Linear programming problems on time scales | Zendy

Rasheed Al-Salih | Zendy; Martin Böhner | Zendy

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Linear programming problems on time scales

Author(s) -

Rasheed Al-Salih,

Martin Böhner

Publication year - 2017

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm170426003a

Subject(s) - mathematics , duality (order theory) , linear programming , dual (grammatical number) , weak duality , mathematical optimization , discrete time and continuous time , strong duality , order (exchange) , discrete mathematics , optimization problem , art , statistics , literature , finance , economics

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.

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