This text takes a broad view of multiobjective programming, emphasizing the methods most useful for continuous problems. It reviews multiobjective programming methods in the context of public decision-making problems, developing each problem within a context that addresses practical aspects of planning issues. Topics include a review of linear programming, the formulation of the general multiobjective programming problem, classification of multiobjective programming methods, techniques for generating noninferior solutions, multiple-decision-making methods, multiobjective analysis of water resource problems, and multiobjective analysis of facility location problems. 1978 edition.
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Multiobjective Programming and Planning
By Jared L. Cohon
Dover Publications, Inc.Copyright © 2003 Jared L. Cohon
All rights reserved.
The focus of this book is the theory of multiobjective programming, a new specialization of mathematical programming, and its application to real-world public decision-making problems. We can trace the seeds of what is now a strong branch of operations research to the early work of Kuhn and Tucker (1951) and Koopmans (1951). Multiobjective programming was not really considered a separate speciality, however, until a 1972 conference in South Carolina (Cochrane and Zeleny, 1973). Multiobjective programming is indeed new, but it is a very rich field. It is an area that has attracted an enormous amount of attention [see the imposing reference lists of Cochrane and Zeleny (1973) and Zeleny (1976)] because it is so useful for real-world decision making.
Multiobjective programming and planning is concerned with decision-making problems in which there are several conflicting objectives. Such problems are ubiquitous, particularly in the public sector, which must be concerned with society's objectives. A few examples of multiobjective public decision-making problems are offered in Section 1.2. Detailed discussions of multiobjective water resource and facility location problems are presented in Chapters 9 and 10. For now it is sufficient to observe that such phrases as "tradeoff" and "conflict resolution" are now part of every public decision maker's vocabulary.
In the remainder of this chapter the value of multiobjective analysis is considered before the discussion of example problems. A brief history of multiobjective analysis is then provided and the scope of the book is defined. The chapter concludes with a plan for the remainder of the book.
1.1 VALUE OF MULTIOBJECTIVE APPROACHES
Multiobjective programming and planning represents a very useful generalization of more traditional, single-objective approaches to planning problems. The consideration of many objectives in the planning process accomplishes three major improvements in problem solving. First, multiobjective programming and planning promotes more appropriate roles for the participants in the planning and decision-making processes. Second, a wider range of alternatives is usually identified when a multiobjective methodology is employed. Third, models (if they are used) or the analyst's perception of a problem will be more realistic if many objectives are considered. Each of these aspects is discussed in more detail below.
1.1.1 Multiobjective Approaches and the Public Decision-Making Process
The public decision-making process is complex and, apparently, poorly understood. There is little agreement as to how it works: Is the process guided by a knowledge of the public interest, by selfish pursuit of personal interests, or by a haphazard intermingling of special interests? It is not the role of this book to discuss alternative models of the public decision-making process. Rather, our interest in the process is motivated by our concern with the impact of analytical techniques on that process.
For our purposes, it suffices to hypothesize two types of actor in the decision-making process: analysts (or planners) and decision makers. Analysts are technicians who provide information about a problem to decision makers who decide which course of action to take. This simple model can take on many forms, depending on the context. For example, within a federal bureau the analysts are the staff economists, engineers, systems analysts, and sociologists who develop alternatives and investigate their relative impacts on measures of effectiveness. The decision maker, in this case, may be the office director, an agency administrator, or a member of the secretary's office. It is conceivable that Congress may be the ultimate decision maker, although it is usually called on to accept or reject a previous decision.
Programming and planning techniques are tools which analysts may use to develop useful information for the decision makers. It is the contention here that traditional single-objective approaches often expand the analyst's role, resulting in a decrease in the decision maker's control of decision situations. Single-objective models require that all project effects be measurable in terms of a single unit. Project evaluation can be accomplished only by subsuming all impacts such as environmental degradation or income redistribution under a single measure of effectiveness such as net economic efficiency benefits. Thus, one-dimensional approaches place the burden of decision making squarely on the shoulders of the analyst. It is the analyst who must decide the monetary equivalent of a specific environmental impact. (If the impact is ignored, this is equivalent to placing a value of zero on environmental quality.) It may appear that this decision regarding the monetary value of a nonmonetary project impact is of minor significance since it concentrates on a so-called "design parameter." This would be a serious mistake, however, since project selection is critically sensitive to the choice of such parameters.
Multiobjective approaches pursue an important decision-making result: an explicit consideration of the relative value of project impacts. By systematically investigating project alternatives, the range of choice and the relationship between alternatives and the relative values of the objectives are identified. In this manner the responsibility of assigning relative values remains where it belongs: with the decision makers.
