The multistage capacity expansion of a municipal water treatment system is investigated to determine the sizes of new treatment plants and the times at which these new plants are added to the system. The capital and operating costs of these plants are given by concave functions reflecting economies of scale available with an increase in capacity. To determine the optimum sizes and installation times of the new plants, this expansion problem is formulated as a dynamic programing model.
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Hirohide Hinomoto (1972) studied this question.
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