On the use of multi-state multi-census techniques for modelling the survival of elderly people in institutional long-term care

^** Corresponding author. Email: chausst{at}wmin.ac.uk A good estimate of the length of stay (LOS) of elderly peoplein institutional long-term care (ILTC) is essential to bothcare providers (care home owners) and purchasers (local authoritiesin the UK) in order to forecast their resource availabilityand future requirements. Existing methods usually rely on cohortdata, which needs to be collected on a continuous basis forseveral years and are often not available electronically. Inthis paper we develop an approach based on multi-census datato fit a Markov model in continuous-time for the LOS of elderlypeople in ILTC (residential and nursing care). We use 3 yearplacement data provided by London Borough of Merton Social Servicesto compare the estimates of the model parameters obtained usingmulti-census data with those derived from cohort data, henceto validate the multi-census approach in this context. The implicationsof the proposed multi-census approach and its advantages inthe context of long-term care planning are discussed.     

Administrative days in acute care facilities: a queueing-analytic approach.

After acute care services are no longer required, a patient in an acute care hospital often must remain there while he or she awaits the provision of extended care services by a nursing home, through social support services, or by a home health care service. This waiting period is often referred to as "administrative days" because the time is spent in the acute facility not for medical reasons, but rather for administrative reasons. In this paper we use a queueing-analytic approach to describe the process by which patients await placement. We model the situation using a state-dependent placement rate for patients backed up in the acute care facility. We compare our model results with data collected from a convenience sample of 7 hospitals in New York State. We conclude with a discussion of the policy implications of our models.     

Planning Aids for London Borough Housing Committee

The process by which a London Borough makes decisions relating to its provision and management of council housing is described, and the problems of integrated policy planning in a system of decentralized control stated. Optimality of a housing strategy can only be related to the subjective and political aims of the housing committee, so optimization techniques are replaced by a decision evaluating model. This model has been used by the chairman of the committee and officers of the Borough to take decisions upon the Borough's medium range building plan with adequate recognition of effects upon the financial and social responsibilities of the committee. A critique points out the directions in which the model should be developed, and indications are given of the way in which these developments might be implemented.     

A matheuristic algorithm for stochastic home health care planning

Efficient human resource planning is the cornerstone of designing an effective home health care system. Human resource planning in home health care system consists of decisions on districting/zoning, staff dimensioning, resource assignment, scheduling, and routing. In this study, a two-stage stochastic mixed integer model is proposed that considers these decisions simultaneously. In the planning phase of a home health care system, the main uncertain parameters are travel and service times. Hence, the proposed model takes into account the uncertainty in travel and service times. Districting and staff dimensioning are defined as the first stage decisions, and assignment, scheduling, and routing are considered as the second stage decisions. A novel algorithm is developed for solving the proposed model. The algorithm consists of four phases and relies on a matheuristic-based method that calls on various mixed integer models. In addition, an algorithm based on the progressive hedging and Frank and Wolf algorithms is developed to reduce the computational time of the second phase of the proposed matheuristic algorithm. The efficiency and accuracy of the proposed algorithm are tested through several numerical experiments. The results prove the ability of the algorithm to solve large instances.     

Newsvendor-type models with decision-dependent uncertainty

Models for decision-making under uncertainty use probability distributions to represent variables whose values are unknown when the decisions are to be made. Often the distributions are estimated with observed data. Sometimes these variables depend on the decisions but the dependence is ignored in the decision maker??s model, that is, the decision maker models these variables as having an exogenous probability distribution independent of the decisions, whereas the probability distribution of the variables actually depend on the decisions. It has been shown in the context of revenue management problems that such modeling error can lead to systematic deterioration of decisions as the decision maker attempts to refine the estimates with observed data. Many questions remain to be addressed. Motivated by the revenue management, newsvendor, and a number of other problems, we consider a setting in which the optimal decision for the decision maker??s model is given by a particular quantile of the estimated distribution, and the empirical distribution is used as estimator. We give conditions under which the estimation and control process converges, and show that although in the limit the decision maker??s model appears to be consistent with the observed data, the modeling error can cause the limit decisions to be arbitrarily bad.     

