Introducing health gains in location-allocation models: A stochastic model for planning the delivery of long-term care

Although the maximization of health is a key objective in health care systems, location-allocation literature has not yet considered this dimension. This study proposes a multi-objective stochastic mathematical programming approach to support the planning of a multi-service network of long-term care (LTC), both in terms of services location and capacity planning. This approach is based on a mixed integer linear programming model with two objectives – the maximization of expected health gains and the minimization of expected costs – with satisficing levels in several dimensions of equity – namely, equity of access, equity of utilization, socioeconomic equity and geographical equity – being imposed as constraints. The augmented ε-constraint method is used to explore the trade-off between these conflicting objectives, with uncertainty in the demand and delivery of care being accounted for. The model is applied to analyze the (re)organization of the LTC network currently operating in the Great Lisbon region in Portugal for the 2014-2016 period. Results show that extending the network of LTC is a cost-effective investment

Predictive and Prescriptive Analytics for Multi-Site Modeling of Frail and Elderly Patient Services

Recent research has highlighted the potential of linking predictive and prescriptive analytics. However, it remains widely unexplored how both paradigms could benefit from one another to address today's major challenges in healthcare. One of these is smarter planning of resource capacities for frail and elderly inpatient wards, addressing the societal challenge of an aging population. Frail and elderly patients typically suffer from multimorbidity and require more care while receiving medical treatment. The aim of this research is to assess how various predictive and prescriptive analytical methods, both individually and in tandem, contribute to addressing the operational challenges within an area of healthcare that is growing in demand. Clinical and demographic patient attributes are gathered from more than 165,000 patient records and used to explain and predict length of stay. To that extent, we employ Classification and Regression Trees (CART) analysis to establish this relationship. On the prescriptive side, deterministic and two-stage stochastic programs are developed to determine how to optimally plan for beds and ward staff with the objective to minimize cost. Furthermore, the two analytical methodologies are linked by generating demand for the prescriptive models using the CART groupings. The results show the linked methodologies provided different but similar results compared to using averages and in doing so, captured a more realistic real-world variation in the patient length of stay. Our research reveals that healthcare managers should consider using predictive and prescriptive models to make more informed decisions. By combining predictive and prescriptive analytics, healthcare managers can move away from relying on averages and incorporate the unique characteristics of their patients to create more robust planning decisions, mitigating risks caused by variations in demand

Planning of mental health services in Portugal under uncertain conditions

The demand for mental health care services is increasing significantly in the World and in Europe. For a country like Portugal, that is one of the countries with the largest prevalence of mental illnesses in Europe and with a level of supply that is not enough for the level of demand that exists nowadays, the urgency to be able to present a mental health care network able to respond to the expected increase in the demand for mental health services is higher and higher. In this thesis, a mathematical programming model - MHCU model - is presented in order to assist the decision makers to plan a mental health network that can respond to the current and future situation of the mental health care in Portugal. The model focus in the Great region of Lisbon and considers the different services provided and multiple objectives relevant in the mental health sector like the minimization of the cost or the maximization of the different equities values that are used in the model. The MHCU model is a stochastic model in order to be able to take into consideration the uncertainty associated with the mental health sector in different parameters like the demand for service and the length of stay in the network for each patient.A procura por serviços da rede de saúde mental está a aumentar significativamente no mundo e na Europa. Para um país como Portugal, que é um dos países com maior número de doentes mentais na Europa e com um nível de oferta deste tipo de serviços que não é suficiente para corresponder ao nível de procura que existe. A urgência de conseguir reformular a rede de saúde mental em Portugal de forma a que consiga responder ao expectável aumento da procura é cada vez maior. Nesta tese, é apresentado um modelo matemático - modelo MHCU - como forma de assistir os responsáveis pela gestão da saúde mental em Portugal a tomar decisões que permitam reformular a rede de saúde mental em Portugal de forma a que esta consiga responder a atual e futura realidade deste sector em Portugal Este modelo é focado na grande região de Lisboa e considera os diferentes serviços e diferentes objetivos que são relevantes para o sector da saúde mental, como minimizar o custo ou maximizar as diferentes equidades que são utilizadas no modelo. O modelo MHCU é um modelo estocástico de forma a que consiga ter em consideração a incerteza que se encontra associada ao sector da saúde mental em diferentes parâmetros como a procura pelos serviços e o tempo de permanencia nos serviços por parte de cada paciente