The multiobjective result is more desirable because analysts are not required to make important value judgments that they are not in a good position to articulate. There is a tendency for bureaucratic staff to confuse agency objectives with special objectives. One would expect, for example, that an engineer employed by a federal design agency would be under some pressure to evaluate social objectives in a manner that would promote the construction of large projects. This is easy to understand, particularly when the evaluation of objectives is done implicitly, as with single-objective approaches.
An agency administrator or departmental secretary would be subject to the same criticism and skepticism. If the decision-making process were open to public scrutiny, however, one would expect more responsiveness to social objectives on the part of these decision makers. They are in a better (more lofty) position from which socially consistent value judgments can be made. The pressures to which these decision makers may be subjected are from more scattered origins.
Regardless of the actual nature of the public decision-making process, multiobjective approaches can be useful in promoting the explicit consideration of the value judgments which are implicitly made in the application of single-objectives approaches. In addition, multiobjective methods allow decision makers and analysts to maintain appropriate roles in the process. The analyst is in the position of generating alternatives and tradeoffs among objectives. Important value judgments regarding the relative significance of the objectives are made by the decision makers.
1.1.2 Multiobjective Approaches and the Generation of Alternatives
Most project and program design and planning problems are characterized by a large (frequently infinite) number of alternatives. Single-objective methods are predicated on a unique measure of effectiveness, so that they lead to the unambiguous identification of an optimal alternative. Decision makers will therefore be in the position of accepting or rejecting this single alternative identified as the best.
Multiobjective methods are used to generate and evaluate more than a single alternative. The number of alternatives that are ultimately presented to decision makers varies from one multiobjective programming technique to another. It is generally true, however, that multiobjective approaches will indicate to decision makers a range of choice larger than the one "optimal" project identified by single-objective methods. This larger range of choice is due to the articulation of value judgments regarding the objectives by decision makers in the project selection phase rather than during analysis.
This aspect of multiobjective programming and planning is perceived as an advantage. A general rule for decision making which is assumed here is that more information (carefully presented) is better than less information. The decision to accept or reject a single optimal alternative is an uninformed decision. Informed, rational decision making requires a knowledge of the full range of possibilities. This can be provided by multiobjective analysis.
1.1.3 Multiobjective Approaches and Analytical Reality
Perhaps the strongest support for the use of multiobjective methods comes from reality: Real-world problems are multiobjective. Public action generally impacts many different groups and social concerns. The imposition of a single-objective approach on such problems is overly restrictive and unrealistic. Multiobjective analysis allows several noncommensurable effects to be treated without artificially combining them. This is clearly a significant improvement in analytical capability.
1.2 EXAMPLES OF MULTIOBJECTIVE PROBLEMS
Multiobjective programming and planning is applicable to a wide range of problems in both the private and public sectors. Each of our lives is filled with daily multiobjective problems, decision situations with noncommensurable objectives. Should I take the car or the bus? Well, the bus is cheaper (when the cost of gasoline, maintenance, and insurance are computed for the car), but the car is more convenient, particularly since I should stop at the store on my way home from work. The bus will save energy, but I can listen to the radio in the car. There are probably other attributes or objectives in addition to cost, convenience, energy consumption, and comfort that might be considered in choosing between the car and the bus. The point is that there is no single measure of what is best, like dollars. Instead, there are several measures or objectives of importance and making a decision requires the decision maker (the author, in this case) to articulate value judgments, at least implicitly, on the relative importance of the objectives. Problems like this abound.
Our interest is in the public sector where multiobjective problems are the rule rather than the exception, due primarily to the multiplicity of interests that are embodied by social welfare or the so-called public interest. In the remainder of this section a few public sector problems are mentioned. The goal here is to tempt you, to excite your imagination, to give you a sense of the richness of multiobjective analyses in the public sector so that you may have the will to wade through some of the heavier going in later chapters.
In an attempt to span the range of public sector problems, we will talk about three types: public investment, regulation and control of economic activity, and programs and policy. These arbitrary categories were invented for this section only; they were chosen for convenience.
1.2.1 Public Investment Problems
Public investment is the problem area which has attracted the attention of most multiobjective analysts. It was in this area, in the context of water resource planning, that Marglin (1962, 1967) and Major (1969) pioneered the development of multiobjective analysis. Most of the practical applications have also been accomplished for public investment decision making—primarily for water resource systems (Miller and Byers, 1973; Cohon and Marks, 1973; Major, 1974; Haimes, 1977) and in transportation (Hill, 1973; Keeney, 1973b). Multiobjective analyses of water resource problems are considered in detail in Chapter 9.
