Abstract
Separated linear programming problems can be used to model a wide range of real-world applications such as in communications, manufacturing, transportation, and so on. In this paper, we investigate novel formulations for two classes of these problems using the methodology of time scales. As a special case, we obtain the classical separated continuous-time model and the state-constrained separated continuous-time model. We establish some of the fundamental theorems such as the weak duality theorem and the optimality condition on arbitrary time scales, while the strong duality theorem is presented for isolated time scales. Examples are given to demonstrate our new results
Highlights
Time Scales CalculusInstead of introducing the basic definitions, derivative, and integral on time scales, we refer the reader to the monographs [12,16,17], in which comprehensive details and complete proofs are given
In this paper, we demonstrate that separated problems can be efficiently formulated and solved using time scales techniques
An efficient formulation and a computational approach have been successfully constructed in this paper to solve two classes of separated linear programming problems on arbitrary time scales
Summary
Instead of introducing the basic definitions, derivative, and integral on time scales, we refer the reader to the monographs [12,16,17], in which comprehensive details and complete proofs are given. For readers not familiar with the time scales calculus, we give the following few examples. If T = R, σ(t) = t, μ(t) ≡ 0, f ∆(t) = f ′(t) for t ∈ T, and b b f (t)∆t = f (t)dt, where a a is the usual Riemann integral from calculus. If T = {tk ∈ R : k ∈ N0} with tk < tk+1 for all k ∈ N0 consists only of isolated points (i.e., it is an isolated time scale), σ(tk) = tk+1, μ(tk) = tk+1 − tk, f ∆(tk).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
