What is the role and contribution of models to management and research in the health services? A view from Europe

Modelling in different forms has long been regarded as a cornerstone of health OR as in other fields of application. Models are now tending to become a standard tool in health services management and research. What are the lessons we as operational researchers have learnt during this development? How can health care managers and health service researchers benefit from modelling — with or without OR-analysts to guide them between the pitfalls? After an introductory overview concerning the nature and objectives of modelling, examples will be given of modelling applications from different health service areas in order to illustrate the versatility of the method. Further, the choice of methods and models is discussed with special attention to the problems of interpretation and implementation of results. From this overview some conclusions are drawn with regards to advantages and disadvantages of modelling as tools for policy planning and decision-making in the health area. Finally some observations are made concercing the conditions for the future development in the field.     

Special volume on ‘Recent Developments in Queueing Theory’ of the third ECQT conference

Queueing Systems - This paper introduces a load-balancing policy that interpolates between two well-known policies, namely join the shortest queue (JSQ) and join the least workload (JLW), and...     

Feynman’s Operational Calculi: Disentangling Away from the Origin

In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are not necessarily analytic at the origin in ℂ ⁿ . The method of disentangling follows Feynman’s heuristic rules from in (Feynman in Phys. Rev. 84:18–128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ ⁿ while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established.     

Operational aspect of the policy coordination for financial stability: role of Jeffreys–Lindley’s paradox in operations research

This study analyses the implications of Jeffery–Lindley’s paradox and Global Financial Crisis (GFC) for the operational aspect of macroeconomic policy coordination for financial stability. Using a Bayesian Vector Auto-regressive model and data from Jan 1985 to June 2016, our key findings suggest that the claim of macroeconomic policy interaction, interdependence and significance of coordinated policy operations for the financial stability holds its ground. The argument in the support for policy coordination for financial stability was found to be robust against the Jeffreys–Lindley’s paradox and in the Post-GFC era. A profound practical, operational and philosophical implication of this study is the positive aspects of Jeffreys–Lindley’s paradox and the possibility of employing the Frequentist and Bayesian estimation techniques as complementing rather competing frameworks.

     

Applying a hybrid DEA model to evaluate the influence of marketing activities to operational efficiency on Taiwan’s international tourist hotels

This study uses the hybrid DEA model, in which the proportionate inputs are evaluated with a radial measure and the non-proportionate inputs are evaluated with a non-radial measure in order to evaluate the impact of marketing expense on the efficiency of Taiwan's international tourist hotels. We further introduce the hybrid DEA into the technology gap measurement to evaluate the technology gaps of marketing expense utilization between different operating types. The empirical results indicate that the inefficiency caused from excess marketing expense is the main reason for lower efficiency in many tourist hotels, especially to chain-operated hotels and hotels that cater to domestic clients. Through the hybrid technology gap measurement, we find that the utilization of marketing resources is more effective for independent, city type hotels, as well as those that cater to international clients.     

Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation

In this paper, we seek to broaden the sense in which the word ‘dynamic’ is applied to computational media. Focussing exclusively on the problem of design, the paper describes work in progress, which aims to build a computational system that supports students’ engagement with mathematical generalisation in a collaborative classroom environment by helping them to begin to see its power and to express it for themselves and for others. We present students’ strengths and challenges in appreciating structure and expressing generalities that inform our overall system design. We then describe the main features of the microworld that lies at the core of our system. In conclusion, we point to further steps in the design process to develop a system that is more adaptive to students’ and teachers’ actions and needs.     

Preface to the special issue on “Mathematical modeling and analysis in health and natural sciences”

Ricerche di Matematica -     

Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time-Dependent Setting

We obtain lower bounds on blow-up of solutions for the 3D magneto-micropolar equations. More precisely, we establish some estimates for the solution \((\mathbf{u},\mathbf{w},\mathbf{b}) (t)\) in its maximal interval \([0,T^{*})\) provided that \(T^{*}<\infty\), which show for \(\delta\in(0,1)\) that \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) is at least of the order \((T^{*}-t)^{-(\delta s)/(1+2\delta)}\) for \(s\geq1/2+\delta\). In particular, by choosing a suitable \(\delta\), one concludes that \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) is at least of the order \((T^{*}-t)^{-s/4}\), and \((T^{*}-t)^{1/4-s/2}\) for \(s\geq1\), and \(1/2< s<3/2\), respectively. We also show that \((T^{*}-t)^{-s/3}\) is a lower rate for \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) if \(s>3/2\).     

A stylized model of ‘Momentum’ processes: a research note

Several phenomena of interest like stock price movements, online auction bidprices or inventory levels, can be stylized as ‘momentum processes’,whereby the very start of activity (‘up’ or ‘down’) cantrigger subsequent activity in that direction. We calculate the transientprobabilities of being in a particular state (eg, stock price or current auctionbid level) in such activities. The calculations can be used to estimate theexpected time to reach a certain price, inventory level or bid. The processescan be modified to show the phenomenon where the lack of activity can have an‘inertia of rest’.     

How to find the volume of a solid of revolution——by using the definite integral

<正>You've already learned that area is one of the many applications of definite integral.This means area is an important application in finding the area in the plane(the two dimensional area).This means the application of integrals to the computation of areas in the plane can be extended to the three dimensional solid.We have another important application is computation of certain volumes in space.