A multi-phase DES modelling framework for patient-centred care

We provide a framework for simulating the entire patient journey across different phases (such as diagnosis, treatment, rehabilitation and long-term care) and different sectors (such as GP, hospital, social and community services), with the aim of providing better understanding of such processes and facilitating evaluation of alternative clinical and care strategies. A phase-type modelling approach is used to promote better modelling and management of the specific elements of a patient pathway, using performance measures such as clinical outcomes, patient quality of life, and cost. The approach is illustrated using stroke disease. Approximately 5% of the United Kingdom National Health Service budget is spent treating stroke disease each year. There is an urgent need to assess whether existing services are cost-effective or new interventions could increase efficiency. This assessment can be made using models across primary and secondary care; in particular we evaluate the cost-effectiveness of thrombolysis (clot busting therapy), using discrete event simulation. Using our model, patient quality of life and the costs of thrombolysis are compared under different regimes. In addition, our simulation framework is used to illustrate the impact of internal discharge queues, which can develop while patients are awaiting placement. Probabilistic Sensitivity Analysis of the value parameters is also carried out.     

A modelling framework for comparative testing of energy forecasts

A project is described in which a methodology was developed for the comparative testing of medium-term national energy forecasts. The basis of the approach is a computer modelling system which can be used flexibly to investigate the dynamics of alternative assumptions about energy futures. The application of the methodology to the forecasts produced by a particular research group is discussed and the educative value of a modelling approach for the users in this case is explained. The study is intended as a contribution to the U.K. national debate on energy policy.     

A unified framework for approximation of general telecommunication networks

In this paper, we develop a unified framework for approximation of the performance of general telecommunication networks based on a decomposition strategy. The method is an extension of the work presented in [15]. The algorithms assume finite buffer space at each switch, state-dependent arrival rates of data packets, and general service time distribution at the switches. Two methods of buffer space allocation at the switches, and two congestion control mechanisms are modeled. The proposed algorithms have been extensively tested against simulation values. The results show that the proposed framework yields robust, reliable and accurate estimates of network performance measures, such as throughput, number of packets in the system, and switch and link utilization. The computation time required is minimal. The unified framework presents a useful set of tools for telecommunication network designers in evaluating numerous network designs.     

Conceptual modelling for simulation Part II: a framework for conceptual modelling

Following on from the definition of a conceptual model and its requirements laid out in a previous paper, a framework for conceptual modelling is described. The framework consists of five iterative activities: understanding the problem situation, determining the modelling and general project objectives, identifying the model outputs, identify the model inputs, and determining the model content. The framework is demonstrated with a modelling application at a Ford Motor Company engine assembly plant. The paper concludes with a discussion on identifying data requirements from the conceptual model and the assessment of the conceptual model.     

A modelling framework for solving restricted planar location problems using phi-objects

This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multi-facility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.     

A geometric modelling of nonlinear RLC networks

A new approach to nonlinear RLC circuits, which is based on the geometric Birkhoffian formalism, is described in this note. The configuration space and a special Pfaffian form, called Birkhoffian, are obtained from the constitutive relations of the involved resistors, inductors and capacitors and from Kirchhoff's laws. No assumptions are placed upon the topology of the network. Properties of the corresponding Birkhoffian such as its regularity, or its dissipativeness, are discussed in this context. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A framework for identifying student blockages during transitions in the modelling process

In this article we present, illustrate, test and refine a framework developed by Galbraith, Stillman, Brown and Edwards (2006) for identifying student blockages whilst undertaking modelling tasks during transitions in the modelling process. The framework was developed with 14~15 year old students who were engaging in their first experiences of modelling at the secondary level.     

A co-opetitive framework for the hub location problems in transportation networks

In this paper, we present the first model of co-opetition for a Hub Location Problem between two logistics service provider (LSPs) companies where the mother company is the owner of infrastructure. The LSPs would like to cooperate with each other by establishing joint edges with limited capacities connecting their service networks. Such services are in form of pendulum services (a direct service between two points) between nodes of different networks. Additional market can be generated as a result of joining the two networks. At the same time, a competition is taking place between the two operators to increase their share from the additional market generated. In order to solve this problem, we propose a matheuristic approach combining a local search algorithm and a Lagrangian relaxation-based approach. In our matheuristic algorithm, the neighbourhood solutions are evaluated using a Lagrangian relaxation-based approach. Numerical results of applying the proposed algorithm on a real case study of the problem are presented.     

System dynamic modelling and simulation of hydrodynamic machines

A graph-theoretic framework for the dynamic simulation of hydrodynamic (both axial and radial flow) machines is presented in this article. The physics based analytical models are developed by considering the dynamics of the hydraulic fluid flow and its interaction with the mechanical components. A linear graph is used to capture the topology of the system and the interconnection of the constituent components. Using the graph-theoretic framework, a dynamic model of an automotive hydrodynamic torque converter is developed to simulate its behaviour under different flow conditions. The ability of the model to capture different features of the torque converter will also be demonstrated by simulation. The simulation results are compared with and validated by experimental results in the literature.     

Spreadsheet modelling as a didactical framework for inequality-based reduction

This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards for teaching and recommendations for teachers in North America. They are designed for prospective teachers of secondary mathematics.     

Newsvendor equations for production networks

We consider production networks with stochastic activity leadtimes. When activities finish early holding costs are incurred and when end products are delivered late penalty costs are incurred. Objective is to find the activity start and finish times that minimize the total cost. We introduce the concept of a tardy path and derive the optimality equations for each node in the network. We show that under the optimal solution, for a set of nodes the tardiness probability satisfies the Newsvendor equations.     

