Analysis of a mathematical model for tumor growth under indirect effect of inhibitors with time delay in proliferation

In this paper, a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied. The delay represents the time taken for cells to undergo mitosis. Nonnegativity of solutions is investigated. The steady-state analysis is presented with respect to the magnitude of the delay. Existence of Hopf bifurcation is proved for some parameter values. Local and global stability of the stationary solutions are proved for other ones. The analysis of the effect of inhibitor's parameters on tumor's growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding non-retarded problems for some parameter values.     

A Model of the Perishable Inventory System With Reference to Consumer-Realized Product Expiration

A new model of the perishable inventory system is presented, which recognizes and incorporates the effects of consumer-realized product expiration. Such expiration has not been explicitly treated within the perishable inventory literature, and occurs when units are expired at the time of sale or expire within some short period of time subsequent to purchase. The model treats the age at which the vendor outdates units as a decision variable, and allows for analysis of the interaction between inventory ordering and outdate policy for a perishable item with random lifetime. As such, the model represents a synthesis of the fixed versus random lifetime perishable inventory literatures. Sensitivity analysis conducted with respect to the new model provides insight into the trade-offs between the costs of carrying, shortage, outdating, and consumer-realized product expiration.     

Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns

This paper investigates a single-period inventory model in which the demand of the product is a deterministic, multivariate function of price, time, and level of inventory. Models are formulated for the basic pricing case and the case with a price markdown during the season. Solution methodologies are presented for each case when the pricing decisions are predetermined and when they are decision variables. Comments on the practical use of this model are presented, and sensitivity analysis is conducted on the decision variables and demand parameters.     

Continuous Galerkin finite element methods for a forward‐backward heat equation

A space‐time finite element method is introduced to solve a model forward‐backward heat equation. The scheme uses the continuous Galerkin method for the time discretization. An error analysis for the method is presented. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 257–265, 1999     

需求对时间和价格敏感产品的最优动态定价与订购策略

探讨了需求对时间和价格敏感产品的最优动态定价和订购策略,建立了使零售商利润最大化的库存模型.然后对模型的性质进行了分析,给出了一个寻找最优价格调整次数的算法和数值例子,得到一些有意义的管理经验.     

Asymptotic properties of an HIV/AIDS model with a time delay

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe.     

Extension of a simplified Baldwin–Lomax model to nonequilibrium turbulence: Model,analysis and algorithms

Complex turbulence not at statistical equilibrium is impossible to simulate using eddy viscosity models due to a backscatter. This research presents the way to correct the Baldwin–Lomax model for nonequilibrium effects and gives an analysis of the energy evolution in the corrected model. Furthermore, a finite element approximation of the corrected eddy model with first‐order and second‐order time discretization is also presented. A numerical test is given to support the theory.     

A local discontinuous Galerkin method for pattern formation dynamical model in polymerizing action flocks

In this paper, we apply local discontinuous Galerkin methods to the pattern formation dynamical model in polymerizing action flocks. Optimal error estimates for the density and filament polarization in different norms are established. We use a semi-implicit spectral deferred correction time method for time discretization, which allows a relative large time step and avoids computation of a Jacobian matrix. Numerical experiments are presented to verify the theoretical analysis and to show the capability for simulations of action wave formation.

     

有随机投资回报的随机保费模型的渐近破产概率(英文)

本文研究了随机投资回报环境下扰动的随机保费模型的破产问题.利用鞅方法和随机分析的理论讨论了盈余过程的一些基本性质,得到了一个可以用来求解破产时刻的Laplace变换的积分微分方程,结果推广了已有的随机投资问报风险模型的结论.     

Towards a general condition based maintenance model for a stochastic dynamic system

This paper considers a stochastic dynamic system subject to random deterioration, with regular condition monitoring and preventive maintenance. A model is presented to advise at a monitoring check what maintenance action to take based upon the condition monitoring and preventive maintenance information obtained to date. A general assumption adopted in the paper is that the performance of the system concerned can not be described directly by the monitored information, but is correlated with it stochastically. The model is relevant to a large class of condition monitoring techniques currently employed in industry including vibration and oil analysis. The model is constructed under fairly general conditions and includes two novel developments. Firstly, the concept of the conditional residual time is used to measure the condition of the monitored system at the time of a monitoring check, and secondly, contrary to previous practice, the monitored observation is now assumed to be a function of the system condition. Relationships between the observed history of condition monitoring, preventive maintenance actions, and the condition of the system are established. Methods for estimating model parameters are discussed. Since the model presented is generally beyond the scope for an analytical solution, a numerical approximation method is also proposed. Finally, a case example is presented to illustrate the modelling concepts in the case of non-maintained plant.     

