A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”

A recently published paper by Lee [C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, European Journal of Operational Research 174 (2006) 861–873] considers different dispatching models for the two-warehouse inventory system with deteriorating items, in which Pakkala and Achary’s LIFO (last-in–first-out) model [T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European Journal of Operational Research 57 (1992) 71–76] is first modified, and then the author concludes that the modified LIFO model always has a lower cost than Pakkala and Achary’s LIFO model under a particular condition specified by him. The present note points out that this conclusion is incorrect and misleading. Alternatively, we provide a new sufficient condition such that the modified LIFO model always has a lower cost than Pakkala and Achary’s model. Besides, we also compare Pakkala and Achary’s original LIFO model with Lee’s FIFO (first-in–first-out) model for the special case where the two warehouses have the same deteriorating rates. Finally, numerical examples are provided to investigate and examine the impact of corresponding parameters on policy choice. The results in this note give a much clearer picture than those at Lee’s paper about the relationships between the different dispatching policies for the two-warehouse inventory system with deterioration items.     

The modified model of Koiter’s type for nonlinearly elastic shell

In this paper, we proposed a modified model of Koiter’s type for nonlinearly elastic shell. The change of metric tensor and the change of curvature tensor play an important role in constructing the linearly and nonlinearly elastic shell model of Koiter’s type. The approximate expressions of them once were proposed by Ciarlet. In this paper, the exact full expressions of the change of metric tensor and the change of curvature tensor are provided by tensor analysis. The former coincides with Ciarlet’s expression. And the latter is more exact than Ciarlet’s expression. Thus the modified model is better than Ciarlet’s model. At the same time, a numerical experiment of special hemispherical shell is provided to validate the modified model of Koiter’s type.     

Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise

A stochastic differential equation modelling a Marchuk’s model is investigated. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Firstly, the stochastic Marchuk’s model has been simplified by applying stochastic center manifold and stochastic average theory. Secondly, by using Lyapunov exponent and singular boundary theory, we analyze the local stochastic stability and global stochastic stability for stochastic Marchuk’s model, respectively. Thirdly, we explore the stochastic bifurcation of the stochastic Marchuk’s model according to invariant measure and stationary probability density. Some new criteria ensuring stochastic pitchfork bifurcation and P-bifurcation for stochastic Marchuk’s model are obtained, respectively.     

A model of students’ combinatorial thinking

Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students’ ways of thinking at a level that facilitates deeper understanding of how students conceptualize counting problems. To this end, a model of students’ combinatorial thinking was empirically and theoretically developed; it represents a conceptual analysis of students’ thinking related to counting and has been refined through analyzing students’ counting activity. In this paper, the model is presented, and relationships between formulas/expressions, counting processes, and sets of outcomes are elaborated. Additionally, the usefulness and potential explanatory power of the model are demonstrated through examining data both from a study the author conducted, and from existing literature on combinatorics education.     

Effects of Young’s modulus on response of railway sleeper

As a main part of a railroad system, sleepers have important duty in conveying the load from rails to the ballast. The different situations in which the sleepers should function necessitate making them from different materials, such as various types of wood, reinforced concrete and even steel. In this work, the effects of Young’s modulus on response of railway sleeper are evaluated. As a main consideration, Winkler’s theorem is used to model the behavior of the elastic foundation. First, the response of a sleeper on a Winkler’s foundation is found. To evaluate the results of the closed form solution, a finite element model is used. Good agreement between the results of the closed form solution and the finite element model proves the validity of the results. In the next stage, the Young’s modulus is considered as a variable and the fundamental diagrams of the beam are plotted based on the variation of Young’s modulus.     

Economic order quantity model and Taguchi’s cost of poor quality

In this paper we consider defective products and Taguchi’s cost of poor quality in the economic order quantity (EOQ) model. We assume that the product quality performs a normal distribution function, and the Taguchi’s poor quality cost has been involved. From our analysis, it has been found that the annual profit will be decreased if the poor quality of product and Taguchi’s quality cost are involved in the model. It has also been found that economic order quantity in our model is larger than that in a traditional EOQ model.     