Promoção de uma oferta equitativa no setor dos cuidados continuados integrados: desenvolvimento de uma abordagem multi-período e multiobjetivo para apoio ao planeamento da oferta de cuidados

Este estudo propõe um modelo de programação matemática multi‑objetivo e multi‑período para apoiar as decisões de planeamento no setor dos cuida‑ dos continuados integrados (CCI). O modelo proposto permite apoiar o pla‑ neamento da oferta de CCI em regime de internamento, tanto em termos de seleção das melhores localizações para esses serviços, como também da capa‑ cidade a instalar, e isto com o propósito de construir uma rede de cuidados mais equitativa. Serão, assim, considerados três objetivos de equidade – equi‑ dade de acesso, equidade geográfica e equidade socioeconómica. Serão tam‑ bém contabilizados os custos, mas na forma de restrições do modelo. A funçãoobjetivo do modelo incorpora estes múltiplos objetivos de equidade através da atribuição de pesos que são obtidos com recurso à metodologia Measuring Attractiveness by a Category‑Based Evaluation TecHnique (MACBETH). A uti‑ lidade do modelo é ilustrada através da sua aplicação a um caso de estudo na região da Grande Lisboa em Portugal.info:eu-repo/semantics/publishedVersio

A Data-Driven Optimization Model for Medical Resource Allocation during the Pandemic

The outbreak of Covid-19 in recent years has once again brought the critical issue of medical resource allocation during a pandemic to the forefront of research and public attention. The dynamic and rapid nature of the pandemic has posed significant challenges in accurately predicting the demands for medical resources and developing effective strategies for their distribution. In this study, we aim to address these challenges by studying the medical resource allocation problem during a pandemic and proposing a data-driven optimization methodology that combines mathematical programming and machine learning techniques. To tackle the problem of demand prediction, we utilize a Long Short-Term Memory(LSTM) model to predict medical resource demand using historical pandemic time series data. Building upon the demand predictions, we develop a linear programming model to optimize the allocation of medical resources. The objective is to maximize the total accessibility of hospitals within each region while also ensuring a balanced distribution of accessibility across all regions. We also conducted a case study on the application of this framework to the Quebec, Canada, pandemic hospitalization case scenarios. The dataset we utilized consisted of hospitalization case numbers from 16 regions in Quebec, along with the geographical locations of 15 regions and their corresponding healthcare facilities. The prediction performance is evaluated by mean absolute error(MAE) and root mean square error(RMSE), which yielded average values of 3.079 and 5.491, respectively. And after optimizing, the total accessibility of all regions is 4.503. The results indicate the effectiveness of our proposed method in accurately predicting future hospitalization numbers and determining the necessary increase in bed capacity for each region, showcasing its potential to assist in resource planning and allocation during a pandemic

SOLVING STOCHASTIC TRANSPORTATION ELECTRICITY PROBLEM WITH FUZZY INFORMATION ON PROBABILITY DISTRIBUTION USING MATLAB PROGRAM

This study focuses on MATLAB code programs of the entire stages of solving Stochastic Transportation Linear Programming Problems with Fuzzy Uncertainty Information on Probability Distribution Space (STLPPFI) with its algorithm outlines. A MATLAB code program of STLPPFI problem solver with algorithm outlines are proposed to solve STLPPFI model problems, and it utilizes many concepts as Alpha-Cut technique, Truth Degrees technique, Linear Fuzzy Membership Function (LFMF), Trapezoidal Fuzzy Number , Triangular Fuzzy Number , Linear Fuzzy Ranking Function (LFRF), Expectation Weighted Summation technique (EWS) and analyzing cases via second condition test of alpha-cut technique. The STLPPFI problem solver is utlized to convert STLPPFI into its corresponding equivalent Deterministic Transportation Linear Programming Problem (DTLPP) via defuzzifying from fuzziness on probability distribution space and derandomization randomness of problem formulation respectively. In addition, Dual-Simplex algorithm method with Vogel Approximation Algorithm Method (VAM) are used to obtain optimal solution from DTLPP. All MATLAB code programs with their proposed algorithm outlines are new except Dual-Simplex and VAM. The MATLAB code program of STLPPFI problem solver are more efficient along with a numerical example on electricity field illustrating practicability of this proposed MATLAB code program with its algorithm. Finally, the solution procedure illustrates the MATLAB code program of the proposed method is practical and applicable in the fields of energy and industry as it facilitates the method of transforming the energy at the lowest cost, least time running and is commercially applicable. Comparative comments are provided between Dual-Simplex and VAM in solution process