To borrow or insure? Long term care costs and the impact of housing

We assess the impact of housing, the availability of reverse mortgages and long-term care (LTC) insurance on a retiree’s optimal portfolio choice and consumption decisions using a multi-period life cycle model that takes into consideration individual longevity risk, health shocks and house price risk. We determine how much an individual should borrow against their home equity and how much to insure health care costs with LTC insurance. We introduce an endogenous grid method, along with a regression based approach, to improve computational efficiency and avoid the curse of dimensionality. Our results confirm that borrowing against home equity provides higher consumption in earlier years and longevity insurance. LTC insurance transfers wealth from healthy states to disabled states, but reduces early consumption because of the payment of insurance premiums. Housing is an illiquid asset that is important in meeting bequest motives, and it reduces the demand for LTC insurance for the wealthy. We show that the highest welfare benefits come from combining a reverse mortgage with LTC insurance because of strong complementary effects between them. This result highlights the benefits of innovative products that bundle these two products together.     

Deployment of rural health facilities in a developing country

This study describes the problem of finding suitable sites for additional health facilities in a rural area in Bangladesh. The objective is to improve the accessibility of people to the health care system given the existing set of facilities. As is frequently the case in developing countries, activities designed to develop and improve differing sectors of the infrastructure are poorly integrated and ill-coordinated. As a result, decision-makers may make independent and individual decisions about locating new service facilities. Often, as has been the case in Bangladesh, these decisions are taken at a relatively low level, by officers of local government or by elected leaders in a region, or by a combination of these. In the absence of any formal analysis and generation of alternatives, the final decision may be made on political or pragmatic considerations. As a result the decisions are often far from optimal. Ultimately, better health care will enhance many sectors of a regional economy, and so the decision about where to invest in new or better resources is important for reasons over and above that of providing health care for the population. In this paper, the role of location-allocation modelling in developing countries is considered, and the specific Bangladeshi problem is considered as a maximal covering location problem which is solved by an efficient heuristic method.     

Raising the bar: strategic multi-criteria decision analysis

This paper discusses the use of multi-criteria decision analysis for supporting strategic decision making in organisations. It begins by exploring the notions of strategic decisions and the strategic decision-making process. We suggest that structuring strategic objectives, dealing with high levels of uncertainty about the future, as well as considering the interconnectedness of strategic options and their long-term consequences are key aspects of strategic decision making support. We then consider the discursive nature of the processes within which strategic decisions are created and negotiated. Our exploration of these concepts leads us to propose a number of adaptations to the standard multi-criteria decision analysis approach, if it were to provide effective strategic decision support, particularly in strategy workshops. We make suggestions on how to implement these proposals, and illustrate their potential with examples drawn from real-world interventions in which we have provided strategic decision support.     

An integrated optimization model for managing the global value chain of a chemical commodities manufacturer

The realization of supply chain management concepts goes along with the introduction of comprehensive software systems for supporting decisions at the strategic, tactical, and operational planning level. Moreover, in industry the focus has shifted from a pure logistics-oriented view towards the integration of pricing and revenue issues into cross-functional value chain planning models. This paper presents a practical decision support tool for global value chain planning in the production of chemical commodities. The proposed linear optimization model consists of various modules that reflect sales, distribution, production, and procurement activities within a company-internal value chain. The objective of the model is to maximize profit by coordinating all activities within the supply chain. The model formulation is related to a real industry case. It is shown how the model can be used to support decision making from sales to procurement by volume and value.     

Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

The Definition of Parliamentary Constituencies in Great Britain: A Computer-Based Information System

The periodic reviews of parliamentary constituencies in Great Britain require the Parliamentary Boundary Commission in each country to propose any necessary changes in order that constituencies shall be as near the electoral quota (i.e. the average electorate per constituency) as possible, within certain constraints. For each unit (county, London borough etc.) with which they work, the number of potential solutions to their problem is very large. This paper describes a computer program that can be used to inform the Commission about all those solutions, so improving the information base from which they select the new set of constituencies.     

