Use of mathematical models to generate alternative solutions to water resources planning problems

Chang, S.-Y., Brill, E.D., Jr., and Hopkins, L.D. (1982) Use of mathematical models to generate alternative solutions to water resources planning problems, WATER RESOURCES RESEARCH, VOL. 18, NO. 1, PP. 58-64, 1982

The author provides Modeling Generate Alternatives (MGA) techniques to reduce the weakness of optimization models, which do not usually give us a perfect solution about a complex problem in real world. The author argues that various alternatives from MGA should be also provided for decision makers to minimize the weakness. Introducing three kinds of methods to generate alternatives, the definition and characteristic of each method are informed and compared by applying an example of water resources planning problems.

1.      Hop, Skip, and Jump (HSJ)

‘The sum of the nonzero variables in the initial solution is minimized subject to a target constraint on the cost objective.’

2.      Ransom Generation Method

‘Maximizing the sum of several randomly selected decision variables and the number of variables selected can be arbitrarily specified or randomly determined.’

3.      Branch and Bound Screening

‘Obtaining feasible solutions within a certain limit of the objective function value’

From the analysis of a provided example, the result of HSJ method is binding with the cost constraint, and the random and BBS method’s result is little better about the cost. All the methods can generate many alternatives but BBS method can generate less number of alternatives comparing to the other methods.

We can also know that HSJ method tends to generate different number of plants in centralization, the random method tends to change the location of plants and interceptors in the similar number, and BBS tends to rearrange the certain system with making the other system constant.

In conclusion, the author argues that these three methods can be potential to help decision maker to be able to choose the best solution in a public sector problem. Though an optimization model can only contain one objective, MGA techniques make it possible to include multi-objective in the model.

Discussion

This article is interesting because it shows how to generate alternatives from an optimization model, which would be helpful for decision maker and can improve a role of optimization in public scale problem. It also provides examples the methods for generating the alternatives to easier understand us. However, I am unsatisfied with the lack of various examples because the article shows the characteristics and patterns of the models only from one example. Therefore, I would like to apply the methods into various problems to verify the characters of each method for generating alternatives.