Looking in the wrong place for healthcare improvements: A system dynamics study of an accident and emergency department

Accident and Emergency (A&E) units provide a route for patients requiring urgent admission to acute hospitals. Public concern over long waiting times for admissions motivated this study, whose aim is to explore the factors which contribute to such delays. The paper discusses the formulation and calibration of a system dynamics model of the interaction of demand pattern, A&E resource deployment, other hospital processes and bed numbers; and the outputs of policy analysis runs of the model which vary a number of the key parameters. Two significant findings have policy implications. One is that while some delays to patients are unavoidable, reductions can be achieved by selective augmentation of resources within, and relating to, the A&E unit. The second is that reductions in bed numbers do not increase waiting times for emergency admissions, their effect instead being to increase sharply the number of cancellations of admissions for elective surgery. This suggests that basing A&E policy solely on any single criterion will merely succeed in transferring the effects of a resource deficit to a different patient group.     

Optimal ordering policy of a sequencing model

In this note, we are concerned with the study of a sequencing problem applicable to situations where the optimal choice amongn! sequences is sought. A class of sequencing problems is proposed. Based on the adjacent pairwise interchange of two objects, necessary and sufficient conditions for an optimal ordering policy are given. Examples from the literature are considered and shown to be special cases of the proposed model. The results of this paper improve recent results given in Refs. 1 and 2.The author would like to thank a referee for comments that improved the presentation of the paper. He also thanks Professor R. Combs of West Texas A&M University for comments.     

A generalized activity network model

In recent years activity networks for projects with both random and deterministic alternative outcomes in key nodes have been considered. The developed control algorithm chooses an optimal outcome direction at every deterministic alternative node which is reached in the course of the project's realization. At each routine decision-making node, the algorithm singles out all the subnetworks (the so-called joint variants) which correspond to all possible outcomes from that node. Decision-making results in determining the optimal joint variant and following the optimal direction up to the next decision-making node. However, such models cover a limited class of alternative networks, namely, only fully-divisible networks which can be subdivided into nonintersecting fragments. In this paper, a more generalized activity network is considered. The model can be applied to a broader spectrum of R&D projects and can be used for all types of alternative networks, for example, for non-divisible networks comprising nodes with simultaneously ‘must follow’, random ‘exclusive OR’ and deterministic ‘exclusive or’ emitters. The branching activities of the third type refer to decision-making outcomes; choosing the optimal outcome is the sole prerogative of the project's management. Such a model is a more universal activity network; we will call it GAAN—Generalized Alternative Activity Network. The problem is to determine the joint variant optimizing the mean value of the objective function subject to restricted mean values of several other criteria. We will prove that such a problem is a NP-complete one. Thus, in general, the exact solution of the problem may be obtained only by looking through all the joint variants on the basis of their proper enumeration. To enumerate the joint variants we will use the lexicographical method in combination with some techniques of discrete optimization. A numerical example will be presented. Various application areas are considered.     

An oil outflow model for tanker collisions and groundings

In this paper we have developed an oil outflow model for collision and grounding accidents of tankers. The collision model explicitly links input variables such as tanker hull design (single or double), displacement and speed, striking vessel displacement and speed, and the interaction angle of both vessels to output variables: longitudinal and transversal damage extents of the tanker. Overlaying these damage extents on the tank vessel’s design yields an oil outflow volume totaling the capacity of the damaged tank compartments. A similar model is developed for grounding accidents. A total of 80,000 simulation accident scenarios described in the National Research Council SR259 report published in 2001 served as the joint data set of input and output variables used in this “linking” process. The oil outflow model herein was designed keeping computational efficiency in mind to allow for its integration with a maritime transportation system (MTS) simulation. We shall demonstrate the use of the oil outflow model as a final analysis layer to evaluate double-hull effectiveness in a geographic context of an MTS simulation model developed for the oil transportation routes traversing the environmentally sensitive San Juan Islands area in Washington State.     