Is It Better to Forget? Stimulus-Response, Prediction, and the Weight of Past Experience in a Fast-Paced Bargaining Task

Decision makers in dynamic environments such as air traffic control, firefighting, and call center operations adapt in real-time using outcome feedback. Understanding this adaptation is important for influencing and improving the decisions made. Recently, stimulus-response (S-R) learning models have been proposed as explanations for decision makers' adaptation. S-R models hypothesize that decision makers choose an action option based on their anticipation of its success. Decision makers learn by accumulating evidence over action options and combining that evidence with prior expectations. This study examines a standard S-R model and a simple variation of this model, in which past experience may receive an extremely low weight, as explanations for decision makers' adaptation in an evolving Internet-based bargaining environment. In Experiment 1, decision makers are taught to predict behavior in a bargaining task that follows rules that may be the opposite of, congruent to, or unrelated to a second task in which they must choose the deal terms they will offer. Both models provide a good account of the prediction task. However, only the second model, in which decision makers heavily discount all but the most recent past experience, provides a good account of subsequent behavior in the second task. To test whether Experiment 1 artificially related choice behavior and prediction, a second experiment examines both models' predictions concerning the effects of bargaining experience on subsequent prediction. In this study, decision models where long-term experience plays a dominating role do not appear to provide adequate explanations of decision makers' adaptation to their opponent's changing response behavior.     

Multi-objective modeling for engineering applications:DIDASN++ system

Modeling and simulation of various physical, technical, environmental or socioeconomic processes is often a preliminary step for using the resulting models in computer-aided design or decision support. In engineering computer-aided design, the decisions of the designer might be supported by multicriteria optimization - which in this case should not be considered as a tool for supporting the final choice of the design, but much more as a tool for helping in a flexible analysis of various design options or even various modeling and simulation options. The paper shows how multicriteria optimization techniques can be used for multi-objective analysis of a model from the beginning stages of model construction. With the advancement of computing technology and the methodology of decision support, it is now possible to revise this way basic approaches to modeling and simulation. Various formats of defining nonlinear and time-discrete models are discussed together with related problems of inverse and softly constrained multi-objective simulation. Algebraic differentiation and sensitivity analysis, fuzzy set representation of modeler preferences are also useful techniques of multi-objective modeling. Such techniques are illustrated by engineering applications of a software package DIDASN++ in mechanics and automatic control.     

Correct or incorrect application of CAPM? Correct or incorrect decisions with CAPM?

This paper focuses on inconsistencies arising from the use of NPV and CAPM for capital budgeting. It shows that: (i) CAPM capital budgeting decision-making based on disequilibrium NPV is deductively inferred by the capital asset pricing model, (ii) the use of the disequilibrium NPV is widespread in finance both as a decision rule and as a valuation tool, (iii) the disequilibrium NPV does not guarantee additivity nor consistency with arbitrage pricing, so that it is unreliable for valuation, (iv) Magni’s [Magni, C.A., 2002. Investment decisions in the theory of finance: Some antinomies and inconsistencies. European Journal of Operational Research 137, 206–217; Magni, C.A., 2007a. Project valuation and investment decisions: CAPM versus arbitrage. Applied Financial Economics Letters 3 (2), 137–140] criticism of the NPV criterion refers to the disequilibrium NPV, and De Reyck’s [De Reyck, B., 2005. On investment decisions in the theory of finance: Some antinomies and inconsistencies. European of Operational Research 161, 499–504] project valuation method, on the basis of which Magni’s criticism to NPV is objected, leaves decision makers open to arbitrage losses and incorrect decisions.     

DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.     