Prediction of risers’ tubes temperature in water tube boilers

A dynamic model is developed which enables the prediction of risers’ tubes temperature of water tube boilers under various operating conditions. The model is composed of fluid dynamics model representing the fluid flow in the drum-downcomer-riser loop and a dynamic thermal model of the riser’s temperature. The model gives a detailed account of the two-phase heat transfer process which takes place between the risers’ inner walls and the water–steam mixture flow inside the tubes. The model is used to simulate various operational scenarios of water tube boilers. Results of the simulation provide insight into the dynamic interactions of the boiler’s main variables including the drum pressure, water volume, steam quality and risers’ temperature. Such a model is useful in checking operational scenarios before their actual plant implementation, can be a basis for developing boiler start up procedures and online temperature predictions to prevent eminent tube overheating.     

The role of retailer’s performance in optimal wholesale price discount policies

The main goal of this paper is to model the effects of wholesale price control on manufacturer’s profit, taking explicitly into account the retailer’s sales motivation and performance. We consider a stylized distribution channel where a manufacturer sells a single kind of good to a single retailer. Wholesale price discounts are assumed to increase the retailer’s motivation thus improving sales. We study the manufacturer’s profit maximization problem as an optimal control model where the manufacturer’s control is the discount on wholesale price and retailer’s motivation is one of the state variables. In particular in the paper we prove that an increasing discount policy is optimal for the manufacturer when the retailer is not efficient while efficient retailers may require to decrease the trade discounts at the end of the selling period. Computational experiments point out how the discount on wholesale price passed by the retailer to the market (pass-through) influences the optimal profit of the manufacturer.     

Optimal insurance in the presence of insurer’s loss limit

In this paper we consider the optimal insurance problem when the insurer has a loss limit constraint. Under the assumptions that the insurance price depends only on the policy’s actuarial value, and the insured seeks to maximize the expected utility of his terminal wealth, we show that coverage above a deductible up to a cap is the optimal contract, and the relaxation of insurer’s loss limit will increase the insured’s expected utility.When the insurance price is given by the expected value principle, we show that a positive loading factor is a sufficient and necessary condition for the deductible to be positive. Moreover, with the expected value principle, we show that the optimal deductible derived in our model is not greater (lower) than that derived in Arrow’s model if the insured’s preference displays increasing (decreasing) absolute risk aversion. Therefore, when the insured has an IARA (DARA) utility function, compared to Arrow model, the insurance policy derived in our model provides more (less) coverage for small losses, and less coverage for large losses.Furthermore, we prove that the optimal insurance derived in our model is an inferior (normal) good for the insured with a DARA (IARA) utility function, consistent with the finding in the previous literature. Being inferior, the insurance can also be a Giffen good. Under the assumption that the insured’s initial wealth is greater than a certain level, we show that the insurance is not a Giffen good if the coefficient of the insured’s relative risk aversion is lower than 1.     

Some comments on “A simple method to compute economic order quantities”

In this note, we emphasize that the arithmetic–geometric-mean-inequality approach proposed by Teng [Teng, J.T., 2008. A simple method to compute economic order quantities. European Journal of Operational Research. doi:10.1016/j.ejor.2008.05.019] is not a general solution method. Teng’s approach happens to work and give the correct results when the two terms in an objective function are any functions such that their product is a constant. The classical EOQ model works fine since the product of the two terms is indeed a constant! When the product is not a constant, Teng’s approach is of little use. This is exemplified in Comment 1 via solving the EOQ model with complete backorders (where the model is regarded as having two decision variables). Comment 2 is generally valid for an algebraic method when it is used to solve an objective function with two decision variables.     

Responses and comments to “A comment on “An extended assignment problem considering multiple inputs and outputs””

This note is to response the comments from Jahanshahloo and Afzalinejad for the problem of DEA model formulation in Chen and Lu’s paper [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Model. 31 (2007) 2239–2248]. The models adopted in that paper are formulated as the output-oriented BCC models, but not input-oriented BCC models stated in Jahanshahloo and Afzalinejad’s comments. Actually, the applied models are adopted in the relevant literature. Four examples, including the example from Jahanshahloo and Afzalinejad, are provided for justifying the responses.     

On the prisoner’s dilemma in R&D with input spillovers and incentives for R&D cooperation

This paper considers a standard model of strategic R&D with spillovers in R&D inputs, and extends the result that duopoly firms engaged in a standard two-stage game of R&D and Cournot competition end up in a prisoner’s dilemma situation for their R&D decisions, whenever spillover effects and R&D costs are relatively low. In terms of social welfare, this prisoner’s dilemma always works to the advantage of both consumers and society. This result allows a novel and enlightening perspective on some issues of substantial interest in the innovation literature. In particular, the incentive firms face towards R&D cooperation in the form of an R&D cartel is shown to be maximal for the case of zero spillovers, which is when the prisoner’s dilemma has the largest scope.     

