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# optimization models

Models, many of them adapted from mathematics and operational research, which search for the optimal solution to a problem.

Common to these models is their definition of a quantity (in some cases quantities) to be either minimized or maximized: this is often termed the model\'s objective function. For example, the goal may be to maximize food production in an agricultural system or to minimize the total transport costs involved in an industrial location decision (see industrial location theory). Most problems will also have constraints which limit the range of solutions â€” parameters within which the solution must lie if it is to be either or both acceptable and feasible: the amount of agricultural production may be limited by fertilizer and labour availability, for example, whereas the capacity of certain transport links may constrain the industrial location decision. The optimum solution for the system as a whole may differ from the optima for individual actors â€” the solution which maximizes agricultural production throughout a system may not be the best for each individual farmer.

The methods of modelling and solving optimization problems vary substantially: a few are capable of direct mathematical, or even graphical, solution, but most involve iterative stepwise search algorithms which converge on the optimum (see linear programming). Some models assume that the system being analysed is entirely predictable, but an important group of methods (based on game theory) assumes that there is some uncertainty in the environment. In such cases, the objective function may have to be made conditional â€” for example, farm output is to be optimized in the agricultural system such that land is allocated to various uses so as to maximize the minimum output in the most unfavourable weather conditions that might occur.

The scope of such models is very wide, covering industrial location issues, agricultural location (see von ThÃ¼nen model), retail location, transport network development, transport flows (see transportation problem) and the definition of legislative districts (see districting algorithm). There are three main types: explanatory, normative-critical, and prescriptive. In a few cases it can be claimed that the model is a realistic representation of the \'real-world\' causal processes, and so the model can be used as an explanatory device for how decisions are made. More generally, however, models may be used to demonstrate the inadequacies of existing solutions â€” hence these are normative-critical. And in some applications, when the model fully represents both the system and its constraints, they can be used as prescriptive devices, to suggest what should be.Â (AMH)

##### optimum city size

Other Terms : geographical imagination | economies of scale | ghetto
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