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A Five Phase Procedure for Implementing a Vector-Maximum Algorithm for Multiple Objective Linear Programming Problems

1976; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-642-87563-2_11

2196-9957

Ralph E. Steuer,

Multi-Criteria Decision Making

Previously developed algorithms for the vector-maximum problem can be thought of in terms of three phases. Phases I and II consist of finding an initial feasible extreme point and an initial efficient extreme point, respectively. Phase III involves finding all remaining efficient extreme points. When applying such algorithms to multiple objective linear programming problems, they have not been found to be very useful because of the large numbers of efficient extreme points generated. In an attempt to reduce the amount of efficiency information to be presented to the decision-maker and to facilitate the final selection process by which the decision-maker is to choose his extreme point of greatest utility, the research of this paper describes an expanded five phase vector-maximum procedure. Phase O is the first of the two additional phases. In Phase O the decision-maker can express partial information about his preferences in terms of interval criterion weights. The effect of this is to limit the portion of the efficient surface of the feasible region from which extreme points are to be generated. Phase IV is the second of the two additional phases. It follows Phases O, I, II, and III. It subjects the subset of efficient extreme points produced to a filtering technique in order to eliminate the most redundant extreme point solutions. By proper manipulation, neighborhoods of relatively evenly dispersed efficient extreme points of any reduced size can be obtained.