Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties

In this work, we address the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We first propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second is Lagrangean decomposition. We present numerical results for a process network and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly.