Comparison of Subsidy Schemes for Reducing Waiting Times in Healthcare Systems

Qu Qian, Pengfei Guo, Robin Lindsey

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)


We assume that public healthcare service has no user fee but an observable delay, while private healthcare service has a fee but no delay. Patients in the public system are given a subsidy s to use private service if their waiting times exceed a pre-determined threshold t. We call these subsidy schemes (s, t) policies. As two extreme cases, the (s, t) policy is called an unconditional subsidy scheme if t = 0, and a full subsidy scheme if s is equal to the private service fee. There is a fixed budget constraint so that a scheme with larger s has a larger t. We assess policies using two criteria: total patient cost and serviceability (i.e., the probability of meeting a waiting time target for public service). We prove analytically that, if patients are equally sensitive to delay, a scheme with a smaller subsidy outperforms one with a larger subsidy on both criteria. Thus, the unconditional scheme dominates all other policies. Using empirically derived parameter values from the Hong Kong Cataract Surgery Program, we then compare policies numerically when patients differ in delay sensitivity. Total patient cost is now unimodal in subsidy amount: the unconditional scheme still yields the lowest total patient cost, but the full subsidy scheme can outperform some intermediate policies. Serviceability is unimodal too, and the full subsidy scheme can outperform the unconditional scheme in serviceability when the waiting time target is long.
Original languageEnglish
Pages (from-to)2033-2049
Number of pages17
JournalProduction and Operations Management
Issue number11
Publication statusPublished - 1 Nov 2017


  • equilibrium analysis
  • health care
  • queueing
  • subsidy policy

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation

Cite this