On Some Optimal Control Problems Arising from Project Management

The complexity of modern industrial and governmental enterprises with the consequent increase in the quantity and sophistication of managerial decisions, on the one hand, and the fact that the payoffs from good decisions are greater than ever before, on the other hand, offer a challenge to build up conforming scientific methods for decision making. The systems programmed approach or the programmed control method is a practical method to manage large and complex systems. In general it is a feed-back decision-making process which implies many time planning processes and consists of such elements as forecasting, formulation of goals and objectives, collection of available alternative strategies to achieve the goals, selection of the best alternative, realization of the strategy, comparison of the results with predicted outcome, new forecasting, reformulation of goals and so on. Thus the process includes both formal (strict) and informal (heuristic) procedures. To find the application and to emphasize the necessity for using rigorous mathematical methods in the decision-making process in the economic systems, we shall briefly describe some decision-making elements and the corresponding mathematical models

Computer Assisted Procedures in Water Project Evaluation

The paper describes a methodology which can be used in solving water economy capital investment problems. These problems concern water economy expansion to meet an increasing demand for municipal, industrial, and other uses within given resource limitations. A water economy is considered as an individiual branch of a region. Its connections and interactions with other branches of that region (industry, agriculture, etc.) are taken into account. We presumed that the interaction of the regional management (Center) and the branch manager takes place within the framework of a centralized hierarchical system. The Center distributes the resources (money, manpower, etc.) among the managers of separate branches. The information a manager receives may be represented by the vector function of resources C(t) during the planning period [t_o,T]. The output information is considered as a scalar function I(t), which characterizes the loss to the branch if it is not sufficiently supplied with hydrotechnical structures. The process of decision-making consists of three phases. The first phase is formulating all feasible alternatives for the development of a given regional water management system. The second phase is calculating all versions of the development program for the branch. The third phase is estimating the loss which the branch may incur with a given program of branch development. The latter two phases are provided with appropriate mathematical models and numerical algorithms. This system of models differs from all known capital investment models in water economy in that it incorporates the process of building hydrotechnical structures over a planning horizon

Water Economy Program Evaluation with Respect to Total Losses Expected

Given the management goal of minimizing the total losses that occur within the existing construction and design of a water economy system, particular problem of water economy development is stated and solved numerically. The paper is a continuation of a study in complex water economy planning (RR-75-27). As before, it is assumed that the planning process is consistent with the following procedures: formulation of all development alternatives considered, calculation of all alternative development programs, and water economy damage estimation for each alternative development program. The problem of total loss minimization is a particular case of a general problem statement. It allows one to reduce the latter two planning procedures to a single one and solve it effectively. With this approach it is possible to simultaneously obtain solutions to both short-term control and long-term development strategy for a given water economy system

Gaming Model to Study the Problem of Sharing Natural Resources

The problems of sharing natural resources (SNR) are constantly growing in their practical importance. The pattern of the distribution of natural resources is highly irregular and the price for natural resource extraction is high. Moreover, due to intensive exploitation, some resources are becoming scarce and others are approaching exhaustion. These problems affect the pattern of resource exploitation in different parts of the world and eventually the strategies for national development. Thus there is stress upon the necessity for defining reasonable proportions of development with due regard for the trade-offs between restricted natural resources and the requirements for growth over time. One approach to dealing with the SNR problem is based on the direct involvement of men in a model. This enriches the properties of a model considerably and moves it closer to reality. Such an approach to the solution of complex problems is known as gaming or interactive simulation and has been under development for some time. Existing experience with gaming simulation shows its high potentiality as an instrument for studying development strategies in systems with multiple conflicting goals

Energy Resources: Economy Development Models

This paper is an attempt to extend methodological research of complex systems development at IIASA. The most typical and probably most urgent example is analysis and planning of long-range development of energy systems. During the last decade interest in energy problems has considerably increased all over the world and we are now witnesses of significant progress in the field. This concerns however mostly the particular implementation of different energy models. As for methodological mathematical analysis of the problem we deal here, at initial stages, with inevitable lags, though first attempts have already been made in this direction. Meanwhile, in analyzing outputs of energy models implemented in different ways, many methodological problems are arising: for example, how to link energy supply, resources and economy models into a whole system? what is the world ("global") energy model: is that game-theoretical, optimization or simulation? how does our uncertainty in the "future" input data influence our "certainty" of present decisions? etc. These questions do not only relate to energy models but are also of concern for any problems of long-range development of a complex system (for example, analysis of interaction of manpower-economy development in the long run. IIASA seems to be an unique place for stimulating such kind of methodological work. Different approaches, different opinions, different models, which are under permanent discussion or investigation at IIASA -- all of this eventually and inevitably becomes a point of view, a starting point of any methodology. This paper, as mentioned above, should be considered as an initial attempt in this direction

Dynamic Linear Programming Models of Energy, Resource, and Economic-Development Systems

This report develops a unified dynamic linear programming approach to studying long-range development alternatives in the energy sector. With the demand for energy and the supply of nonenergy resources needed to develop the energy supply system given exogenously, the report first seeks the optimal mix, phased over time, of different energy technologies. Next it considers the problem of finding, for primary energy resources, the optimal mix over time of different exploration and extraction technologies. The third part of the report uses an optimization version of a dynamic input-output model to study the macroeconomic impacts of the energy sector. Finally, the report discusses the interactions among these models, presents a general dynamic linear programming framework, and takes up some related methodological issues

An Interactive System for Experimenting with Development Planning

An interactive system which is directed to serve as an instrument for resolving development planning problems is presented. Manuals for programmers and players and a few numerical examples are attached

INTERLINK, An Interindustrial Model for Simulating a Balanced Regional Economic Development and its Links to IIASA's Set of Energy Models

The INTERLINK model is a dynamic linear model simulating development of a national or regional economy as a whole. The objective of the model is to provide projections of the potential long-term economic development of a region or a nation under various assumptions on the present and the potential future structures of the overall system. The model allows one to evaluate the potential economic growth of a region or a nation within and after the transition period (.i.e., the change from the use of conventional to nonconventional energy sources), to describe the internally consistent operation of several production sectors, to provide information required for energy demand projections, and to identify limiting factors in the development of regional economies. The model is a dynamic input-output Leontief system with a set of variables, such as GNP, export, import, employment, investment, and final consumption, given both as totals and by sectors. Structural parameters, such as technological and capital coefficients, final consumption profile vectors, and labor-output ratios, are exogenously changeable over time. The model can be used both as an optimization model, with various assumptions on the objectives of a given nation or region in the transition period, and as a simulation model, with assumed growth rates for various production sectors and final consumption. As a result, the model provides estimates of GNP, final consumption, and investment changing over time, for a regional energy system development strategy under consideration