An inventory model for increasing demand under two levels of trade credit linked to order quantity

During the growth stage of a product life cycle especially for high-tech products, the demand function increases with time. In this paper, we extend the constant demand to a linear non-decreasing demand function of time and incorporate a permissible delay in payment under two levels of trade credit into the model. The supplier offers a permissible delay linked to order quantity, and the retailer also provides a downstream trade credit period to its customers. The objective is to find the optimal replenishment cycle that minimizes the retailer’s annual total relevant cost per unit time. The condition for an optimal solution to the generalized model is presented and some fundamental theoretical results are established. Finally, numerical examples to illustrate the proposed model are provided. Sensitivity analysis is performed and some relevant managerial insights are obtained.     

Derivation of the N-step interdeparture time distribution in GI/G/1 queueing systems

The departure process of a queueing system has been studied since the 1960s. Due to its inherent complexity, closed form solutions for the distribution of the departure process are nearly intractable. In this paper, we derive a closed form expression for the distribution of interdeparture time in a GI/G/1 queueing model. Without loss of generality, we consider an embedded Markov chain in a general K_M/G/1 queueing system, in which the interarrival time distribution is Coxian and service time distribution is general. Closed form solutions of the equilibrium distribution are derived for this model and the Laplace–Stieltjes transform (LST) of the distribution of interdeparture times is presented. An algorithmic computing procedure is given and numerical examples are provided to illustrate the results. With the analysis presented, we provide a novel analytic tool for studying the departure process in a general queueing model.     

Generalized First Transit Times with an Illustration in Human Service System Planning

This paper is concerned with extending the notion of first transit time analysis in Markov chains to sets of states rather than individual states. The motivation for the research came as a result of the state structure of a Markov chain model being developed to aid government planners in operating service systems for the elderly. The mathematics of the analysis is presented, followed by numerical results showing the expected transit times from service to service for a country service system for the elderly in Pennsylvania.     

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system’s entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results.     

Automatic Box-Jenkins Forecasting

Many authors have demonstrated the superiority of the Box-Jenkins Procedure for forecasting. The only problem preventing more widespread use has been the skill and time needed to produce an acceptable model. This paper describes an approach to the automation of the modelling procedure, which combines a pattern recognition procedure and objective model order testing criterion. The results from an automatic Box-Jenkins modelling program are presented and compare favourably with results from manual analysis given in the literature.     

A modified (S − 1, S) inventory system for deteriorating items with Poisson demand and non-zero lead time

An inventory system is considered for continuous decaying items with non-zero lead time and stochastic demand when shortages are allowed and all unsatisfied demands are backlogged. In this research we consider orders as separate packages where replenishment is one-for-one and a modified base stock policy is applied. In this paper, a penalty cost is introduced for stochastic inventory models with decaying items when less than one unit of the product is delivered to the customers. The objective of the warehouse is to maximize his average profit. Since the concavity analysis of the model is extremely complicated, an upper bound is introduced and an algorithm is presented for finding the optimal solution. Finally, a numerical example is presented and sensitivity analysis is carried out for a number of important parameters.     

Financing policies via stochastic control: a dynamic programming approach

This paper deals with a theoretical stochastic dynamic optimization model for the external financing of firms. We aim at searching for the best intensity of payment that a financier has to apply to a company in order to have a loan repaid. The techniques involved are related to the optimal control theory with exit time. We follow a dynamic programming approach. Our model also presents a distinction between the legal and the illegal financier, and a theoretical comparison analysis of the results is presented. Some numerical examples provide further validation of the theoretical results.     

A better project performance prediction model using fuzzy time series and data envelopment analysis

Earned value management (EVM) is a critical project management methodology that evaluates and predicts project performance from cost and schedule perspectives. The novel theoretical framework presented in this paper estimates future performance of a project based on the past performance data. The model benefits from a fuzzy time series forecasting model in the estimation process. Furthermore, fuzzy-based estimation is developed using linguistic terms to interpret different possible conditions of projects. Eventually, data envelopment analysis is applied to determine the superior model for forecasting of project performance. Multiple illustrative cases and simulated data have been used for comparative analysis and to illustrate the applicability of theoretical model to real situations. Contrary to EVM-based approach, which assumes the future performance is the same as the past, the proposed model can greatly assist project managers in more realistically assessing prospective performance of projects and thereby taking necessary and on-time appropriate actions.     

Plant residual time modelling based on observed variables in oil samples

This paper presents a model and methodology for estimating the residual time of a plant item. This plant item can be an engine or any complex technical system monitored by a regularly spaced oil analysis programme. Typically in the oil samples taken, two groups of observed variables are available, namely, metal concentrations and variables related to the condition of the lubricant and contaminants. We term the former as internal variables and the latter as external variables. External variables are those that may cause the change of the underlying condition of the plant item and therefore the residual time, while internal variables are those variables that only reflect the residual time but cannot change it. We modelled both variables in an oil-based monitoring case, but the principle can be generalized to other monitoring situations. The main techniques used are stochastic filtering for residual time prediction and the maximum likelihood method for parameters estimation. The model established was fitted to the real data of marine diesel engines monitored by an oil analysis programme and the results are presented.