The methods of solving problems of allowable power allocation (or equivalent problems of power
shortage allocation [1,2]) based on traditional principles of allocating resources [3], proportional
allocation, optimal allocation, and inverse priorities, have substantial drawbacks. In particular,
the use of the principle of proportional allocation leads to a tendency of overstating consumer
demands while ignoring the necessity of maximizing their incomes or minimizing their losses [3,4].
When applying the principle of optimal allocation, such a solution is obtained that provides a
maximum of total consumer income or a minimum of total consumer loss. However, the use of thisprinciple also leads to a tendency of overstating consumer demands. The construction of damagefunctions is complicated, and they contain considerable uncertainties [1,2]. Besides, the idea oftotal income maximization or total loss minimization is questionable because of a possibility ofunjustifiably discriminating against separate consumers in real situations [4]. The principle of
inverse priorities is artificial and forces consumers to decrease their demands. This principle as
well as other principles indicated above does not provide stimulating influences for consumers.
Finally, when allocating resources or their shortages, it is necessary to take into account diverse
consequences that cannot be reflected within the framework of traditional damage functions.
Significant improvement can be achieved in the framework of multiobjective optimization models
[1,2,4] which Mlow one to consider and optimize diverse criteria in power allocation (or power
shortage Mlocation) and to create incentives for consumers. This also relates to production, distribution,and resource allocation models which should be formulated as nonscalarized multicriteriaproblems. The same can be said about engineering mega projects design, see, e.g., [5].
The application of the multicriteria approach to resource allocation presents a new look at
problems of load management [6] and problems generated by industry deregulation and restructuring[7] with a new, and more realistic content. In particular, market participants aspire tomaximize their benefits (including economical, technological, ecological, social, and political factors).
The goals of market participants, as a rule, come in conflict, which may be resolved by a
compromise with the objective to create a mutually advantageous and harmonious solution for
the problem.
The present paper is dedicated to solving allocation problems within the framework of multiobjectiveoptimization models. The use of its results allows one to improve the validity and
efficiency in allocating power or its shortages (real or associated with the utility of load management).
The approach can serve as a methodological and computational basis for developing
load management systems. The results are also applicable to energy market problems (dispatchingstrategies, contract market management, transaction congestion management, etc. [7]), andto allocating diverse types of resources (financial, water, computational, human, etc.) on themultiobjective basis in planning and control of complex systems.
The paper is organized as follows. In Section 2, a canonical form for general resource allocation,
production, or power distribution problems is presented and transformed into a box-triangular
mathematical programming problem. Simple consistency conditions are discussed and research
objectives are listed. In Section 3, the linear case of the problem is considered and satisfaction
level functions are described that do not disturb the linearity of the original problem and are
convenient in practice especially for load management and energy market applications. Section 4
presents the transformation that allows us to express the balance set in terms of satisfaction levelparameters (functions), then model examples are considered to illustrate the procedures for computingthe balance set equations and transforming them into the satisfaction level representation.
In Section 5, the case of linearly dependent cost functions is discussed. Section 6 presents variouscriteria formulated on the balance set and corresponding goal-optimal Pareto solutions. An algorithmis described that in regular cases converges to a certain goal-optimal Pareto solution inthe state space, and conditions are presented to verify that this solution is, indeed, Pareto. An
example for power shortage allocation computed with this algorithm is presented. Conclusions
in Section 7 summarize the results of the research.
Box-triangular multiobjective linear programs are studied which serve as models for different
resource allocation, load management, and energy market problems. The balance space methodis extended onto the satisfaction level representation of the cost function space including the caseof linearly dependent cost functions. Procedures for determining the balance set and its imagein the satisfaction level representation are described and illustrated in examples.
On this basis, different goal criteria on the balance set are discussed, such as equi-importance,
preferential arrangements, minimum distance, maximin, and minimax criteria. The correspondenceis established between the maximin criterion in the satisfaction level space and the minimaxcriterion in the balance space with important consequences for iterative algorithms acting in thestate space. One such algorithm based on maximin optimization process with respect to satisfactionlevels is described and compared with the well-known Boldur's method on practical examplesof multiobjective power shortage allocation.
The results of the paper are well illustrated in order to clearly explain the procedures and
outline the methodological issues to facilitate development of computer codes for large scale
practical applications.
