High dimension dynamic programming model for water resources expansion projects

An optimization model for High Dimension Dynamic Programming (HDDP) was developed to determine the optimal size of water resources projects within a planning period. The model uses Objective Space Dynamic Programming (OSDP) technique to determine the size of the projects and a Mixed Integer Programming (MIP) formulation to overcome the ‘inner’ and ‘outer’ problems of OSDP and to check for the global optimality of the solution. The model is applied to determine the optimal capacity of proposed desalination plants needed to satisfy a number of demand points from different cities, during a planning period of 20 years in Egypt. The model's speed towards the optimal solution depends on the objective space bounds and search method for these bounds. The integration of OSDP and MIP is shown to be an efficient approach for solving optimization problems. Results show that the model is well suited for solving large-scale water resources expansion problems.