Demand and Capacity Modelling of Acute Services Using Simulation and Optimization Techniques

The level of difficulty that hospital management have been experiencing over the past decade in terms of balancing demand and capacity needs has been at an unprecedented level in the UK. Due to shortage of capacity, hospitals are unable to treat patients, and in some cases, patients are transferred to other hospitals, outpatient referrals are delayed, and accident and emergency (A&E) waiting times are prolonged. So, it’s time to do things differently, because the current status quo is not an option. A whole hospital level decision support system (DSS) was developed to assess and respond to the needs of local populations. The model integrates every component of a hospital (including A&E, all outpatient and inpatient specialties) to aid with efficient and effective use of scarce resources. An individual service or a specialty cannot be assumed to be independent, they are all interconnected. It is clear from the literature that this level of generic hospital simulation model has never been developed before (so this is an innovative DSS). Using the Hospital Episode Statistics and local datasets, 768 forecasting models for the 28 outpatient and inpatient specialties are developed (to capture demand). Within this context, a variety of forecasting models (i.e. ARIMA, exponential smoothing, stepwise linear regression and STLF) for each specialty of outpatient and inpatient including the A&E department were developed. The best forecasting methods and periods were selected by comparing 4 forecasting methods and 3 periods (i.e. daily, weekly and monthly) according to forecast accuracy values calculated by the mean absolute scaled error (MASE). Demand forecasts were then used as an input into the simulation model for the entire hospital (all specialties). The generic hospital simulation model was developed by taking into account all specialties and interactions amongst the A&E, outpatient and inpatient specialties. Six hundred observed frequency distributions were established for the simulation model. All distributions used in the model were based on age groups. Using other inputs (i.e. financial inputs, number of follow ups, etc.), the hospital was therefore modelled to measure key output metrics in strategic planning. This decision support system eliminates the deficiencies of the current and past studies around modelling hospitals within a single framework. A new output metric which is called ‘demand coverage ratio’ was developed to measure the percentage of patients who are admitted and discharged with available resources of the associated specialty. In addition, a full factorial experimental design with 4 factors (A&E, elective and non-elective admissions and outpatient attendance) at 2 levels (possible 5% and 10% demand increases) was carried out in order to investigate the effects of demand increases on the key outputs (i.e. demand coverage ratio, bed occupancy rate and total revenue). As a result, each factor is found to affect total revenue, as well as the interaction between elective and non-elective admissions. The demand coverage ratio is affected by the changes in outpatient demands as well as A&E arrivals and non-elective admissions. In addition, the A&E arrivals, non-elective admissions and elective admissions are most important for bed occupancy rates, respectively. After an exhaustive review of the literature we notice that an entire hospital model has never been developed that combines forecasting, simulation and optimization techniques. A linear optimization model was developed to estimate the required bed capacity and staff needs of a mid-size hospital in England (using essential outputs from forecasting and forecasting-simulation) for each inpatient elective and non-elective specialty. In conclusion, these results will bring a different perspective to key decision makers with a decision support tool for short and long term strategic planning to make rational and realistic plans. This hospital decision support system can become a crucial instrument for decision makers for efficient service in hospitals in England and other parts of the world

