Some other equations may be introduced to express other global or specific constraints (such as natural or agreed limits of some levels of activity, e.g. areas available for agriculture, or quantities of usable water, or numbers of people active in the population, etc.). As this information generally permits and infinity of solutions (because it is sub-determined, including more variables than constraints), it is also necessary to introduce a criterion for optimization.
Fig. 3: Arrangement of data types processed
Linear programming is a powerful tool, useful for helping the description of complex structures whose elements are linked by many constraints. It knew a lot of applications in agriculture and industry, to plan managementofresourcesand/ordevelopmentprocesses… At the level of regions or states, it may also be applied to the evaluation of the impacts of global policies, or of localprojects,givingalotofinformationonthechanges that any action has, directly and indirectly, on all its environment. A «scenario» is a combination of constraints and objectives which translate a given global orientation of the economic system concerned. A «solution» for such a scenario is a list of all the values of the variables, that indicates the levels of the activities, and which permits the position of all goods and services in the system to be analysed. This representation of the reality can be very complete (i.e. describe hundreds of activities, and hundreds of goods or services), rather long to realize and not very easy to use, but it can include and make consistent a lot of technical or economical informations, and give a lot of useful results under the form of very complete
evaluations of different kinds of actions, from local projects to general policies. In the field of resource management, it has the interest to allow as good as possible estimations of the amounts of resources which may be produced and consumed, in different scenarios of development, of any country of a region. These evaluations include the direct effects of described actions, which is generally easy, but they also their induced (or indirect) effects, by takinginaccountinteractions through goods and services other than directly studied resources. This approach finds in islandaspecialinterest,because most of their exchanges with their economic environment (in the sense of «the rest of the world») are generally registered, either directly in value (asimportsorexports),either through their issues in terms of transports. It is also very coherent, in this application, with the fact that autonomy versus many goods and services is «naturally» a stronger constraint in islands that in continental sites or regions. The last but not the least interest of linear programming is that it allows in depth analyses of the sensitivity of «solutions» (or optimal combinations of activities) to changes of the optimization criteria, which is not necessarily economic as in classical models, and so can express any other (or complementary) objective of policy. So it can give evaluations of the relative costs and benefits of taking in account environmentalist contraints, concerning for example air and water pollutions, and so allow some non-contingent estimations of corresponding «externalities». It is to note the development of powerful algorithms for solving large systems of different kinds of equations recently made it possible to go beyond some classical bounds of linear programming, concerning for example the respect of whole number and threshold 11 constraints on some variables, or the description of scale effects (implying fractional exponents). So new formal connections between linear programming and other (notably econometric) models are now possible, by integration of non linear equations [ANDRIES, 1997]. 267