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-upto 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.

On Construction of Solutions of Linear Differential Systems with Argument Deviations of Mixed Type

“…which is also helpful in cases where the initial value problem (1), (24) for the original equation is not uniquely solvable. It should be noted that the last mentioned issue may arise even for very simple equations of type (6); for example, it is easy to verify that if (1) has the form…”

“…For delay equations, the classical method of steps [1] allows one to construct the solution of the Cauchy problem by extending it from the initial interval in a stepwise manner; in this way, an ordinary differential equation is solved at every step, with every preceding part of the curve serving as a historical function for the next one. This technique, together with the ODE solvers available in the mathematical software, is commonly used in the practical analysis of dynamic models based on equations with retarded argument under the initial conditions (e.g., in economical models [4][5][6]).…”

“…is not a restriction of generality because the setting involving initial functions can be reduced to the present one by a suitable transformation [15]. The retarded character of the equation is not assumed (in particular, for (6), it is not required that τ ij (t) ≤ t for all i, j) and, therefore, the method of steps is inapplicable.…”

On the construction of solutions of general linear boundary value problems for systems of functional differential equations

“…On Figures 1 and 2 shown below, the function of "history" u is marked by a dotted line , the "starting function" x 0 of the iterative process is marked by a dashed line , approximations of solutions are marked by a dot-and-dash line , and the last calculated approximation of solution x is marked by a solid line --. Analogous problems are solved by MAPLE in the works [3,15,16].…”

An Artificial Neural Network Model for a Wholesale Company's Order-Cycle Management

“…The study of miscellaneous model situations, focusing on simulating conditions, searching for results and optimal solutions are among the most important contemporary trends [3, 4]. Over the years, countless studies have looked for the optimum result for inventory management or similar issues from supply chain management [5, 6].…”