Using a Markov reward model to estimate spend-down costs for a geriatric department

A Markov model is used to describe movements of geriatric patients within a hospital system where the states of the Markov chain are acute/rehabilitative, long-stay care, discharge or death. By assigning costs to the states of this model, we can estimate the spend-down costs of running down services given that there are no more admissions and different costs are assigned to acute/rehabilitative and long-stay care. The model is used to estimate the spend-down costs using data previously validated for three Departments of Geriatric Medicine in the South West Thames Region of England. Our approach allows hospital planners to identify cost-effective strategies which take into account the fact that some geriatric patients remain in long-stay care for very long periods of time.     

Service network design for freight railway transportation: the Italian case

In this paper, we present a case study on freight railway transportation in Italy, which is a by-product of research collaboration with a major Italian railway company. We highlight the main features of the Italian reality and propose a customized mathematical model to design the service network, that is, the set of origin-destination connections. More specifically, the model suggests the services to provide, the number of trains travelling on each connection, the number of cars and their type. We consider both full and empty freight car movements and take handling costs into account. All decisions are taken in order to minimize the total costs. The quality of service is guaranteed by satisfying all the transportation demand and by implicitly minimizing the waiting time of cars at intermediate railway stations. Our approach yields to a multi-commodity network design problem with a concave cost function. To solve this problem, we implement a specialized tabu search procedure. Computational results on realistic instances show a significant improvement over current practice.     

Error Bounds for the Solution Sets of Quadratic Complementarity Problems

In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standard violation measure of the polynomial equalities and inequalities. These fractional local error bounds are given with explicit exponents. A fractional local error bound with an explicit exponent via the natural residual function is new in the tensor/polynomial complementarity problems literature. The other fractional local error bounds take into account the sparsity structures, from both the algebraic and the geometric perspectives, of the third-order tensor in a quadratic complementarity problem. They also have explicit exponents, which improve the literature significantly.     

A framework for predicting gross institutional long-term care cost arising from known commitments at local authority level

As the UK population ages, it is forecasted that there will be an unsustainable increase in the need for, and therefore in the costs of long-term care. Although several studies have been performed to estimate these costs, they do not take into account the impact of survival patterns on costs. Focussing only on residents already in care (known commitments), we have developed, in association with an English local authority, a framework for estimating the future gross cost incurred by this group, built around a survival model. We apply this framework to forecast the cost over a given period of time, of maintaining a group of individuals in residential and nursing care, funded by the local authority. One of the novelties in the model is that it translates survival inputs and unit fees for care into cost in a manner, which was useful and meaningful to decision makers.     

Exploring the use of DEA for formative evaluation in primary diabetes care: An application to compare English practices

Primary care is currently at the heart of the UK National Health Service policy. Primary care trusts have the crucial role of improving the efficiency and equity in primary care delivery. However, few studies have focused on performance assessment in primary care provision. In this paper, we examine the role of data envelopment analysis (DEA) in helping decision makers to understand and improve the performance of primary care practices. We discuss the results from a study of 14 practices in England in terms of their delivery of diabetes services. In order to take into account the multiple values that underlie public services provision, we have considered several different perspectives for evaluation. These were: technical, allocative and cost efficiency, clinical and patient-focused effectiveness, and equity. The approach adopted involved a deep engagement with the practices. The purpose was to understand the structures and processes supporting effective practice using DEA in a formative role rather than the more usual summative role with a large data set. This approach is in the tradition of the developmental engagement approach of operational research.     

The Placing of Service Points to Minimize Travel

We wish to site a given number of offices or other service points in a district, so that the mean travelling distance between clients and their nearest office is as low as possible. It is shown that the density of the offices should be proportional to the two-thirds power of the population density. This theoretical result does not take account of local conditions, but it may be made the basis for a study on the ground.     

Splitting multidimensional BSDEs and finding local equilibria

We introduce a new notion of local solution of backward stochastic differential equations (BSDEs) and prove that multidimensional quadratic BSDEs are locally but not globally solvable. Applied in a financial context on optimal investment, our results show that there exist local but no global equilibria when agents take both the absolute and the relative performance compared to their peers into account.     

Cost and Utility: Where Does the Balance Lie for Governments?

An hypothetical, but typical, example of defence procurement is used to illustrate the problems in Government of balancing costs with the services they provide. Difficulties arise because most Government activities cannot be measured in money terms and balanced in a profit and loss account. Commercial techniques for policy appraisal, such as discounting, seem to have limited relevance to the problems of managing departmental budgets where there is no recourse to a banker. A mathematical programme is used to solve the hypothetical problem and demonstrate that simplistic comparisons of the costs and utilities for various policy options yield little information. Good choices can be found, but are not always obvious ones. They are heavily dependent upon the richness of the problem context. Finally, the authors wonder to what extent the problems they ascribe to Government are also faced from time to time by Industry.     

