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2013

Mathematical Contest in Modeling (MCM/ICM) Summary Sheet

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We devise the best water strategy for Egypt from 2013 to 2025 on the basis of the following three models.

? Model 1 (water demand prediction model) According to the trends of cultivation area, per capita GDP and population of Egypt, we predict the three variable values from 2013 to 2025. By employing BP network model, we first calculate predicted water demand value for agriculture, industry and the municipal respectively and then get total water demand in the future 13 years of Egypt. According to the prediction of model one, we find that the water demand trend of Egypt accords with Logistic growth model, and we calculate the maximum water demand is about 76.4 billion cubic meters.

? Model 2 (water allocation model) From literatures, we find the amount of current available fresh water is about 77 billion cubic meters, meaning it can meet water demand in theory as long as we allocate water resources reasonably. Using economic benefits of crops to measure total benefits from water consumption, we build an optimal model targeted at maximizing net social benefits by taking drainage system, soil salination and water transfer distance as main factors influencing crop yield and cost. By making a simulation in a small-scale area, we present an allocation scheme among four geographical areas in 2013, 2017, 2021 and 2025 respectively.

? Model 3 (Desalination model) Considering high water transfer costs caused by geographic barriers, we find that building desalination plants in Egypt is a good choice for Egypt water strategy. Basing on the principle of light radiation, we creatively put forward a concept of water transfer capacity, which represents the capacity of a desalination plant transferring water to the point with distance r. On that basis, we calculate the plant service radius under the economic theory that marginal benefit equals marginal cost. At last, by using the data of service radius and coastline length, we find that Egypt government should build 12 desalination plants during the period of 2013 to 2025.

At last, we discuss the economic, physical, and environmental implications of our strategy and believe the best water strategy should be a systematic strategy with the combination of proper water allocation, water desalination and other methods in line with Egypt real situation.

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