A review of two journal articles covering the applications of linear programming and public systems.
Liebman, J. (1976) “Some simple-minded observations on the role of optimization in public systems decision making” Interfaces 6(4):102-108
In his article “Some simple-minded observations on the role of optimization in public systems decision making” Jon Liebman advances the idea that the inherent differences between public and private systems operations result in the need for new approaches to applying optimization models. In contrast to the systems that had previously yielded successful optimization models, e.g. private industry and military applications, the nebulous nature of public systems causes tried and true optimization methods and results to be equally nebulous. Public systems are by nature impacted by multiple view points, conflicting or unclear objectives and unlike private systems have to incorporate both “winners and losers” in the final decision. Ultimately, Liebman borrows from (and agrees with) previous authors on the subject in describing the optimization of public systems “wicked” problems.
In spite of the “wicked” nature of problems regarding the optimization of public systems Liebman goes on to suggest a series of ideas that can help to make these problems more tractable. The majority of the suggestions focus on the process of model creation. The fact that public systems are subject to the multiple stakeholder groups suggests that there is no single model that best describes the system. Liebman goes on to argue that: 1) each group should produce its own models and 2) the models should be as concise as possible. By having each group produce its own model of the system the groups are able to convey what they consider to be the most important elements of the systems and their perception of the relationships within the system. By creating “simple” models stakeholder groups can ensure that the their ideas are easily understood by other groups and decisions makers. Ultimately Liebman states that in the public systems arena the optimization models are best served as tools to aid in the decision making process. This is a change from the historic application of optimization models as the final word in decision making. Liebman's paper argues for the creation of more models and simpler that incorporate a variety of views to help decision makers.
Heidari, M. (1982) “Application of Linear System's Theory and Linear Programming to Ground Water Management in Kansas” Water Resources Bulletin 18(6):1003
Manoutchehr Heidari applied linear programming to study the management options of a small aquifer in central Kansas. The aquifer that underlies the Pawnee Valley in Kansas is used primarily to supply water for crop irrigation and had shown significant decline in storage in the years preceding the study. Heidari used the known hydrologic characteristics of the aquifer to create a model of the ground water flow in the aquifer. Through the use of linear programming he was able to create a series of functions that were bounded by physical and “legal” constraints on well pumping. The solutions to the linear program allowed for Heidari to evaluate the the short (five year) and longer (ten year) term viability of individual well fields under various pumping constraints. The end results showed that even under the most constrained pumping regimes the aquifer was highly over appropriated and that several well fields would need to be taken off line to meet the legal allocations of the aquifer.