Fostering long-term care planning in practice: extending objectives and advancing stochastic treatment within location-allocation modelling

Abstract Many countries are currently concerned with the planning of networks of Long-Term Care (LTC), which requires considering a multiplicity of policy objectives and anticipating the impact of key uncertainties. Nevertheless, location-allocation literature has not been modelling key health policy objectives, and the use of stochastic planning models entails low practical usability due to prohibitive computational times. This study tackles these issues by proposing an approach that supports the reorganization of LTC networks (in terms of services location, capacity planning and patients allocation) while exploring different health policy objectives and considering uncertainty within a reasonable computational time, leading to the development of a stochastic multi-objective mathematical programming model – the LTCNetPlanner. The LTCNetPlanner builds upon health economics and policy concepts to model the maximization of health and wellbeing together with cost- and equity-related objectives within location-allocation literature. Concerning uncertainty, a scenario-based stochastic approach is developed and alternative scenario reduction methods enabling a faster model resolution are explored within the LTCNetPlanner. Specifically, it is proposed a novel Morphol-KMG method able to reduce the number of scenarios while accounting for experts’ knowledge. A case study in the Great Lisbon region is explored, showing the usefulness of the proposed scenario reduction method to reduce computational times, and how planning decisions change when health and wellbeing benefits are considered.

[1]  João Carlos Lourenço,et al.  A Socio-technical Approach for Group Decision Support in Public Strategic Planning: The Pernambuco PPA Case , 2014 .

[2]  Hossein Zolfagharinia,et al.  Considering short-term and long-term uncertainties in location and capacity planning of public healthcare facilities , 2020, Eur. J. Oper. Res..

[3]  Angel Ruiz,et al.  A stochastic approach for designing two-tiered emergency medical service systems , 2018 .

[4]  Shijin Wang,et al.  Efficient methods for a bi-objective nursing home location and allocation problem: A case study , 2018, Appl. Soft Comput..

[5]  Peter Kall,et al.  Stochastic Programming , 1995 .

[6]  Zaid Chalabi,et al.  Uncertainty and value of information when allocating resources within and between healthcare programmes , 2008, Eur. J. Oper. Res..

[7]  Mark S. Daskin,et al.  Strategic facility location: A review , 1998, Eur. J. Oper. Res..

[8]  João Gregório,et al.  A scenario-planning approach to human resources for health: the case of community pharmacists in Portugal , 2014, Human Resources for Health.

[9]  Sara R. Machado,et al.  Portugal. Health system review. , 2011, Health systems in transition.

[10]  P. Beraldi,et al.  Enhancing community based health programs in Iran: a multi-objective location-allocation model , 2017, Health care management science.

[11]  Stefan Nickel,et al.  Location Problems in Healthcare , 2015 .

[12]  M. Kruk,et al.  Assessing health system performance in developing countries: a review of the literature. , 2008, Health policy.

[13]  Hark Hwang,et al.  The design of capacitated facility networks for long term care service , 2015, Comput. Ind. Eng..

[14]  Gonçalo Santinha,et al.  Policy integration: placing the spatial dimension in the health agenda. Evidence from Portugal , 2016 .

[15]  Mónica Duarte Oliveira,et al.  Organizing hospitals into networks: a hierarchical and multiservice model to define location, supply and referrals in planned hospital systems , 2012, OR Spectr..

[16]  Stefan Nickel,et al.  An integrated approach for planning a long-term care network with uncertainty, strategic policy and equity considerations , 2015, Eur. J. Oper. Res..

[17]  Kurt M. Bretthauer,et al.  Locating specialized service capacity in a multi-hospital network , 2011, Eur. J. Oper. Res..

[18]  Reza Tavakkoli-Moghaddam,et al.  A Stochastic Optimization Approach to a Location-Allocation Problem of Organ Transplant Centers , 2018 .

[19]  Zorica Stanimirovic,et al.  Hybrid metaheuristic method for determining locations for long-term health care facilities , 2015, Ann. Oper. Res..

[20]  Abdur Rais,et al.  Operations Research in Healthcare: a survey , 2011, Int. Trans. Oper. Res..

[21]  Mir Saman Pishvaee,et al.  Accessible, stable, and equitable health service network redesign: A robust mixed possibilistic-flexible approach , 2018 .

