Optimal package pricing in healthcare services

Abstract Fixed pricing for healthcare services is emerging as an attractive business model for private healthcare service providers. Under fixed pricing (or flat rate) contract, the patient is charged a fixed price for the healthcare services irrespective of the actual cost incurred by the hospital. Such contracts increase the risks for the healthcare service provider, thus making pricing decision crucial. In this paper, we study uncertainty and analyse the flat rate pricing contract for a profit maximising hospital to find the optimal price of treatment and examined value-at-risk (VaR) associated with such contracts for a risk minimising hospital. Bounds on price were derived to support healthcare providers with price negotiations. We extended the basic models by adding constraints to obtain risk-adjusted optimal price. We proved analytically that the optimal price lies between profit maximisation value and risk minimisation value of price, which we refer to as the efficient pricing interval. Our models and insights provide practical support to private healthcare service providers for optimal pricing and keep them informed about their risk position.

[1]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[2]  M. Rosenthal,et al.  Increased price transparency in health care--challenges and potential effects. , 2011, The New England journal of medicine.

[3]  P H Millard,et al.  Modelling Patient Duration of Stay to Facilitate Resource Management of Geriatric Hospitals , 2002, Health care management science.

[4]  Eren Demir,et al.  Modelling length of stay and patient flows: methodological case studies from the UK neonatal care services , 2014, J. Oper. Res. Soc..

[5]  A. R.,et al.  Review of literature , 1951, American Potato Journal.

[6]  J. Ausman,et al.  Lessons from India , 2017 .

[7]  Andrew M. Odlyzko,et al.  Paris metro pricing for the internet , 1999, EC '99.

[8]  Joseph P. Newhouse,et al.  A MODEL OF PHYSICIAN PRICING , 1970 .

[9]  Sally I. McClean,et al.  A multi-phase DES modelling framework for patient-centred care , 2016, J. Oper. Res. Soc..

[10]  Adele H Marshall,et al.  Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital , 2004, Health care management science.

[11]  Phattrawan Tongkumchum,et al.  Methods for Analyzing Hospital Length of Stay with Application to Inpatients Dying in Southern Thailand , 2009 .

[12]  D A Dittman,et al.  Optimal pricing of hospital services. , 1981, Inquiry : a journal of medical care organization, provision and financing.

[13]  Dittman Da,et al.  Optimal pricing of hospital services. , 1981 .

[14]  K. Schulman,et al.  Lessons from India in Organizational Innovation: A Tale of Two Heart Hospitals , 2008, Health affairs.

[15]  C. Garg,et al.  Reducing out-of-pocket expenditures to reduce poverty: a disaggregated analysis at rural-urban and state level in India. , 2009, Health policy and planning.

[16]  A. H. Marshalla,et al.  Conditional phase-type distributions for modelling patient length of stay in hospital , 2003 .

[17]  Arun Sundararajan,et al.  Nonlinear Pricing of Information Goods , 2002, Manag. Sci..

[18]  Margaret Holmes-Rovner,et al.  Estimating mean hospital cost as a function of length of stay and patient characteristics. , 2003, Health economics.

[19]  Christos Vasilakis,et al.  Modelling nationwide hospital length of stay: opening the black box , 2005, J. Oper. Res. Soc..

[20]  T. Ayer,et al.  The Impact of Health Information Exchanges on Emergency Department Length of Stay , 2018, Production and Operations Management.

[21]  J Doyle,et al.  Medicare Provider Utilization and Payment Data: The Book to Bill Gap. , 2014, Value in health : the journal of the International Society for Pharmacoeconomics and Outcomes Research.

[22]  Nicholas Graves,et al.  Modeling length of stay in hospital and other right skewed data: comparison of phase-type, gamma and log-normal distributions. , 2009, Value in health : the journal of the International Society for Pharmacoeconomics and Outcomes Research.

[23]  A Marazzi,et al.  Fitting the distributions of length of stay by parametric models. , 1998, Medical care.

[24]  Fitting the variable “ Length of Hospital Stay ” with mixtures from different distribution families , 2005 .

[25]  Ben Vollaard,et al.  The Elasticity of Demand for Health Care: A Review of the Literature and Its Application to the Military Health System , 2002 .

[26]  J. Muñoz-Pichardo,et al.  An application of mixture distributions in modelization of length of hospital stay , 2008, Statistics in medicine.

[27]  Stephen E. Margolis.  The Pricing of Physicians' Services , 1983 .

[28]  Ha T Tu,et al.  Impact of health care price transparency on price variation: the New Hampshire experience. , 2009, Issue brief.

[29]  Colin Michael Hall,et al.  Medical Tourism : The Ethics, Regulation, and Marketing of Health Mobility , 2012 .

[30]  Michele Sonnessa,et al.  An agent-based simulation model to evaluate alternative co-payment scenarios for contributing to health systems financing , 2017, J. Oper. Res. Soc..

[31]  Bridger M. Mitchell.  Optimal Pricing of Local Telephone Service , 2016 .

[32]  G. J. Rodgers,et al.  A power law distribution in patients’ lengths of stay in hospital , 2007 .

[33]  Panagiota Galetsi,et al.  A review of the literature on big data analytics in healthcare , 2019, J. Oper. Res. Soc..

[34]  Daniel E. Geer,et al.  Power. Law , 2012, IEEE Secur. Priv..

[35]  U. Reinhardt.  The pricing of U.S. hospital services: chaos behind a veil of secrecy. , 2006, Health affairs.

[36]  Nils Gutacker,et al.  Waiting time prioritisation: Evidence from England. , 2016, Social science & medicine.

[37]  Alysson M. Costa,et al.  A sequential stochastic mixed integer programming model for tactical master surgery scheduling , 2018, Eur. J. Oper. Res..

[38]  Fabian Herweg,et al.  Uncertain Demand, Consumer Loss Aversion, and Flat-Rate Tariffs , 2011 .

[39]  Kenneth Train,et al.  Optimal Regulation: The Economic Theory of Natural Monopoly , 1991 .