Linear Programming Problems on Time Scales

Author

Rasheed Al-Salih
Martin Bohner, Missouri University of Science and TechnologyFollow

Abstract

In this work, we study linear programming problems on time scales. This approach unifies discrete and continuous linear programming models and extends them to other cases "in between." After a brief introduction to time scales, we formulate the primal as well as the dual time scales linear programming models. Next, we establish and prove the weak duality theorem and the optimality conditions theorem for arbitrary time scales, while the strong duality theorem is established for isolated time scales. Finally, examples are given in order to illustrate the effectiveness of the presented results.

Recommended Citation

R. Al-Salih and M. Bohner, "Linear Programming Problems on Time Scales," Applicable Analysis and Discrete Mathematics, vol. 12, no. 1, pp. 192 - 204, University of Belgrade, Jan 2018.

The definitive version is available at https://doi.org/10.2298/AADM170426003A

Department(s)

Mathematics and Statistics

Keywords and Phrases

Optimality condition; Primal and dual problem; Strong duality theorem; Time scales; Weak duality theorem

International Standard Serial Number (ISSN)

1452-8630; 2406-100X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Applicable Analysis and Discrete Mathematics, All rights reserved.

Publication Date

01 Jan 2018