An inventory model for stock with advertising sensitive demand

K. S. Chaudhuri Department of Mathematics, Jadavpur University, Kolkata-700 032, West Bengal, India Corresponding author. Email: shib_sankar{at}yahoo.com Email: k_s_chaudhuri{at}yahoo.com The effect of advertising media and sales effort on future demandof merchandize is considered. In an oligopolistic marketingsystem, it is quite natural to boost sales by using advertisingand sales effort to earn more money from a business sector.Determination of demand and costs due to advertising and saleseffort is quite difficult. The approach in this paper is toconcentrate on investment for the purpose of advertising andincreasing sales effort in order to maximize profit. The paperextends an inventory model over finite and infinite time horizonswhere demand is influenced by the level of stock, advertisingmedia and sales effort. The associated profit maximization problemis solved by the ‘Euler–Lagrange method’.The model is illustrated with a numerical example.     

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

Estimation and decomposition of cost efficiency in the health care food service sector: an extended stochastic frontier approach

K. M. Matawie School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith South DC NSW 1797, Australia Email: a.assaf{at}uws.edu.au Corresponding author. Email: k.matawie{at}uws.edu.au Received on 11 February 2007. Accepted on 14 September 2007. This paper introduces and implements an extended stochasticfrontier model to estimate and decompose cost efficiency (CE)in the health care foodservice sector. The interesting featureof this model is that it allows differentiation between thethree different types of efficiency: technical efficiency (TE),allocative efficiency (AE) and their associated CE. A completeillustration of these efficiencies is presented using a cross-sectionalsample of 101 hospital foodservice operations. Results showedthat the model and all its parameter coefficients were plausible,significant and satisfy all theoretical requirements. It wasalso clear that the average efficiency scores were lower forTE (80%) than AE (88%), indicating that TE is the main sourceof CE and requires further attention.     

Control consolidation with a threshold: an algorithm

Email: ariane.chapelle{at}ulb.ac.be Corresponding author. Email: aszafarz{at}ulb.ac.be Received on 14 October 2005. Accepted on 21 November 2006. Besides multiple voting rights, board representation and shareholders’monitoring, control tunnelling over firms can be reached throughpyramids, cross-ownership and other complex features. This phenomenonis frequent in Europe and Asia. However, the theoretical literaturehas not yet converged towards a well-defined and robust measurementof integrated control that takes into account the thresholdfor control as applied in practice. Based on graph theory, thispaper aims at filling this gap and proposes a new algorithmfor evaluating the control tunnelling exerted by the firms’ultimate shareholders. Then, the paper discusses the variousforms of control existing next to voting shares, like multiplevoting rights, board representation and active monitoring, beforesuggesting ways to include them into the modelling of control.     

On computing eigenvalues of second-order linear pencils

^** Email: mhannaby{at}yahoo.com^*** Email: zahraa26{at}yahoo.com In this paper, we use sinc techniques to compute the eigenvaluesof a second-order operator pencil of the form Q – P approximately.Here Q and P are self-adjoint differential operators of thesecond and first order, respectively. Also the eigenparameterappears in the boundary conditions linearly.     

Multiple criteria models for evaluation of competitive bids

Email: slliu{at}mail.east.net.cnAuthor for correspondence Email: mskklai{at}cityu.edu.hkEmail: sywang{at}iss02.iss.ac.cn In this paper, two general bidding systems are proposed to aidan owner to select one contractor based on multiple-attributedecision making models. They are named the general multiple-attributelower-bidder system and the general multiple-attribute average-bid system and are an extension (and refreshment) of the multiparameterbidding system and the average-bid method, respectively. Thepreference of the owner over the criteria (or attributes) relevantto construction work award is incorporated into the two newsystems if necessary and required by the owner. The values ofthe attributes (excluding the cost) required to be determinedby the owner in the multiparameter bidding system are not necessarilydetermined in the general multiple-attribute lower-bidder system.This reduces the burden to the owner. The two new bidding systemsare demonstrated via an example, and are compared with the multiparameterbidding system and the average-bid method. The comparisons showthat the preference of the owner in regard to the attributesrelevant to selection of contractors has a significant effecton bid evaluation. The two new systems preserve the form ofthe competitive bidding concept and can easily be applied topractice.     

