Stochastic utility maximising dynamic programming applied to medium-term reservoir management
Thesis DisciplineManagement Science
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Medium-term reservoir management is a classic planning problem to which stochastic dynamic programming has been applied. An aspect of reservoir management modelling often neglected is 'risk', although it has been identified as being of prime importance. A utility function can imply an attitude to risk, and in this thesis, a modified stochastic dynamic programming model (SUMDP) is presented which can maximise expected utility, where utility is defined over the range of terminal storage and 'wealth' outcomes and hence is dependent on all decisions made over the planning horizon. SUMDP is applied to reservoir management in regulated and deregulated representations of the New Zealand electricity system. Experimental results showed that increasing the relative risk aversion to low terminal wealth values reduced the mean and variability of wealth and was achieved by conserving water and hence increasing storage. This effect was amplified by the contract level of the hydro firm in a deregulated case where the reservoir firm was a price setter with financial contracts and the remaining players were price takers. SUMDP can be applied to other problem classes, one of which is stochastic route choice in acyclic networks. SUMDP is discussed in this context and applied to some example problems. Rather than a single (static) route choice decision being optimal at each node of the network, SUMDP produces optimal non-static decisions which are dependent on the accumulated time taken to reach the node and take into account the utility associated with the time taken to travel the route. There are few approaches discussed in the literature which produce non-static solutions, consider uncertainty, and consider risk, so SUMDP also contributes to this literature.