Mean-variance portfolio rebalancing with transaction costs and funding changes

Investment portfolios should be rebalanced to take account of changing market conditions and changes in funding. Standard mean-variance (MV) portfolio selection methods are not appropriate for portfolio rebalancing, as the initial portfolio, change in funding and transaction costs are not considered. A quadratic mixed integer programming portfolio rebalancing model, which takes account of these factors is developed in this paper. The transaction costs in this portfolio rebalancing model are composed of fixed charges and variable costs, including the market impact costs associated with large market trades of individual securities, where these variable transaction costs are assumed to be non-linear functions of traded value. The use of this model is demonstrated and it is shown that when initial portfolio, funding changes and transaction costs are taken into account in portfolio construction and rebalancing, MV efficient portfolios that include risk-free lending do not have the structure expected from portfolio theory.     

Model-based regression clustering for high-dimensional data: application to functional data

Finite mixture regression models are useful for modeling the relationship between response and predictors arising from different subpopulations. In this article, we study high-dimensional predictors and high-dimensional response and propose two procedures to cluster observations according to the link between predictors and the response. To reduce the dimension, we propose to use the Lasso estimator, which takes into account the sparsity and a maximum likelihood estimator penalized by the rank, to take into account the matrix structure. To choose the number of components and the sparsity level, we construct a collection of models, varying those two parameters and we select a model among this collection with a non-asymptotic criterion. We extend these procedures to functional data, where predictors and responses are functions. For this purpose, we use a wavelet-based approach. For each situation, we provide algorithms and apply and evaluate our methods both on simulated and real datasets, to understand how they work in practice.     

Policy analytics need more than a spreadsheet: a case study in funding formulae

This article presents two case studies, concerning the allocation of £Billions by a mechanism communicated via spreadsheet models. It argues that technical analytic skills as well as policy development skills are a vital component of governance. In the UK, Central Government uses funding formulae to distribute money to local service providers. One commonly stated goal of such formulae is equity of service provision. However, given the complexity of public services, together with variations in need, delivery style and the exercise of stakeholder judgement as to which needs should be met and how, such formulae frequently obscure the process by which equity has been taken into account. One policy ‘solution’ to managing such tensions is to seek ‘transparency’. With respect to funding formulae, this commonly involves publishing the underlying data and formulae in spreadsheets. This paper extends the argument that such ‘transparency’ requires an audience that understands the policy assumptions (and related conceptualisations), data sources, methodological approaches and interpretation of results. It demonstrates how the search for policy ‘transparency’ is also met by the technical quality assurance goals that the operational research community would recognise as best practice in the development both of software generally and spreadsheet models specifically. Illustrative examples of complex formulae acting to subvert equity are drawn from the English Fire and Rescue Service and Police Service allocation formulae. In the former, an increase in the amount of deprivation, as measured by one of six indicators, has the perverse effect of decreasing the financial allocation. In the latter, metropolitan areas such as London are found to gain most from the inclusion of variables measuring sparsity. The conclusion from these scenarios is that the steps needed to for technical quality assurance and policy transparency are mutually reinforcing goals, with policy analysts urged to make greater use of technical analytic skills in software development.     

Optimization of unconstrained functions with sparse hessian matrices-newton-type methods

Newton-type methods for unconstrained optimization problems have been very successful when coupled with a modified Cholesky factorization to take into account the possible lack of positive-definiteness in the Hessian matrix. In this paper we discuss the application of these method to large problems that have a sparse Hessian matrix whose sparsity is known a priori. Quite often it is difficult, if not impossible, to obtain an analytic representation of the Hessian matrix. Determining the Hessian matrix by the standard method of finite-differences is costly in terms of gradient evaluations for large problems. Automatic procedures that reduce the number of gradient evaluations by exploiting sparsity are examined and a new procedure is suggested. Once a sparse approximation to the Hessian matrix has been obtained, there still remains the problem of solving a sparse linear system of equations at each iteration. A modified Cholesky factorization can be used. However, many additional nonzeros (fill-in) may be created in the factors, and storage problems may arise. One way of approaching this problem is to ignore fill-in in a systematic manner. Such technique are calledpartial factorization schemes. Various existing partial factorization are analyzed and three new ones are developed. The above algorithms were tested on a set of problems. The overall conclusions were that these methods perfom well in practice.     

