Linear programming problems on time scales

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.