much tighter.