An Operational Research Approach to Allocation of Clients to a Certain Class of Service Institutions

A model is developed to explain the allocation of clients to different locations of a certain class of service institutions. It can be used for all types of allocation-problems which have the features: clients are travelling from their home locations to the service places. They can choose among several locations of the institution all of which offer the same services. The clients need constant travelling times or costs, and they cause different waiting times or costs at each location, which are a function of the number of clients choosing that service station. The objective of the individual client is to minimize the total time or cost required.Since exact alogrithms cannot be used because of the large number of variables and the non-linearity of the problem, a special approximation algorithm is developed.The paper presents the results of a study concerning the allocation of cars, which must periodically be checked for traffic safety at official test stations.     

A posteriori boundary control for FEM approximation of elliptic eigenvalue problems

We derive new a posteriori error estimates for the finite element solution of an elliptic eigenvalue problem, which take into account also the effects of the polygonal approximation of the domain. This suggests local error indicators that can be used to drive a procedure handling the mesh refinement together with the approximation of the domain. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 369–388, 2012     

Geographical simulation modelling for the regional planning of oral and maxillofacial surgery across London

Oral and maxillofacial surgery (OMFS) is a recognized surgical specialty, with its foundations in dentistry. The current configuration of OMFS services across London has evolved over time and reflects historical rather than contemporary patterns of care. The creation of a London Health Region in 1998 provided the opportunity for rational planning of hospital services to serve the resident population of London (7.2 million) and beyond, with recent change focusing on London's five sectors that are represented within this planning model. A detailed geographical simulation model has been developed and has enabled planners to consider a number of OMFS service configurations and evaluate their impact on providers, variations in caseload, travelling distances and times for patients, and thus inform consultation over change. The research confirms that any in-patient service rationalization which concentrates care in one designated hub (main centre) per sector, involves a significant increase in caseload for the designated hub. Average travelling distances and times for in-patient admissions also increase significantly. However, it does suggest that current commissioned provision of day surgery patterns may not be well aligned to the geographical distribution of need for services, resulting in many patients travelling further than necessary for day surgery treatment. These may be overcome by sending patients to their local centre, which may be out with their sector of residence.     

Sparse Functional Dynamical Models—A Big Data Approach

Nonlinear dynamical systems are encountered in many areas of social science, natural science, and engineering, and are of particular interest for complex biological processes like the spiking activity of neural ensembles in the brain. To describe such spiking activity, we adapt the Volterra series expansion of an analytic function to account for the point-process nature of multiple inputs and a single output (MISO) in a neural ensemble. Our model describes the transformed spiking probability for the output as the sum of kernel-weighted integrals of the inputs. The kernel functions need to be identified and estimated, and both local sparsity (kernel functions may be zero on part of their support) and global sparsity (some kernel functions may be identically zero) are of interest. The kernel functions are approximated by B-splines and a penalized likelihood-based approach is proposed for estimation. Even for moderately complex brain functionality, the identification and estimation of this sparse functional dynamical model poses major computational challenges, which we address with big data techniques that can be implemented on a single, multi-core server. The performance of the proposed method is demonstrated using neural recordings from the hippocampus of a rat during open field tasks. Supplementary materials for this article are available online.     

Examining the feasibility of using a modelling tool to assess resilience across a health-care system and assist with decisions concerning service reconfiguration

Changes in medical practice, demographic shifts and financial pressures are all examples of factors that may contribute to demand for periodic changes in the configuration of health services. When reconfiguring a service, health planners often take into account projected demand for services, patient access criteria and budgetary constraints (among other things), but typically give little consideration regarding its resilience to deliver services during and after external disruptions to its capability to deliver. In this paper we discuss a study conducted in response to a direct request from the National Health Service (NHS) Resilience Project within the Department of Health to explore the feasibility of assessing resilience across local services within the NHS and developing a computer software tool to assess resilience of different service reconfigurations. We give an account of the modelling process used, including the analytical framework we developed using both optimisation and heuristic methods, and an illustrative example of usage of a prototype software tool. We also highlight the key lessons that emerged during this project, which may be helpful to OR analysts working on similar projects regarding resilience in the public sector.     

A model for setting services on auxiliary bus lines under congestion

In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour). Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona.     

A Long Range Financial Resource Planning Model for a Local Authority

This paper describes a planning model developed for an English local authority to help take into account the constraint of limited financial resources associated with physical planning decisions such as slum clearance, housing development and town centre redevelopment. Physical planning assumptions and decision inputs are incorporated into a model of the local authority environment having as major variables population, housing and employment. Each of the local authority services is represented separately and the majority are functions of these key variables. Service levels, where possible, and expenditures are projected and compared with a total resources projection to determine overall financial viability. Examples of the model's application are given.