Chapter Preview
TopThe general format of a chance constrained linear MOFPP can be stated as:
Find X(x1, x2, …, xn) so as to:Maximize 
,Minimize 
,
subject to
,
(1) where
Pr indicates the probabilistically defined constraints,
A = (
aij)
m×n is a coefficient matrix and
b is a resource vector,
and
are the coefficient vectors and where α
k and β
k are constants and
p(0<
p<1) is the vector of satisficing probability levels defined for randomness of parameters associated with the constraints set. It is assumed that the feasible region
S is nonempty (
S≠φ), and where
Key Terms in this Chapter
Fractional Programming: A special field of study in the area of mathematical programming where certain objective(s) appear in the form of ratios for optimizing them in the decision environment.
Fuzzy Programming: Modeling aspects of optimization problems in which model parameters are defined imprecisely owing to inexactness of human judgments as well as inherent impressions in parameters themselves.
Chance Constrained Programming: In a programming environment, satisfying of certain probability levels as chance factors are imposed to objectives and / or system constraints for optimizing problems in a decision making context.
Fuzzy Goal Programming: It is an extension of conventional goal programming, where aspiration level of each objective is taken unity concerning achievement of the highest degree (unity) of fuzzy goals of a problem.
Goal Programming: In a certain programming environment, optimization of a set of objectives is involved there in the decision situation. Here, instead of optimizing them directly, achievement of the estimated / expected target values called aspiration levels of them are considered.
Stochastic Programming: In a certain programming environment, model parameters are random in nature and probabilities of occurrence of various events are considered there in modeling and solving problems.
Multiobjective Programming: A multiplicity of objectives is involved in a mathematical programming environment.