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    Water allocation problem using Dynamic Programming

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    Please solve the attached problem using Dynamic Programming method.

    Consider water supply for a region consisting of three cities. The total available water supply is 8 units. Determine the optimal allocation of water to the three cities that maximizes the total economic return for the region. The relationship between the economic return and the quantity of water allocated for each city are given in the following table:

    City
    1 2 3
    q r1(q) r2(q) r3(q)
    0 0 0 0
    1 6 5 7
    2 12 14 30
    3 35 40 42
    4 75 55 50
    5 85 65 60
    6 91 70 70
    7 96 75 72
    8 100 80 75

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    Hello,

    Please find attached Dynamic Programming solution help for the water allocation problem. Detailed computations are provided along with the formula.
    Hope this helps you. Feel free to contact for any further help required.

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    Consider water supply for a region consisting of three cities. The total available water supply is 8 units. Determine the optimal allocation of water to the three cities that maximizes the total economic return for the region. The relationship between the economic return and the quantity of water allocated for each city are given in the following table:

    City
    1 2 3
    q r1(q) r2(q) r3(q)
    0 0 0 0
    1 6 5 7
    2 12 14 30
    3 35 40 42
    4 75 55 50
    5 85 65 60
    6 91 70 70
    7 96 75 72
    8 100 80 75

    Decision variables: Let Xn be the number of water units allocated to stage i.e. City n
    Let Sn be the number of water units available to be allocated to the remaining cities (n,....,3)
    At stage 1 in which the 3 cities are under consideration ...

    Solution Summary

    The solution provides step by step help on how to solve water allocation problem using Dynamic Programming approach

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