Optimization of European call options considering physical delivery network and reservoir operation rules

This paper develops alternative strategies for European call options for water purchase under hydrological uncertainties that can be used by water resources managers for decision making. Each alternative strategy maximizes its own objective over a selected sequence of future hydrology that is characterized by exceedance probability. Water trade provides flexibility and enhances water distribution system reliability. However, water trade between two parties in a regional water distribution system involves many issues, such as delivery network, reservoir operation rules, storage space, demand, water availability, uncertainty, and any existing contracts. An option is a security giving the right to buy or sell an asset; in our case, the asset is water. We extend a flow path‐based water distribution model to include reservoir operation rules. The model simultaneously considers both the physical distribution network as well as the relationships between water sellers and buyers. We first test the model extension. Then we apply the proposed optimization model for European call options to the Tainan water distribution system in southern Taiwan. The formulation lends itself to a mixed integer linear programming model. We use the weighing method to formulate a composite function for a multiobjective problem. The proposed methodology provides water resources managers with an overall picture of water trade strategies and the consequence of each strategy. The results from the case study indicate that the strategy associated with a streamflow exceedence probability of 50% or smaller should be adopted as the reference strategy for the Tainan water distribution system.