Dynamic optimization of input production factors for urban industrial water supply and demand management

To help minimize urban industrial water consumption and realize the goal of a water-saving society, this paper develops a method for the dynamic optimization of the input production factors in an urban industrial water supply model. A negative exponential curve describes the urban industrial water consumption per Yuan of urban industrial value added, the latter being described by a Gompertz curve. The product of the two describes the urban industrial water demand. The production function of urban industrial water supply is expressed by the fixed substitution proportional production function. Taking investment and labor input as control variables, the system goal is to balance of industrial water supply and demand. The time-varying model can not only solve the stable state problem for infinite time horizon, but also the transient problem for finite time horizon. Taking Jiangsu province in eastern China as an example, the applicability of the method was investigated under different parameter combinations. The simulation results show its effectiveness in these cases. In the earlier period, meeting balance requirements is easier using the straight-line capital depreciation method. In the later period, the fixed rate on declining balance method allows to meet the requirements more easily. In general, it is easier to achieve the goal by choosing a smaller and feasible weight matrix coefficient of the control variables.