Module OptiEco, economic optimum allocation of water

DSS H2O

Modules

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1 -  First one must carry out the conceptual scheme of the basin to model (Figure 1). This scheme is built adding one to one the elements (contributions, reservoirs, uses, conductions, aquifer, etc.) and introducing its characteristics, using for it the Decision Support System H2O.

This scheme is a simplified representation of the basin or Water Resources Systems (WRS) to study, that must preserve the most important relationships among the elements of the system.

Figure 1: scheme of one simple basin.

Figure 2: scheme of WRS and y fe of the uses.

2 -  In second place one must obtain the economic functions (fe) of the elements that have associates costs or benefits.  These fe contains information about the use cost, or of the willing to pay of the elements. This unitary cost/profit will vary in function of the assigned or circulating volume.

In the case of the uses, the fe is (in principle) coincident with the demand curve of water. In the Figure 2 you can see another scheme, with the fe (or demand curve in this case) of the two existent uses in this system.

The obtaining of the fe is a relatively complex task, many times artistic task, that it requires the realization of local economic studies and the summary of data that in few places are obtained in a systematic way.

3 -  Later, is possible to run the OptiEco model. The economics functions (fe) of all the elements they are used jointly to maximize a function objective (FO) no-linear that represents the net profit of the whole system (Equation 1):

The contribution of each element to the FO is the area under the fe from zero until the supply value x' (Figure 3). The group of values x' (assigned flows) of all the elements of the WRS are the incognito of the optimization problem.

Figure 3: fe and contribution to the FO for one element.

4 -  Concluded the execution of the program, the output files text with the optimum values of the variables and the marginal indicators associated to the restrictions can be seen (and chart) with the DSS H2O or import with Excel or another similar program.

A particularly useful indicator is the marginal value of the water in the different points of the basin. This value is the opportunity cost of the resource (water) in that place, or cost of shortage of the water, and it indicates the minimum willing to pay of the users to reduce that shortage.