Dynamic programming of capacity expansion for reverse osmosis desalination plant: Sharm El Sheikh, Egypt

With a reverse osmosis (RO) desalination plant designed to satisfy only the contracted-for water supply, the water company would be missing out on potential benefits that could have been obtained selling water in periods of high demand. On the other hand, sizing the RO desalination plant to produce water to satisfy peak demand means incurring additional costs as well as having the plant partially idle during periods of average or low demand. A model was developed using Excel macros to perform dynamic programming to optimize the capacity expansion of an RO desalination plant. The objective function is to maximize the present value of the total net benefits over the lifetime of the RO desalination plant. The model can be used to test different scenarios to capture time-variant tourism demand and price uncertainties on investment decisions. This study focuses on tourism dominated arid coastal regions, using Sharm El Sheikh (Sharm) in South Sinai, Egypt, as an example.19 RO plants in Sharm were surveyed and data were collected including unit production costs, O&M costs, energy consumption rates, contracted-for water supply, and utilization. Unit production cost of an RO desalination plant varies according to the degree of operation of the plant. This fact has to be taken into consideration when calculating the costs of RO desalination and when deciding on the plant capacity in order to maximize the total net benefit. Using the collected data, cost functions were developed for O&M costs as a function of utilization and plant capacity. The cost model calculated similar values to the actual total net benefit for one of the surveyed RO plant taken as an example. Using the optimization model, the maximum total net benefit is obtained with a smaller installed capacity than the actual case. A modified pricing structure is suggested in the paper that ties the water selling price to consumption in an effort to reduce demand in excess of contracted-for water supply aiding the water company to fulfill its contractual commitments to all users. However, price elasticity has to be taken into consideration to determine the impact of price change on water demand.