Multi-objective optimisation under deep uncertainty

Most of the decisions in real-life problems need to be made in the absence of complete knowledge about the consequences of the decision. Furthermore, in some of these problems, the probability and/or the number of different outcomes are also unknown (named deep uncertainty). Therefore, all the probability-based approaches (such as stochastic programming) are unable to address these problems. On the other hand, involving various stakeholders with different (possibly conflicting) criteria in the problems brings additional complexity. The main aim and primary motivation for writing this thesis have been to deal with deep uncertainty in Multi-Criteria Decision-Making (MCDM) problems, especially with long-term decision-making processes such as strategic planning problems. To achieve these aims, we first introduced a two-stage scenario-based structure for dealing with deep uncertainty in Multi-Objective Optimisation (MOO)/MCDM problems. The proposed method extends the concept of two-stage stochastic programming with recourse to address the capability of dealing with deep uncertainty through the use of scenario planning rather than statistical expectation. In this research, scenarios are used as a dimension of preference (a component of what we term the meta-criteria) to avoid problems relating to the assessment and use of probabilities under deep uncertainty. Such scenario-based thinking involved a multi-objective representation of performance under different future conditions as an alternative to expectation, which fitted naturally into the broader multi-objective problem context. To aggregate these objectives of the problem, the Generalised Goal Programming (GGP) approach is used. Due to the capability of this approach to handle large numbers of objective functions/criteria, the GGP is significantly useful in the proposed framework. Identifying the goals for each criterion is the only action that the Decision Maker (DM) needs to take without needing to investigate the trade-offs between different criteria. Moreover, the proposed two-stage framework has been expanded to a three-stage structure and a moving horizon concept to handle the existing deep uncertainty in more complex problems, such as strategic planning. As strategic planning problems will deal with more than two stages and real processes are continuous, it follows that more scenarios will continuously be unfolded that may or may not be periodic. "Stages", in this study, are artificial constructs to structure thinking of an indefinite future. A suitable length of the planning window and stages in the proposed methodology are also investigated. Philosophically, the proposed two-stage structure always plans and looks one step ahead while the three-stage structure considers the conditions and consequences of two upcoming steps in advance, which fits well with our primary objective. Ignoring long-term consequences of decisions as well as likely conditions could not be a robust strategic approach. Therefore, generally, by utilising the three-stage structure, we may expect a more robust decision than with a two-stage representation. Modelling time preferences in multi-stage problems have also been introduced to solve the fundamental problem of comparability of the two proposed methodologies because of the different time horizon, as the two-stage model is ignorant of the third stage. This concept has been applied by a differential weighting in models. Importance weights, then, are primarily used to make the two- and three-stage models more directly comparable, and only secondarily as a measure of risk preference. Differential weighting can help us apply further preferences in the model and lead it to generate more preferred solutions. Expanding the proposed structure to the problems with more than three stages which usually have too many meta-scenarios may lead us to a computationally expensive model that cannot easily be solved, if it all. Moreover, extension to a planning horizon that too long will not result in an exact plan, as nothing in nature is predictable to this level of detail, and we are always surprised by new events. Therefore, beyond the expensive computation in a multi-stage structure for more than three stages, defining plausible scenarios for far stages is not logical and even impossible. Therefore, the moving horizon models in a T-stage planning window has been introduced. To be able to run and evaluate the proposed two- and three-stage moving horizon frameworks in longer planning horizons, we need to identify all plausible meta-scenarios. However, with the assumption of deep uncertainty, this identification is almost impossible. On the other hand, even with a finite set of plausible meta-scenarios, comparing and computing the results in all plausible meta-scenarios are hardly possible, because the size of the model grows exponentially by raising the length of the planning horizon. Furthermore, analysis of the solutions requires hundreds or thousands of multi-objective comparisons that are not easily conceivable, if it all. These issues motivated us to perform a Simulation-Optimisation study to simulate the reasonable number of meta-scenarios and enable evaluation, comparison and analysis of the proposed methods for the problems with a T-stage planning horizon. In this Simulation-Optimisation study, we started by setting the current scenario, the scenario that we were facing it at the beginning of the period. Then, the optimisation model was run to get the first-stage decisions which can implement immediately. Thereafter, the