Ostrowski’s fourth-order iterative method speedily solves cubic equations of state

Pressure-volume-temperature (P-V-T) data are required in simulating chemical plants because the latter usually involve production, separation, transportation, and storage of fluids. In the absence of actual experimental data, the pertinent mathematical model must rely on phase behaviour prediction by the so-called equations of state (EOS). When the plant model is a combination of differential and algebraic equations, simulation generally relies on numerical integration which proceeds in a piecewise fashion unless an approximate solution is needed at a single point. Needless to say, the constituent algebraic equations must be efficiently re-solved before each update of derivatives. Now, Ostrowski’s fourth-order iterative technique is a partial substitution variant of Newton’s popular second-order method. Although simple and powerful, this two-point variant has been utilised very little since its publication over forty years ago. After a brief introduction to cubic equations of state and their solution, this paper solves five of them. The results clearly demonstrate the superiority of Ostrowski’s method over Newton’s, Halley’s, and Chebyshev’s solvers.     

A retelling of Newton’s work on Kepler’s Laws

This paper details an investigation into Kepler’s Laws. Newton’s technique for deducing an inverse-square law from Kepler’s Laws is given a modern presentation, with necessary background material included. Kepler’s Laws are then deduced from the assumption of an inverse-square law. This is done in a geometric style, inspired by Newton’s work. Finally, a problem involving planetary orbits is stated and solved using the earlier results of the paper.     

Rationale of underwriters’ pricing conduct on competitive insurance market

Underwriters’ desire to show a good annual review is known to be a rationale of the aggressive pricing conduct. On the competitive insurance market, it impacts the global insurance processes and can lead to the competition-originated underwriting cycles. Applying Lundberg’s model of the annual probability mechanism of insurance, we model the influence of a price reduction on migration and consequently on the company’s annual expansion, revenue and solvency.     

A Green’s function model for the analysis of laser heating of materials

An analytical model based on Green’s function method is developed to analyze the temperature distribution and heated regions in a material irradiated by a high-energy laser beam. The model is multi-dimensional, transient and incorporates different types of beam characteristics and boundary conditions. The multi-dimensional integration formulas in the Green’s function solution equation are evaluated using an adaptive numerical integration algorithm. A parametric study is conducted to show the effect of various laser beam parameters and material properties on the laser heating process.     

Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective

This paper examines the impact of three surplus appropriation schemes often inherent in participating life insurance contracts on the insurer’s shortfall risk and the net present value from an insured’s viewpoint. (1) In case of the bonus system, surplus is used to increase the guaranteed death and survival benefit, leading to higher reserves; (2) the interest-bearing accumulation increases only the survival benefit by accumulating the surplus on a separate account; and (3) surplus can also be used to shorten the contract term, which results in an earlier payment of the survival benefit and a reduced sum of premium payments. The pool of participating life insurance contracts with death and survival benefit is modeled actuarially with annual premium payments; mortality rates are generated based on an extension of the Lee-Carter (1992) model, and the asset process follows a geometric Brownian motion. In a simulation analysis, we then compare the influence of different asset portfolios and shocks to mortality on the insurer’s risk situation and the policyholder’s net present value for the three surplus schemes. Our findings demonstrate that, even though the surplus distribution and thus the amount of surplus is calculated the same way, the type of surplus appropriation scheme has a substantial impact on the insurer’s risk exposure and the policyholder’s net present value.     

On positive periodic solution for the delay Nicholson’s blowflies model with a harvesting term

By using Krasnoselskii’s fixed point theorem, we obtain a sufficient condition for the existence of positive periodic solutions for the delay Nicholson’s blowflies model with a harvesting term. Three examples and numerical simulation are given to illustrate the effectiveness of our result.     

Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation

In this paper, a special lattice Boltzmann model is proposed to simulate two-dimensional unsteady Burgers’ equation. The maximum principle and the stability are proved. The model has been verified by several test examples. Excellent agreement is obtained between numerical predictions and exact solutions. The cases of steep oblique shock waves are solved and compared with the two-point compact scheme results. The study indicates that lattice Boltzmann model is highly stable and efficient even for the problems with severe gradients.     

Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

By means of the contraction mapping principle and Gronwall-Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example.