Differentiated service delivery in cooperative IP-based broadcast and mobile telecommunications networks

Email: angelo.centonza{at}brunel.ac.uk Corresponding author. Email: thomas.owens{at}brunel.ac.uk Email: john.cosmas{at}brunel.ac.uk^¶ Email: y.h.song{at}brunel.ac.uk Received on 26 November 2005. Accepted on 20 March 2007. The evolution of wireless systems has led recently to the deploymentof cooperative network infrastructures where networks basedon different technologies cooperate together to offer innovativeservices which the networks individually could not offer. Cooperativenetwork infrastructures are hybrid systems. Examples of hybridsystems are already in use in areas as diverse power systemsand locomotion systems. It is very important to apply efficientsystem management techniques to hybrid systems that produceadvantageous business case scenarios for each participatingsystem and efficient use of the available resources. In thispaper, scenarios are investigated where cooperation betweenan integrated project (IP)-based broadcast network and an IP-basedmobile telecommunications network has the potential to allowservices to be provided to mobile users which would not be economicalto offer over either an IP-based broadcast network or an IP-basedmobile telecommunications network alone. The paper presentsa novel technique for determining which network to use to deliversuch services at a given point in time. The application of thistechnique in appropriate scenarios has the potential to generateadditional income for both the IP-based broadcast network operatorand the IP-based mobile telecommunications network operatorin an infrastructure where the operators cooperate to offerinnovative services. The paper explains the construction ofutility functions for cooperative IP-based broadcast and mobiletelecommunications networks. These utility functions are thenused to provide results that enable the efficiency of the managementof the network to be assessed in terms of the utility volumegenerated by the innovative services provided.     

Numerical stabilization of polynomial and matrix

Email: jdhan{at}sia.cn Email: zhjiang{at}sia.cn Corresponding author Email: nyy{at}sia.cn Received on March 6, 2006; Accepted on September 4, 2006 In this paper, the conception of numerical stabilization, whichis related to mantissa digits of computer and dimensions ofsystem, is described; and several strategies for the numericalstabilization of polynomial and matrix are presented.     

Simultaneous output feedback stabilization of time-delay systems

^** Email: magdi_mahmoud{at}cic-cairo.com^*** Email: hnounou{at}uaeu.ac.ae This paper develops new results to the problem of simultaneousfeedback stabilization using static output feedback (SOF) controlfor a finite collection of linear dynamical systems with unknownstate delay. We establish tractable synthesis conditions fornominal SOF controllers and subsequently extend the resultsto resilient SOF to cope with possible additive controller gainperturbations. In both cases, the design of SOF controllersis based on guaranteed cost and approaches. Previous relatedresults are recovered and all the developed results are convenientlycast in the format of linear matrix inequalities. A numericalexample is presented.     

Arbitrary-norm hyperplane separation by variable neighbourhood search

^** Email: alejandro.karam{at}hec.ca^*** Email: gilles.caporossi{at}gerad.ca^**** Email: pierre.hansen{at}gerad.ca We consider the problem of separating two sets of points ina Euclidean space with a hyperplane that minimizes the sum ofp-norm distances to the plane of points lying on the ‘wrong’side of the plane. A variable neighbourhood search heuristicis used to determine the plane coefficients. For a set of exampleswith L₁-norm, L₂-norm and L-norm, for which the exact solutioncan be computed, we show that our algorithm finds it in mostcases and gets good approximations in the others. The use ofour heuristic solutions for problems in these norms can dramaticallyaccelerate exact algorithms. Our method can be applied on verylarge instances that are intractable by exact algorithms. Sincethe proposed approach works for truly arbitrary norms (otherthan the traditional 1, 2 and ), we can explore for the firsttime the effects of the choice of p on the generalization propertiesof p-norm hyperplane separation.     

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Email: mgt.liu{at}utoronto.ca Email: makis{at}mie.utoronto.ca Received on 4 August 2006. Accepted on 14 December 2006. An effective gearbox failure diagnosis helps prevent catastrophicgearbox failure and can contribute to significant economic benefits.This paper proposes a gear failure diagnosis method based onvector autoregressive modelling of high-frequency vibrationdata, dimensionality reduction applying dynamic principal componentanalysis (PCA) and condition monitoring using a multivariatecontrol chart. After extracting useful information from thevibration data obtained from distinct directions via dynamicPCA, a failure diagnosis scheme is implemented and tested usingreal gearbox vibration data. It is shown that the failure diagnosisscheme can indicate the gear teeth failure pattern when thegear is damaged, which has not been demonstrated in the previousstudies. For a comparison, PCA is applied to the same data set.The results show that the advantages of dynamic PCA over PCAfor failure diagnosis using vibration data consist not onlyin indicating more accurately the occurrence of incipient faultand the actual gear condition, but also in a much lower falsealarm rate.     

Estimating vaccine coverage by using computer algebra

Email: altmannd{at}rki.deEmail: altmann{at}mathematik.hu-berlin.de The approach of N Gay for estimating the coverage of a multivalentvaccine from antibody prevalence data in certain age cohortsis complemented by using computer aided elimination theory ofvariables. Hereby, Gay's usage of numerical approximation canbe replaced by exact formulae which are surprisingly nice, too.     

