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Dragos-Patru Covei

Publications and source records attributed to Dragos-Patru Covei.

At least 37 records · Page 2Linked to original sources
arXiv2025

Stochastic Production Planning with Regime Switching: Numerical and Sensitivity Analysis, Optimal Control, and Python Implementation

This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. This research bridges the gap between theoretical modeling and practical applications, offering a robust framework for dynamic production planning.

math.AP↗
arXiv2023

A nonlinear population model

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

math.GM↗
arXiv2021

Stochastic production planning with regime switching

This paper considers a stochastic production planning problem with regime switching. There are two regimes corresponding to different economic cycles. A factory is planning its production so as to minimize production costs. We analyze this problem through the value function approach. The optimal production is characterized through the solution of an elliptic system of partial differential equations which is shown to have a solution.

math.OC↗
arXiv2019

An elliptic partial differential equations system and its application

This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented. This system seemed not considered before.

math.AP↗
arXiv2019

A Stochastic production planning problem

Stochastic production planning problems were studied in several works; the model with one production good was discussed in [3]. The extension to several economic goods is not a trivial issue as one can see from the recent works [4], [5] and [6]. The following qualitative aspects of the problem are analyzed in [5]; the existence of a solution and its characterization through dynamic programming/HJB equation, as well as the verification (i.e., the solution of the HJB equation yields the optimal production of the goods). In this paper, we stylize the model of [4] and [5] in order to provide some quantitative answers to the problem. This is possible especially because we manage to solve the HJB equation in closed form. Among other results, we find that the optimal production rates are the same across all the goods and they also turn to be independent of some model parameters. Moreover we show that production rates are increasing in the aggregate number of goods produced, and they are also uniformly bounded. Numerical experiments show some patterns of the output.

math.OC↗
arXiv2019

An elliptic partial differential equation and its application

This paper deals with the following elliptic equation \begin{equation*} -2σ^{2}Δz+\left\| \nabla z\right\| ^{2}+4αz=4\left\| x\right\| ^{2}\text{ for }x\in \mathbb{R}^{N}\text{, (}% N\geq 1\text{),} \end{equation*}% where $α>0,$ $σ>0$ are some real parameters. The solution method is based on the sub- and super-solutions approach. The case $N>1$ seemed not considered before. This equation models a stochastic production planning problem.

math.AP↗
arXiv2019

The Keller-Osserman problem for the k-Hessian operator

A delicate problem is to obtain existence of solutions to the boundary blow-up elliptic equation% \begin{equation*} σ_{k}^{1/k}\left( λ\left( D^{2}u\right) \right) =g\left( u\right) \text{ in }Ω\text{, }\underset{x\rightarrow x_{0}}{\lim }% u\left( x\right) =+\infty \text{ }\forall x_{0}\in \partial Ω\text{,} \end{equation*}% where $σ_{k}^{1/k}\left( λ\left( D^{2}u\right) \right) $ is the $k$-Hessian operator and $Ω\subset \mathbb{R}^{N}$ is a smooth bounded domain. Our goal is to provide a necessary and sufficient condition on $g$ to ensure existence of at least one positive blow-up solution. The main tools for proving existence are the comparison principle and the method of sub and supersolutions.

math.AP↗
arXiv2018

Symmetric solutions for a partial differential elliptic equation that arises in stochastic production planning with production constraints

In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type $Δu=a\left( \left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert x\right\vert \right) g\left( u\right) $ for $x\in \mathbb{R}^{N}$, which are called entire large solutions. Here $N\geq 3$, and we assume that $a$ and $b$ are nonnegative continuous spherically symmetric functions on $\mathbb{R}% ^{N} $. We extend results previously obtained for special cases of $h$ and $% g $ and we will describe a real-world model in which such problems may arise.

math.OC↗
arXiv2016

A Profit-maximization Model for a Company that Sells an Arbitrary Number of Products

One of the problems faced by a firm that sells certain commodities is to determine the number of products that it must supply in order to maximize its profit. In this article, the authors give an answer to this problem of economic interest. The proposed problem is a generalization of the results obtained by Stirzaker (Probability and Random Variables: A Beginner's Guide, 1999) and Kupferman (Lecture Notes in Probability, 2009) where the authors do not present a situation where the sale of a quantity from some commodities is constrained by the marketing of another. In addition, the described procedure is simple and can be successfully applied to any number of commodities. The obtained results can be easily put into practice.

q-fin.GN↗
arXiv2015

A remark on the existence of solutions to a (k1,k2)-Hessian system with convection term

In this paper, two new results and short proofs are given for the existence of positive entire large and bounded radial positive solutions for a nonlinear system with gradient term. Our results complete and improve a recently work published by Zhang and Zhou. The main difficulty in dealing with our system is the presence of the convection term.

math.AP↗
arXiv2015

A necessary and a sufficient condition for the existence of the positive radial solutions to Hessian equations and systems with weights

In this article we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Our results complete and improve a recently work published by Zhang and Zhou (Existence of entire positive k-convex radial solutions to Hessian equations and systems with weights, Applied Mathematics Letters, Volume 50, December 2015, Pages 48--55).

math.AP↗
arXiv2014

Existence of blow-up solutions for a class of elliptic system with convection term

The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of the gradient of the solution. This result permits to study the existence of blow-up solution for a large class of systems.

math.AP↗