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

An optimization model is generally not a perfect representation of a complex real world planning problem. Optimization models, however, can be used to generate alternatives that are good and different so that analysts and decision makers can examine a wide range of alternatives to gain insight and understanding. Modeling to generate alternatives (MGA) techniques have been designed to serve this purpose. This paper provides a preliminary assessment of the capabilities of the Hop, Skip, Jump (HSJ) method, a random method, and a branch and bound/screening (BBS) method for generating good and different alternative solutions. These three methods are illustrated using an example water resources planning problem represented by a mixed integer programing model. Each method yields sets of alternatives that are different from each other, but for each method the alternatives are different in different ways. Given that all three methods are efficient, it may be most fruitful to use more than one method and thereby to consider alternatives that are not only different, but different in different ways.