[22]  Mohamad Saeed Jabalameli,et al.  Modeling the budget-constrained dynamic uncapacitated facility location-network design problem and solving it via two efficient heuristics: A case study of health care , 2013, Math. Comput. Model..

[23]  Werner Römisch,et al.  A note on scenario reduction for two-stage stochastic programs , 2007, Oper. Res. Lett..

[24]  M. Oliveira,et al.  Valuing health states: is the MACBETH approach useful for valuing EQ-5D-3L health states? , 2018, Health and Quality of Life Outcomes.

[25]  Lisa R. Findley,et al.  United Kingdom: Health System Review. , 2015, Health systems in transition.

[26]  Kannan Govindan,et al.  Investigating risk and robustness measures for supply chain network design under demand uncertainty: A case study of glass supply chain , 2017 .

[27]  Ignacio E. Grossmann,et al.  Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty , 2015, Comput. Chem. Eng..

[28]  G. Bevan,et al.  Modelling the redistribution of hospital supply to achieve equity taking account of patient's behaviour , 2006, Health care management science.

[29]  David K. Smith,et al.  Use of location-allocation models in health service development planning in developing nations , 2000, Eur. J. Oper. Res..

[30]  Siddhartha S. Syam,et al.  A location–allocation model for service providers with application to not-for-profit health care organizations , 2010 .

[31]  Martin Kunc,et al.  Strategic workforce planning in healthcare: A multi-methodology approach , 2017, Eur. J. Oper. Res..

[32]  Susana Relvas,et al.  Designing Integrated Biorefineries Supply Chain: Combining Stochastic Programming Models with Scenario Reduction Methods , 2017 .

[33]  George Mavrotas,et al.  Effective implementation of the epsilon-constraint method in Multi-Objective Mathematical Programming problems , 2009, Appl. Math. Comput..

[34]  P. Kind,et al.  Measuring the Benefits of Healthcare: DALYs and QALYs – Does the Choice of Measure Matter? A Case Study of Two Preventive Interventions , 2017, International journal of health policy and management.

[35]  L. Phillips,et al.  Faciliated Work Groups: Theory and Practice , 1993 .

[36]  A. Barbosa‐Póvoa,et al.  Moving towards an equitable long-term care network: A multi-objective and multi-period planning approach☆ , 2016 .

[37]  Nils Löhndorf,et al.  An empirical analysis of scenario generation methods for stochastic optimization , 2016, Eur. J. Oper. Res..

[38]  Xiuli Qu,et al.  Applying Scenario Reduction Heuristics in Stochastic Programming for Phlebotomist Scheduling , 2014 .

[39]  Stefan Nickel,et al.  Modeling the demand for long-term care services under uncertain information , 2012, Health Care Management Science.

[40]  Muhammad Amer,et al.  A review of scenario planning , 2013 .

[41]  Vincent A. Knight,et al.  Ambulance allocation for maximal survival with heterogeneous outcome measures , 2012 .

[42]  James C. Benneyan,et al.  Specialty care single and multi-period location–allocation models within the Veterans Health Administration , 2012 .

[43]  Zhe Yan,et al.  Scenario tree reduction methods through clustering nodes , 2018, Comput. Chem. Eng..

[44]  Werner Römisch,et al.  Scenario Reduction Algorithms in Stochastic Programming , 2003, Comput. Optim. Appl..

[45]  Carlos A. Bana e Costa,et al.  Transparent prioritisation, budgeting and resource allocation with multi-criteria decision analysis and decision conferencing , 2007, Ann. Oper. Res..

[46]  Jing Luo,et al.  Two-Step Optimization for Spatial Accessibility Improvement: A Case Study of Health Care Planning in Rural China , 2017, BioMed research international.

[47]  H K Smith,et al.  Bicriteria efficiency/equity hierarchical location models for public service application , 2013, J. Oper. Res. Soc..

[48]  Feng Lin,et al.  Capacity Planning for Publicly Funded Community Based Long-Term Care Services , 2012 .

[49]  Long Term Care in Health Services , 2008 .

[50]  Shaobo Liu,et al.  A multi-objective optimization approach for health-care facility location-allocation problems in highly developed cities such as Hong Kong , 2016, Comput. Environ. Urban Syst..

[51]  P. Ferreira,et al.  The valuation of the EQ-5D in Portugal , 2014, Quality of Life Research.