A participative and facilitative conceptual modelling framework for discrete event simulation studies in healthcare

Existing approaches to conceptual modelling (CM) in discrete-event simulation do not formally support the participation of a group of stakeholders. Simulation in healthcare can benefit from stakeholder participation as it makes possible to share multiple views and tacit knowledge from different parts of the system. We put forward a framework tailored to healthcare that supports the interaction of simulation modellers with a group of stakeholders to arrive at a common conceptual model. The framework incorporates two facilitated workshops. It consists of a package including: three key stages and sub-stages; activities and guidance; tools and prescribed outputs. The CM framework is tested in a real case study of an obesity system. The benefits of using this framework in healthcare studies and more widely in simulation are discussed. The paper also considers how the framework meets the CM requirements.     

A framework for performance measurement during production ramp-up of assembly stations

Production ramp-up is an important phase in the lifecycle of a manufacturing system which still has significant potential for improvement and thereby reducing the time-to-market of new and updated products. Production systems today are mostly one-of-a-kind complex, engineered-to-order systems. Their ramp-up is a complex order of physical and logical adjustments which are characterised by try and error decision making resulting in frequent reiterations and unnecessary repetitions. Studies have shown that clear goal setting and feedback can significantly improve the effectiveness of decision-making in predominantly human decision processes such as ramp-up. However, few measurement-driven decision aides have been reported which focus on ramp-up improvement and no systematic approach for ramp-up time reduction has yet been defined. In this paper, a framework for measuring the performance during ramp-up is proposed in order to support decision making by providing clear metrics based on the measurable and observable status of the technical system. This work proposes a systematic framework for data preparation, ramp-up formalisation, and performance measurement. A model for defining the ramp-up state of a system has been developed in order to formalise and capture its condition. Functionality, quality and performance based metrics have been identified to formalise a clear ramp-up index as a measurement to guide and support the human decision making. For the validation of the proposed framework, two ramp-up processes of an assembly station were emulated and their comparison was used to evaluate this work.     

Probabilistic temporal networks: A unified framework for reasoning with time and uncertainty

Complex real-world systems consist of collections of interacting processes/events. These processes change over time in response to both internal and external stimuli as well as to the passage of time itself. Many domains such as real-time systems diagnosis, story understanding, and financial forecasting require the capability to model complex systems under a unified framework to deal with both time and uncertainty. Current models for uncertainty and current models for time already provide rich languages to capture uncertainty and temporal information, respectively. Unfortunately, these semantics have made it extremely difficult to unify time and uncertainty in a way which cleanly and adequately models the problem domains at hand. Existing approaches suffer from significant trade offs between strong semantics for uncertainty and strong semantics for time. In this paper, we explore a new model, the Probabilistic Temporal Network (PTN), for representing temporal and atemporal information while fully embracing probabilistic semantics. The model allows representation of time constrained causality, of when and if events occur, and of the periodic and recurrent nature of processes.     

Synchronization in cross-docking networks: A research classification and framework

Cross-docking is a distribution strategy that enables the consolidation of less-than-truckload shipments into full truckloads without long-term storage. Due to the absence of a storage buffer inside a cross-dock, local and network-wide cross-docking operations need to be carefully synchronized. This paper proposes a framework specifying the interdependencies between different cross-docking problem aspects with the aim to support future research in developing decision models with practical and scientific relevance. The paper also presents a new general classification scheme for cross-docking research based on the inputs and outputs for each problem aspect. After classifying the existing cross-docking research, we conclude that the overwhelming majority of papers fail to consider the synchronization of local and network-wide cross-docking operations. Lastly, to highlight the importance of synchronization in cross-docking networks, two real-life illustrative problems are described that are not yet addressed in the literature.     

Non-maturing deposits modelling in a Ornstein-Uhlenbeck framework

This paper builds a multivariate Lévy-driven Ornstein-Uhlenbeck process for the management of non-maturing deposits, that are a major source of funding for banks. The contribution of the paper is both theoretical and operational. On the theoretical side, the novelty of this model is to include three independent sources of randomness in a Lévy framework: market interest rates, deposit rates and deposit volumes. The choice of a Lévy background driving process allows us to model rare but severe events. On the operational side, we propose a procedure to include severe volume outflows with positive probability in future scenarios simulation, explaining its implementation with an illustrative example using Italian banking sector data.     

Advanced continuum modelling of gas-particle flows beyond the hydrodynamic limit

The accurate prediction of dilute gas-particle flows using Euler–Euler models is challenging because particle–particle collisions are usually not dominant in such flows. In other words, in dilute flows the particle Knudsen number is not small enough to justify a Chapman–Enskog expansion about the collision-dominated near-equilibrium limit. Moreover, due to the fluid drag and inelastic collisions, the granular temperature in gas-particle flows is often small compared to the mean particle kinetic energy, implying that the particle-phase Mach number can be very large. In analogy to rarefied gas flows, it is thus not surprising that two-fluid models fail for gas-particle flows with moderate Knudsen and Mach numbers. In this work, a third-order quadrature-based moment method, valid for arbitrary Knudsen number, coupled with a fluid solver has been applied to simulate dilute gas-particle flow in a vertical channel with particle-phase volume fractions between 0.0001 and 0.01. In order to isolate the instabilities that arise due to fluid-particle coupling, a fluid mass flow rate that ensures that turbulence would not develop in a single phase flow (Re = 1380) is employed. Results are compared with the predictions of a two-fluid model with standard kinetic theory based closures for the particle phase. The effect of the particle-phase volume fraction on flow instabilities leading to particle segregation is investigated, and differences with respect to the two-fluid model predictions are examined. The influence of the discretization on the solution of both models is investigated using three different grid resolutions. Radial profiles of phase velocities and particle concentration are shown for the case with an average particle volume fraction of 0.01, showing the flow is in the core-annular regime.