Multi-objective decision processes under uncertainty: Applications, problem formulations and solutions

Operating in a changing and uncertain environment, firms must make strategic and operational decisions while trying to satisfy many conflicting goals. Problems of this type arise in many important decision contexts in various industries and pose challenges for both practitioners and researchers due to their complexity. This paper is a contribution to the creation of a general framework for constructing and solving proper formulations for this class of problems. We formulate a firm's decision making in the presence of uncertainty as a multi-stage decision process. Decision makers periodically review the state of the system, which includes the internal process and external environment, and choose decisions according to certain decision rules. This formulation, along with the definition of the multiple optimality criteria, such as expected profit and risk exposure, leads to a multi-objective Markov decision problem, in which one searches for decision policies that optimize multiple objectives. We investigate two major methodologies from different research streams to formulate and solve this class of problems: optimal control and stochastic programming. We show that two methodologies are equivalent in that optimal decisions found by stochastic programming are the same as the corresponding decisions prescribed by the optimal policy found by optimal control. Both solution approaches suffer from the "curse of dimensionality" but in different ways: the former has an immense state space while the latter a large sample space. We discuss and compare the complexity and efficiency of both methods. We examine approximation schemes for each to allow one to approximately solve large-scale realistic problems, which are computationally prohibitive otherwise. Finally we propose and illustrate guidelines to aid in selecting which would be the more appropriate approach for a specific problem.