Adapting and refining in multi-criteria decision-making

This paper describes the implementation of a Structured Methodology for Direct-Interactive Structured-Criteria (DISC) Multi-Criteria Decision-Making (MCDM), an eight-stage nomological adjusting cycle of activities that shape the information used to make a decision, requiring it be accessible, differentiable, abstractable, understandable, verifiable, measurable, refinable and usable. It shows, in a major IT strategic investment case, that Structured DISC MCDM provides a robust model that can be used for deep and serious consideration of multi-criteria decisions by a group of decision-makers over a long period. The paper describes the case as it moves through stages of the adjusting cycle and shows that, after completing the cycle, it reverses and becomes an adapting process, starting with refining the information. Refining is shown to be more extensive than previously understood, and to cover ‘alternatives & scores’, ‘criteria & weights’ and ‘set of alternatives’. Next the form of measurement is adapted. As the number of alternatives are reduced it can become more appropriate to directly compare the two or three most preferred alternatives relative to one another rather than objectively. Finally the criteria tree can be adapted using a ‘magnifying glass’ approach. This confines the evaluation to that part of the criteria tree in which the difference between a few preferred alternatives is mainly emphasised.     

Developing a Visual Interactive Model for Corporate Cash Management

The operational research/management science journals contain an extensive literature that addresses the corporate cash management problem; yet few, if any, companies make use of any of this published work in their daily cash-management decision making. A review of the literature suggests that the reason for this lack of applications may well be poor problem formulation—the problems that are solved in the literature as ‘cash management’ problems evolve from a ‘hard systems’ view of real-world cash management. However, the problem as perceived by cash managers involves both dynamic and loosely structured components which are difficult to model using classical (i.e. ‘hard systems’) approaches.We therefore decided to approach the cash management problem as an experiment in the use of a novel visual interactive problem solving (VIPS) methodology. The aim of the experiment was to develop an implementable, visual interactive model to support daily cash management decision making. Working closely with a corporate cash manager, we first developed a visual model of his daily decision problem and then agreed on the feasible options and the interactive requirements. At this stage, the problem was sufficiently well defined for a mathematical model to be built and the visual model made ‘smart’.This paper discusses the results of this experiment and suggests that VIPS may have distinct advantages as a problem-solving technique in loosely structured, ‘messy’ problem situations.     

Exploring alternative routes to realising the benefits of simulation in healthcare

Discrete event simulation should offer numerous benefits in designing healthcare systems but the reality is often problematic. Healthcare modelling faces particular challenges: genuine, fundamental variations in practice and an opposition to any suggestion of standardisation from some professional groups. This paper compares the experiences of developing a new simulation in an Accident and Emergency (A&E) Department, a subsequent adaptation for modelling an outpatient clinic and applications of a generic A&E simulation. These studies provide examples of three distinct approaches to realising the potential benefits of simulation: the bespoke, the reuse and the generic route. Reuse has many advantages: it is relatively efficient in exploiting previous modelling experience, delivering timely results although providing scope for adaptations to local practice. Explicitly demonstrating this willingness to adapt to local conditions and engaging with stakeholders is particularly important in healthcare simulation.     

A structural model for sales in the e-retailing industry

This article analyses intangible constructs that affect sales on the Internetretailing industry. We suggest an explanatory model for the success of retailersthat operate on the Internet. Non-financial information has been used toidentify several intangible constructs: ‘web trafficgeneration’, ‘relevance in search engines’,‘link popularity’, and ‘blogspopularity’. The success is measured through items derived fromfinancial statements: sales and profits. The model has been built within astructural modelling framework. It has been estimated using Partial LeastSquares with a sample of USA e-tailers. The results show that there is asignificant relationship between the intangible constructs and accountingfigures. This relationship is stronger when we consider Sales from InternetOperations rather than Total Sales or Net Profit.     

The Development of a Mathematical Model of the Operations of a National Glass Manufacturer

In this paper, a mathematical model of the entire operations of a national glass manufacturer is developed. This includes the float glass manufacture, distribution, storage operations and the technical considerations dictated by the plant as well as the operating procedures. The model is initially for a planning year, and is generated from a ‘monthly model’. This monthly model interconnects with other monthly models primarily via stock flows. The mathematical model is formulated in a unique way that allows certain production aspects to be modelled using a ‘pseudo-continuous’ time frame, rather than a discrete one. The generation of the overall model (as a mixed integer linear programming problem) and its solution is also discussed.     

