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

Abstract

In this paper, we present a new formulation for the Leontief production model using quantum calculus analogue. This formulation unifies discrete and continuous Leontief production models. Also, the classical Leontief production model is obtained by choosing q = 1. In addition, briefly give an introduction to quantum calculus. We present the formulation for continuous Leontief production models as well as quantum calculus models. Moreover, we establish the weak duality theorem and the strong duality theorem for quantum calculus analogue. Furthermore, using the objective functions for the primal and the dual quantum calculus models, we can easily obtain upper and lower bounds for the value of production at any production plan. Finally, examples are provided in order to illustrate the given results.