Numerical Solution of the Inventory Balance Delay Differential Equation

Abstract

Inventory represents an essential part of current assets, which are typically characterized by their transience. This paper aims to outline a numerical solution of the inventory balance equation supplemented by an order-up-to replenishment policy for a case in which the problem is described by a differential equation with delayed argument. The results are demonstrated on a specific example and the behaviour of the model is presented using a computer simulation. The results are graphically shown in the Maple system. The solution makes use of the theory of functional differential equations, especially the part dealing with differential equations with delayed arguments.

Inventory represents an essential part of current assets, which are typically characterized by their transience. This paper aims to outline a numerical solution of the inventory balance equation supplemented by an order-up-to replenishment policy for a case in which the problem is described by a differential equation with delayed argument. The results are demonstrated on a specific example and the behaviour of the model is presented using a computer simulation. The results are graphically shown in the Maple system. The solution makes use of the theory of functional differential equations, especially the part dealing with differential equations with delayed arguments.