Kriging for interpolation in random simulation

Whenever simulation requires much computer time, interpolation is needed. Simulationists use different interpolation techniques (eg linear regression), but this paper focuses on Kriging. This technique was originally developed in geostatistics by DG Krige, and has recently been widely applied in deterministic simulation. This paper, however, focuses on random or stochastic simulation. Essentially, Kriging gives more weight to ‘neighbouring’ observations. There are several types of Kriging; this paper discusses—besides Ordinary Kriging—a novel type, which ‘detrends’ data through the use of linear regression. Results are presented for two examples of input/output behaviour of the underlying random simulation model: Ordinary and Detrended Kriging give quite acceptable predictions; traditional linear regression gives the worst results.     

Optimal control applied on an HIV‐1 within‐host model

The treatment of human immunodeficiency virus (HIV) remains a major challenge, even if significant progress has been made in infection treatment by ‘drug cocktails’. Nowadays, research trend is to minimize the number of pills taken when treating infection. In this paper, an HIV‐1 within host model where healthy cells follow a simple logistic growth is considered. Basic reproduction number of the model is calculated using next generation matrix method, steady states are derived; their local, as well as global stability, is discussed using the Routh–Hurwitz criteria, Lyapunov functions and the Lozinskii measure approach. The optimal control policy is formulated and solved as an optimal control problem. Numerical simulations are performed to compare several cases, representing a treatment by Interleukin2 alone, classical treatment by multitherapy drugs alone, then both treatments at the same time. Objective functionals aim to (i) minimize infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood. Copyright © 2015 John Wiley & Sons, Ltd.     

A discrete location model with fuzzy accessibility measures

In crisply defined discrete location problems, a number of facilities are to be located at specific points within an area, according to precisely quantified criteria. However in many location problems, especially those associated with social policies, non-crisply defined criteria are used such as, how ‘near’ or ‘accessible’ a facility is, or how ‘important’ certain issues are, etc. In these cases a fuzzy sets approach is more appropriate.This paper presents an application of the set partitioning (set covering with equality constraints) type of integer programming formulation to a discrete location problem with fuzzy accessibility criteria. The solution method suggested uses the symmetry of the objectives and the constraints introduced by Bellman and Zadeh.     

Comparative evaluation of performance of national R&D programs with heterogeneous objectives: A DEA approach

The strategic importance of performance evaluation of national R&D programs is highlighted as the resource allocation draws more attention in R&D policy agenda. Due to the heterogeneity of national R&D programs’ objectives, however, it is intractably difficult to relatively evaluate multiple programs and, consequently, few studies have been conducted on the performance comparison of the R&D programs. This study measures and compares the performance of national R&D programs using data envelopment analysis (DEA). Since DEA allows each DMU to choose the optimal weights of inputs and outputs which maximize its efficiency, it can mirror R&D programs’ unique characteristics by assigning relatively high weights to the variables in which each program has strength. Every project in every R&D program is evaluated together based on the DEA model for comparison of efficiency among different systems. Kruskal–Wallis test with a post hoc Mann–Whitney U test is then run to compare performance of R&D programs. Two alternative approaches to incorporating the importance of variables, the AR model and output integration, are also introduced. The results are expected to provide policy implications for effectively formulating and implementing national R&D programs.     

A quantum model of atoms (the energy levels of atoms)

In 1913, Niels Bohr developed an accurate model for the hydrogen atom. The mathematics involved and the simplicity of this model is easily understood. The intention of the paper is not to replace Bohr's model, but to find a similar model for all atoms. The model discussed, which was developed on the same basis as Bohr's model for the hydrogen atom, calculates the radii and the energies of the orbits. The wavelength of an emitted photon when an electron makes a ‘jump’ from a higher state to a lower state can also be calculated from the model. Finally, the paper demonstrates that the model obeys the de Broglie's hypothesis that the moving electron exhibits both wave and particle properties.     

Using spatial games to model dynamic evolutionary systems

Modelling the dynamics of evolutionary competing species on a physical grid is a challenging modelling problem. This paper presents a novel modelling approach for synthesizing evolutionary dynamics of competing species using a spatial game perspective. This modelling approach describes the movement of players (‘species’ in our context) across a lattice. The model is based on a payoff function which controls the move likelihood and direction of the players (‘predators’ and ‘preys’). Using simulated results, the paper provides a comparison between the spatial game model and an existing predator-prey dynamic model. Finally, a case study is performed to illustrate the application of this formalism and validate the model.     