A calibration algorithm for simulation-based pricing models

Don L. McLeish Department of Statistics and Actuarial Science, University of Waterloo, Waterloo,Ontario N2L 3G1, Canada Corresponding author. Email: mreesor{at}uwo.ca Email: dlmcleis{at}math.uwaterloo.ca Received on 20 February 2007. Accepted on 15 March 2007. Derivative pricing models require calibration to market conditionsin order to determine quantities such as hedging positions andthe prices of other instruments. For stochastic models and/orcomplex derivatives whose prices are not of an analytic form,prices must be computed via simulation and the calibration ismore difficult. A method to facilitate the calibration of simulation-basedpricing models is proposed. The algorithm uses a statisticallydesigned experiment to select the points at which simulationsare performed. The method is quite general as it is independentof the stochastic model for the underlying and allows for differentobjective functions that can incorporate information such asopen interest and volume. Furthermore, market prices from European-and/or American-style derivatives covering a range of strikeprices and maturities can be handled by this technique. Examplesshow the procedure is successful at calibrating well-known assetpricing models to both simulated and market data.     

A semi-Markov maintenance model with credit rating application

Email: g.damico{at}unich.it Received on 6 December 2006. Accepted on 2 April 2008. The impact of a preventive rating maintenance policy on therating process is investigated through the definition of a semi-Markovmaintenance model with imperfect repair at random times. Theresults allow us to study the rating migrations process in thetransient and the asymptotic case.     

Properties of the weighted logarithmic matrix norms

Mingzhu Liu Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China Email: ghu{at}hit.edu.cn, ghuca{at}yahoo.ca Email: mzliu{at}hit.edu.cn Received on January 31, 2006; Accepted on December 9, 2006 In this paper, we are concerned with the properties of the weightedlogarithmic matrix norms. A relation between the elliptic logarithmicmatrix norm and the weighted logarithmic matrix norm is given.Based on Lyapunov equations, two weighted logarithmic matrixnorms are constructed which are less than 1-logarithmic matrixnorm and -logarithmic matrix norm, respectively. Then, an iterativescheme is presented to obtain the logarithmically -efficientmatrix norm. Numerical examples are given to illustrate theresults.     

Lattice Boltzmann simulations of complex fluids

Email: j.yeomansl{at}physics.oxford.ac.uk We discuss how lattice Boltzmann simulations can be used tomodel the self-assembly and flow properties of complex fluids.The aim is to include both the hydrodynamic (viscous, diffusive)and the equilibrium (phase ordering, interface profiles) fluidproperties. Examples include the decomposition of a dropletunder extensional flow and phase separation of binary and lamellarfluids.     

A methodology for measuring the relative effectiveness of healthcare services

^** Email: giorgio.vittadini{at}unimib.it^*** Email: simona.minotti{at}unicatt.it In this paper we propose a methodology for measuring the ‘relativeeffectiveness’ of healthcare services (i.e. the effectof hospital care on patients) under general conditions, in which:) a healthcare outcome underlies qualitative and quantitativeobservable indicators; ß) we are interested in studyingthe simultaneous dependency of multiple outcomes on covariates(where the outcomes can also be correlated to each other); )the relative effectiveness is adjusted for hospital-specificcovariates; ) we hypothesise a general distribution for randomdisturbances and the random parameters of relative effectiveness.For this topic, a generalisation of the SURE (seemingly unrelatedregression equations) multilevel model is proposed. The solutionsare obtained by means of Bayesian inference methods. Since thereis currently no software available to estimate this model, anSAS procedure based on Markov Chain Monte Carlo methods hasbeen developed by the authors, in line with Goldstein &Spiegelhalter (1996, J. R. Stat. Soc. Ser. A, 159, 385–443),Spiegelhalter et al. (1996, Bayesian Using Gibbs Sampling Manual.Cambridge: MRC Biostatistic Unit, Institute of Public Health)and Albert & Chib (1997, J. Am. Stat. Assoc., 92, 916–925).In addition, a new theoretical result regarding the joint posteriordistribution for the parameters is provided. The model proposedhas been implemented for an effectiveness study of a selectionof Lombard hospitals.     

Neural networks and flexible approximations

Email: cuny{at}cardiff.ac.uk This paper supports the view that neural networks are best seenas devices that can approximate a wide range of functions. Theauthors argue the need to consider the precise details of howthe approximations operate in practice. The paper shows howstandard network models can be regarded as polynomial functions,obtained from expanding exponential terms. Multivariate Taylor-seriesexpansions, obtained through the MAPLE software package, areused for this purpose. The expansions serve to cast light onthe role of the hidden nodes. Also considered is the relativedifficulty of fitting different types of function. Quadraticfunctions are compared with Gaussian shapes.     

The dynamic control of risk in optimised portfolios

E-mail: c.j.adcock{at}sheffield.ac.uk or adcock{at}intonet.co.uk This paper presents a theoretical treatment of the statisticalproperties of optimal portfolios. The results demonstrate theway in which the statistical properties of forecast returnsaffect the performance of optimised portfolios. The paper thenindicates how these methods may be used in principle to controlthe performance of an optimised portfolio. This is exemplifiedby an optimal portfolio of foreign currencies.     

The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.