Learning and transfer in dynamic decision environments

An important aspect of learning is the ability to transfer knowledge to new contexts. However, in dynamic decision tasks, such as bargaining, firefighting, and process control, where decision makers must make repeated decisions under time pressure and outcome feedback may relate to any of a number of decisions, such transfer has proven elusive. This paper proposes a two-stage connectionist model which hypothesizes that decision makers learn to identify categories of evidence requiring similar decisions as they perform in dynamic environments. The model suggests conditions under which decision makers will be able to use this ability to help them in novel situations. These predictions are compared against those of a one-stage decision model that does not learn evidence categories, as is common in many current theories of repeated decision making. Both models' predictions are then tested against the performance of decision makers in an Internet bargaining task. Both models correctly predict aspects of decision makers' learning under different interventions. The two-stage model provides closer fits to decision maker performance in a new, related bargaining task and accounts for important features of higher-performing decision makers' learning. Although frequently omitted in recent accounts of repeated decision making, the processes of evidence category formation described by the two-stage model appear critical in understanding the extent to which decision makers learn from feedback in dynamic tasks. Faison (Bud) Gibson is an Assistant Professor at College of Business, Eastern Michigan University. He has extensive experience developing and empirically testing models of decision behavior in dynamic decision environments.     

Mental representations of important real-life decisions

Two studies investigated how decision makers characterize alternatives in important real-life decisions, which they themselves had made (to leave a partner, to choose an education and to choose a home). First, the participants indicated a very high degree of involvement in the decisions studied and about half of the participants gave maximum involvement ratings for the partner decision. Second, the results showed that concepts that are essential in most decision theories, such as, consequence, probability and value were important characteristics of the decisions. Third, emotion, positive and negative affect were also important characteristics. Fourth, value and emotion were uncorrelated. Fifth, the patterns of characteristics of decisions made in the past did not differ markedly from the characteristics given to future decisions. Principal component analyses were performed on the ratings of applicability of the different characteristics across participants for each decision situation. Three factors were extracted. There was one factor for positive affect/emotions and another factor for negative affect/emotions verified in oblique solutions. Thus, different scales are needed to represent emotion/affect components (and not bipolar scales) in real-life important decisions. The third factor represented the way in which a decision was represented (moving pictures dialogue etc.). An analysis restricted to the participants who rated 100% involvement showed an additional fourth factor with “what others would think”, “similar situations”, “values” and “money” as the most prominent characteristics. This points to the importance of controlling for participant involvement in studies of human decision making to enable generalizations to real-life decisions.     

Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

An exact approach for relating recovering surgical patient workload to the master surgical schedule

No other department influences the workload of a hospital more than the Department of Surgery and in particular, the activities in the operating room. These activities are governed by the master surgical schedule (MSS), which states which patient types receive surgery on which day. In this paper, we describe an analytical approach to project the workload for downstream departments based on this MSS. Specifically, the ward occupancy distributions, patient admission/discharge distributions and the distributions for ongoing interventions/treatments are computed. Recovering after surgery requires the support of multiple departments, such as nursing, physiotherapy, rehabilitation and long-term care. With our model, managers from these departments can determine their workload by aggregating tasks associated with recovering surgical patients. The model, which supported the development of a new MSS at the Netherlands Cancer Institute–Antoni van Leeuwenhoek Hospital, provides the foundation for a decision support tool to relate downstream hospital departments to the operating room.     

A fuzzy set approach to financial ratio analysis

Ratio analysis is a useful tool of financial analysis. Nevertheless, the traditional ratio analysis is under several constraints: over-empiricist, certainty, standard of reference not useful in all circumstances, etc. Recent researches have pointed out that to overcome those constraints formal decision models can be applied. In this article, fuzzy set theory is applied to ratio analysis with respect to one of the major management problems: liquidity. This approach enables the decision maker to include his own experience and any other type of information to that obtained by the ratio. If all the possible decisions are uniform in time, it is possible to adopt them by the decision maker in each period of analysis in a programmed form through a simple model inputs combination. The approach provided in this article can be extended to other ratio or ratio sets.