On a game of chance in Marc Elsberg’s thriller “GREED”

Mathematische Semesterberichte - A (possibly illegal) game of chance, which is described in Chap. 14 of Marc Elsberg’s thriller “GREED”, seems to offer an...     

Combining problem structuring methods to conduct applied research: a mixed methods approach to studying fitness-to-drive in the UK

This paper describes a mixed methods approach using problem structuring methods to conduct applied research into fitness-to-drive arrangements within the UK Department for Transport. Computer-supported group causal mapping was used to collect and structure qualitative data from stakeholder groups concerning the delivery of medical standards on fitness-to-drive. The data were subsequently coded and analysed using the modelling language of soft systems methodology. This enabled data to be linked to the concept of a ‘fitness-to-drive system’ and developed further in the form of systems models based on alternative worldviews. The paper reports on the process of developing and implementing the approach and discusses issues concerning the conduct of mixed methods research using problem structuring methods.     

System dynamics and microworlds for policymakers

In the past ten years, system dynamics has become more accessible to policymakers and to the academic community. The paper reviews four major developments in the subject that have brought about this change. There have been improvements in the symbols and software used to map and model system structure. New ideas have been adopted from behavioural decision theory which help to transfer policymakers' knowledge into computer models. There have been improvements in methods of simulation analysis that enable modelers and model users to gain better insight into dynamic behaviour. Greater emphasis has been placed on small transparent models, on games and on dialogue between ‘mental models’ and computer simulations. Together these developments allow modelers to create computer-based learning environments (or microworlds) for policymakers to ‘play-with’ their knowledge of business and social systems and to debate policy and strategy change. The paper concludes with some thoughts on future research.     

Budget and long-range planning in public transportation — An applicative linear programming model

Economic and financial planning is an actual problem for Italian Transport Authorities, since in Italy there are scarce financial resources, to cover either the difference between costs and fares proceeds or investment needs. The proposed model is ‘just tailored’ on public transport, subjected to the Italian laws; it takes into account the particular activities (‘functions’) connected with public transport operating (e.g.: fare collection, service production, maintenance, purchases, inventories, administration). Each function is considered as a ‘module’ with its own constraints, and it is connected with the other ‘modules’, so that we can get a ‘representative’ model. Also the most significant parameters of the ‘public transport operating problem’ (e.g.: vehicle miles, passenger journeys, number of vehicles, number of employees, and so on) are connected one another. Since all relations and constraints, connecting the ‘problem variables’ can be represented as linear, the model structure is based on linear programming; this fact allows to pursue an optimum for one or more objective functions, each of them identifing an operational policy. So it is possible to connect simulation with optimization. A multi-period model can be used for long-range planning, pursuing a multi-year optimum; this is the most significant use. The Administrative Module contains Balance-Sheet, Cash-Flow, Profit and Loss Account, which are ‘constraints’ in the model and are expressed as Italian financial laws require; this structure is one of the main characteristics. Modules' dimensions and additional constraints (e.g. economic or financial ratios, fare level, turnover of inventories, and so on) can be ‘tailored’ on each particular case, driving the model towards more realistic solutions.     

Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development

Starting from the context of mathematics learning in the East and West, this paper discusses the position and role of algorithms within school mathematics and argues that learning of algorithms has suffered from an alleged dichotomy between procedures and understanding, in that algorithms have been associated with low-level cognition. The paper first introduces a broad perspective about algorithms in school mathematics, and then, partially drawing on Bloom’s taxonomy and Säljö’s categorization of learning, proposes a model for the learning of algorithms with focus on students’ cognitive development. The model consists of three cognitive levels: (1) Knowledge and Skills, (2) Understanding and Comprehension, and (3) Evaluation and Construction. The model suggests that the learning of algorithms does not simply imply a low level of cognition, and provides a new perspective and framework to analyse the learning of algorithms. Following the model, we present examples to demonstrate the three levels and discuss related teaching strategies. We propose that the model can be used as an analysis tool to reconceptualize the role of algorithms in school mathematics and pose some questions for further research and scholarly discourse in this direction.