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Many authors have made contributions in the development of duality theory for multiple objective programming problems.
Its methodological procedure can easily be incorporated into multiple objective programming formulations with interactive solution process.
Sener and Karsak (2011) combined fuzzy linear regression and fuzzy multiple objective programming for setting target levels in the QFD.
Then, we establish optimality conditions for a nonlinear fractional multiple objective programming problem (VFP) involving weaker E-η-semidifferentiable functions.
In [14], optimality and duality were further studied for a fractional multiple objective programming involving semilocal E-convexity.
The objective methods determine weights by solving mathematical models automatically without any consideration of the decision maker's preferences, for example, the entropy method and multiple objective programming.
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In comparison, inexact multiple-objective programming (IMOP) can be developed to handle different objectives more explicitly.
Integer programming models of these three single objectives were estimated to provide the ideal and anti-ideal values for use in several multiple-objective programming models.
The results of the multiple-objective programming models show that reducing the inbreeding coefficient for a group of sires purchased will decrease the Net Merit.
The sub-sections include: two-stage stochastic programming, chance-constrained programming, fuzzy flexible programming, fuzzy robust programming, interval-parameter programming, inexact mixed-integer programming, inexact multiple-objective programming, and inexact nonlinear programming.
(2) Combined with the basic facilities location models, a multiple-objective programming model for SPR storage site location that satisfies the limitations of a set of constraints, such as reserve scale, storage capacity, and emergency periods, is introduced.
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