next scenario was randomly generated by using Monte Carlo simulation methods. In deep uncertainty, we do not have enough knowledge about the likelihood of plausible scenarios nor the probability space; therefore, to simulate the deep uncertainty we shall not use anything of scenario likelihoods in the decision models. The two- and three-stage Simulation-Optimisation algorithms were also proposed. A comparison of these algorithms showed that the solutions to the two-stage moving horizon model are feasible to the other pattern (three-stage). Also, the optimal solution to the three-stage moving horizon model is not dominated by any solutions of the other model. So, with no doubt, it must find better, or at least the same, goal achievement compared to the two-stage moving horizon model. Accordingly, the three-stage moving horizon model evaluates and compares the optimal solution of the corresponding two-stage moving horizon model to the other feasible solutions, then, if it selects anything else it must either be better in goal achievement or be robust in some future scenarios or a combination of both. However, the cost of these supremacies must be considered (as it may lead us to a computationally expensive problem), and the efficiency of applying this structure needs to be approved. Obviously, using the three-stage structure in comparison with the two-stage approach brings more complexity and calculations to the models. It is also shown that the solutions to the three-stage model would be preferred to the solutions provided by the two-stage model under most circumstances. However, by the "efficiency" of the three-stage framework in our context, we want to know that whether utilising this approach and its solutions is worth the expense of the additional complexity and computation. The experiments in this study showed that the three-stage model has advantages under most circumstances(meta-scenarios), but that the gains are quite modest. This issue is frequently observed when comparing these methods in problems with a short-term (say less than five stages) planning window. Nevertheless, analysis of the length of the planning horizon and its effects on the solutions to the proposed frameworks indicate that utilising the three-stage models is more efficient for longer periods because the differences between the solutions of the two proposed structures increase by any iteration of the algorithms in moving horizon models. Moreover, during the long-term calculations, we noticed that the two-stage algorithm failed to find the optimal solutions for some iterations while the three-stage algorithm found the optimal value in all cases. Thus, it seems that for the planning horizons with more than ten stages, the efficiency of the three-stage model be may worth the expenses of the complexity and computation. Nevertheless, if the DM prefers to not use the three-stage structure because of the complexity and/or calculations, the two-stage moving horizon model can provide us with some reasonable solutions, although they might not be as good as the solutions generated by a three-stage framework. Finally, to examine the power of the proposed methodology in real cases, the proposed two-stage structure was applied in the sugarcane industry to analyse the whole infrastructure of the sugar and bioethanol Supply Chain (SC) in such a way that all economics (Max profit), environmental (Min CO₂), and social benefits (Max job-creations) were optimised under six key uncertainties, namely sugarcane yield, ethanol and refined sugar demands and prices, and the exchange rate. Moreover, one of the critical design questions - that is, to design the optimal number and technologies as well as the best place(s) for setting up the ethanol plant(s) - was also addressed in this study. The general model for the strategic planning of sugar- bioethanol supply chains (SC) under deep uncertainty was formulated and also examined in a case study based on the South African Sugar Industry. This problem is formulated as a Scenario-Based Mixed-Integer Two-Stage Multi-Objective Optimisation problem and solved by utilising the Generalised Goal Programming Approach. To sum up, the proposed methodology is, to the best of our knowledge, a novel approach that can successfully handle the deep uncertainty in MCDM/MOO problems with both short- and long-term planning horizons. It is generic enough to use in all MCDM problems under deep uncertainty. However, in this thesis, the proposed structure only applied in Linear Problems (LP). Non-linear problems would be an important direction for future research. Different solution methods may also need to be examined to solve the non-linear problems. Moreover, many other real-world optimisation and decision-making applications can be considered to examine the proposed method in the future

A multiobjective stochastic program for hospital bed planning

In this paper, we study hospital bed capacity management for a set of existing hospitals when the demand for beds is random. We propose a multiobjective stochastic program model to assign beds to hospital departments. We consider three objective functions to be minimized, which are the cost of creation and management of new beds and the number of nurses and physicians working in these hospitals, subject to demand satisfaction of three kinds of health-care specialities. A certainty equivalent program was derived based on a mixture between the chance constrained approach, the recourse approach and the goal programming approach. Empirical results using real data from 157 Tunisian national hospitals are reported.