In his evaluation of urban transportation plans, Hill (1973, pp. 69–77) presents a list of 14 objectives. Some of these are the reduction of air pollution, noise, and accidents; the increase of accessibility; fiscal efficiency; and the attainment of a more equitable income distribution. These six objectives conflict and there is no obvious method for collapsing all of them into a single monetary measure. For example, the most direct route for an urban highway will usually maximize accessibility (measured as time of travel) and fiscal efficiency, but give high levels of air pollution and noise impacts. A circuitous route, on the other hand, will lessen air pollution and noise impacts but cost more and require longer travel times.
Which route is better when there are conflicting objectives? One cannot say which route is better without making value judgments about the relative importance of the objectives. Given that the various participants in the decision-making process will usually evaluate the relative importance of the objectives differently, the resolution of the conflicts among objectives will usually require a political process. It would be a mistake for the planner to select only one of these objectives, such as efficiency, or to assume relative values for the objectives. This would preempt the political process and most certainly lead to later impasses in the planning process. Manheim (1974) makes a very strong case for participatory transportation planning for just these reasons.
The location of public facilities represents another area of public investment to which multiobjective planning is applicable. In addition to an investment decision, a governmental entity must also decide on the location for the activity. Such problems present spatial conflicts among the areas served or impacted by the facility. For example, in locating a fire station, should the station be sited near the central business district, which is characterized by high property value and low (nighttime) population, or should it be located near a low-value densely populated area? Again, the resolution of this conflict is the focus of multiobjective planning. Examples of multiobjective facility location problems are presented in Chapter 10.
1.2.2 Regulation and Control of Economic Activity
Recent work has applied multiobjective analysis to the public regulation and control of private economic activities. Perhaps the classic case of government intervention into the private sector is the abatement of water pollution. It is the perceived role of government in water quality control to develop regulations and programs that will induce private interests to treat, or otherwise withhold, their wastes. There is, of course, a public investment aspect to this problem as well, as evidenced by the federal contribution to municipal sewage treatment plants (see Water Pollution Control Act Amendments of 1972, Public Law 92-500). Public investment, however, represents only one of the several tools available to the government in the control of water pollution.
Brill et al. (1976) considered the development of an effluent charge program for the Delaware River Basin. An effluent charge is a tax levied on a polluter's wastes that are discharged into a stream. The tax is intended to induce the polluter to withhold or treat the wastes, thereby avoiding the charge. Brill and his colleagues considered the objectives of economic efficiency and equity. That is, one can develop a charge program that will minimize total costs but the differences in charges from one polluter to the next may be very different; alternatively, a charge scheme which promotes equality of charges results in higher total costs. Once again, the resolution of the conflicting objectives is a political problem that does not permit the planner to identify a single optimal solution.
The current United States law covering water pollution (Public Law 92-500 cited above) exhibits a multiobjective nature. The part of the law dealing with attainment of the 1983 goal of "fishable and swimmable" waters requires dischargers to implement the best available treatment technology (BAT) that is "economically achievable." It is the responsibility of the U.S. Environmental Protection Agency (EPA) to interpret what BAT means in each case. To do this, the EPA must weigh the environmental benefits of a given technology, i.e., the improvement in several measures of water quality, against the cost of implementing the technology. This is a multiobjective problem since the environmental benefits defy reliable quantification in monetary units.
Many other regulatory problems are inherently multiobjective. Other areas of pollution control such as air quality and solid-waste management present conflicts similar to those just discussed: environmental gains versus cost; efficiency versus equity. The National Environmental Policy Act (U.S. Code, Volume 42, Section 4321, 1970) requires the preparation of an environmental impact statement (EIS) for virtually every construction project that uses federal funds, regardless of the project's purposes. The implication of an EIS is that environmental concerns are ultimately brought into play in the final decisions on the project.
Land-use planning is another rich regulatory context for multiobjective analyses and there have been many examples presented in the literature. Vedder (1970) considered approaches to multiobjective planning problems generally. Stuart (1970) used multiobjective analysis to evaluate the effectiveness of the U.S. Department of Housing and Urban Development's Model Cities program. Orne and Wallace (1974) analyzed the conflicts among objectives in new-town developments. Schinnar (1976) used multiobjective analysis for the evaluation of development in an economic demographic framework. Werczberger (1976) analyzed industrial locations when air pollution and economic considerations conflict. Bammi et al. (1976) and Barber (1976) analyzed community development in the face of conflicts among environmental impacts, land-use incompatibilities, accessibility of facilities, and energy consumption.
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Table of ContentsPreface
2. The Multiobjective Planning Problem
3. Review of Linear Programming
4. Formulation of the General Multiobjective Programming Problem
5. Classification of Multiobjective Programming Methods
6. Techniques for Generating Noninferior Solutions
7. Solution Techniques That Incorporate Preferences
8. Multiple-Decision-Making Methods
9. Multiobjective Analysis of Water Resource Problems
10. Multiobjective Analysis of Facility Location Problems
11. Summary and Prospects for Future Development