[52]  Peter M. Verderame,et al.  Planning and Scheduling under Uncertainty: A Review Across Multiple Sectors , 2010 .

[53]  M. Drummond,et al.  Health Care Technology: Effectiveness, Efficiency and Public Policy@@@Methods for the Economic Evaluation of Health Care Programmes , 1988 .

[54]  Ana Paula Barbosa-Póvoa,et al.  Location-allocation approaches for hospital network planning under uncertainty , 2015, Eur. J. Oper. Res..

[55]  António Alvarenga,et al.  Scenarios for population health inequalities in 2030 in Europe: the EURO-HEALTHY project experience , 2019, International Journal for Equity in Health.

[56]  N. Growe-Kuska,et al.  Scenario reduction and scenario tree construction for power management problems , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[57]  K. Haynes,et al.  Siting efficiency of long-term health care facilities , 1998 .

[58]  Christian Stummer,et al.  Determining Location and Size of Medical Departments in a Hospital Network: A Multiobjective Decision Support Approach , 2004, Health care management science.

[59]  Domenico Conforti,et al.  A new organ transplantation location–allocation policy: a case study of Italy , 2006, Health care management science.

[60]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[61]  Sally C. Brailsford,et al.  OR in healthcare: A European perspective , 2011, Eur. J. Oper. Res..

[62]  H. Bourne,et al.  Voices and values: linking values with participation in OR/MS in public policy making , 2007 .

[63]  S. J. Whitehead,et al.  Health outcomes in economic evaluation: the QALY and utilities. , 2010, British medical bulletin.

[64]  M. Koopmanschap,et al.  Quality of life instruments for economic evaluations in health and social care for older people: a systematic review. , 2014, Social science & medicine.

[65]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[66]  Susan Hamer.  Making Sense of the NHS White Papers , 2000 .

[67]  Stein W. Wallace,et al.  Generating Scenario Trees for Multistage Decision Problems , 2001, Manag. Sci..

[68]  Dong-Guen Kim,et al.  A branch and bound algorithm for determining locations of long-term care facilities , 2010, Eur. J. Oper. Res..

[69]  Christodoulos A. Floudas,et al.  Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: II. Sequential reduction , 2016, Comput. Chem. Eng..

[70]  P. Mitropoulos,et al.  A biobjective model for the locational planning of hospitals and health centers , 2006, Health care management science.

[71]  Ignacio E. Grossmann,et al.  A simple heuristic for reducing the number of scenarios in two-stage stochastic programming , 2010, Comput. Chem. Eng..

[72]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[73]  W. Rogowski,et al.  MCDA-based deliberation to value health states: lessons learned from a pilot study , 2019, Health and Quality of Life Outcomes.

[74]  S. Laditka,et al.  Can home care services achieve cost savings in long-term care for older people? , 1998, The journals of gerontology. Series B, Psychological sciences and social sciences.

[75]  L. Alberto Franco,et al.  Different paths to consensus? The impact of need for closure on model-supported group conflict management , 2016, Eur. J. Oper. Res..

[76]  J. Coast,et al.  University of Birmingham Development of a self-report measure of capability wellbeing for adults: the ICECAP-A. , 2012 .

[77]  Kenneth Yip,et al.  Fraser Health Uses Mathematical Programming to Plan Its Inpatient Hospital Network , 2009, Interfaces.

[78]  A. Vieira,et al.  Enhancing knowledge construction processes within multicriteria decision analysis: The Collaborative Value Modelling framework , 2020 .

[79]  T. Peters,et al.  Scoring the Icecap-A Capability Instrument. Estimation of a UK General Population Tariff† , 2013, Health economics.

[80]  Zukui Li,et al.  Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization , 2014, Comput. Chem. Eng..

[81]  T. Ritchey,et al.  Problem structuring using computer-aided morphological analysis , 2006, J. Oper. Res. Soc..

[82]  Sarah M. Ryan,et al.  Scenario construction and reduction applied to stochastic power generation expansion planning , 2013, Comput. Oper. Res..

[83]  Zvi Drezner,et al.  A note on equity across groups in facility location , 2011 .

[84]  Carlos A. Méndez,et al.  Multi-period design and planning of closed-loop supply chains with uncertain supply and demand , 2014, Comput. Chem. Eng..