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By Johannes Bisschop, Alexander Meeraus (auth.), Jean-Louis Goffin, Jean-Marc Rousseau (eds.)

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A general mathematical definition of multi-level programming is not attempted in this paper as it involves an unwieldy expression of symbols and brackets. We have chosen to give a general definition of the two-level programming problem, leaving any generalizations to the reader. Assume that there is one policy maker (or 'outer' decision maker) and one group of independent policy receivers (the 'inner' decision maker). Let x be the (n2• 1)-vector of variables controlled by the outer decision maker, while the (n~ • l)-vector y contains the decision variables of the inner decision maker.

By converting the height of the water table in each polygon to a policy instrument, structural simplifications could be made such that the entire model contains less than 8 000 constraints which is solvable using a large machine and commercial software. The above introduction has been brief and has ignored many fine modeling J. / Indus Basin Model 33 details. It also has made no mention of the extensive data gathering efforts that have taken place partially in support of the model. Despite this brevity and the lack of any mathematical equations (a detailed model statement is almost 40 pages), the reader must have gotten some impression of the size, structure and complexities that are captured by the system.

10] P. Wolfe, "A method of conjugate subgradients for minimizing non-differentiable functions", Mathematical Programming Study 3 (1975) 145-173. A. L A U G H T O N Queen Mary College, University of London, London, England Received 6 May 1980 Revised manuscript received 30 June 1981 The problem of generation planning is studied with particular reference to the modelling of forced outages of power plants in the operation submodel (that is to say, in the section of the planning model which evaluates the production costs of the system over the period of study).

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