BOUNDS AND APPROXIMATIONS FOR MULTISTAGE STOCHASTIC PROGRAMS

Consider (typically large) multistage stochastic programs, which are defined on scenario trees as the basic data structure. It is well known that the computational complexity of the solution depends on the size of the tree, which itself increases typically exponentially fast with its height, i.e. the number of decision stages. For this reason approximations which … Read more

Worst-case-expectation approach to optimization under uncertainty

In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point … Read more

Time consistency of dynamic risk measures

In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. Citation Preprint Article Download View Time consistency of dynamic risk measures

Risk neutral and risk averse Stochastic Dual Dynamic Programming method

In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. Citation Article Download View Risk neutral and risk … Read more

What Multistage Stochastic Programming Can Do for Network Revenue Management

Airlines must dynamically choose how to allocate their flight capacity to incoming travel demand. Because some passengers take connecting flights, the decisions for all network flights must be made simultaneously. To simplify the decision making process, most practitioners assume demand is deterministic and equal to average demand. We propose a multistage stochastic programming approach that … Read more