A Quantum Calculus Analogue of Dynamic Leontief Production Model with Quadratic Objective Function

In this paper, we derive a new formulation for an optimal investment allocation in N-regional economic model using quantum calculus analogue. This model is described as an optimal control model and formulated in both primal and dual models using quantum calculus formulation. This formulation is an extension of regional economic models. Also, the new formulation provides an exact optimal investment allocation. In addition, the classical regional economic model is obtained by choosing q=1. Furthermore, we formulate the primal and the dual regional economic models in quantum calculus. Moreover, we present a new version of the duality theorems for quantum calculus case. Finally, example is provided and solved using MATLAB. in order to show the given new results.

The Analogue of Regional Economic Models in Quantum Calculus

Hamed¹,

Al-Salih²,

Laith³

2020

Flow Optimization in Dynamic Networks on Time Scales

Abraheim¹,

Jaber²,

Al-Salih³

2021

Network flow optimization has a wide range of real world applications such as in transportation, in electric, in civil engineering, in industrial engineering and in communication networks and so on. In the minimum cost network flow model, the goal is to find the values of the decisions variables that minimize the total cost of flows over the given network. In this work, a new formulation of flow optimization in dynamic networks using time scales approach has been presented. The continuous network model and the quantum case model are also obtained as special cases. The formulation has been given for both dynamic models and time scales models. Moreover, the new approach provides the exact optimal solution for this type of optimization problems. Furthermore, a new version of some duality theorems for time scales flow optimization in dynamic networks has been introduced.

Approximate Solutions and Error Bounds for Continuous-Time Separated Linear Programming Problem and Its Extensions

Khlefh

Al-Salih

Laith

2021

Continuous-time separated linear programming problems have a wide range of real-world applications such as in business, economics, finances, communications, manufacturing, and so on. In this paper, we extend the technique that is presented by Wen et al. [1] for two classes of these problems. We introduce both primal and dual models for separated problems. In addition, by using discrete problems we obtain approximate solutions with error bounds. Moreover, we establish a computational procedure, to solve any separated continuous-time model and any state-constrained separated model. Furthermore, after we put the separated problem in the form that is presented by Wen et al. [1], we conclude that approximate solutions converge to an optimal solution for continuous-time separated problems.