Location modelling for sustainable community healthcare facilities

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Location modelling for sustainable community
healthcare facilities

• Honora K. Smith, Paul R. Harper,
• Chris N. Potts,
• OR Group, School of Mathematics,
• University of Southampton

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Community Health Care
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Overview

• Sustainability - Planning or participation?
• Community healthcare schemes in developing
  countries
• Sustainability Efficiency
• Integer programming location models
• Classical basis
• Hierarchical
• Efficiency/ equity
• Sustainability Demand
• Stochastic variation spatio-temporal

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Community health schemes
Emmanuel Hospital Association NGO/FBO
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Community health schemes - development
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Community health schemes - development
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Community health schemes - development
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Community health schemes - development
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Community health schemes - development
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Community health schemes medical
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Elements of sustainability - participation
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Elements of sustainability - participation
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Elements of sustainability - participation
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Community health care - hierarchical facilities
h
cc
Key vw village worker cc community centre h
hospital
vw
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Hierarchical systems

• Highest level most specialised services, fewest
  facilities
• Single-flow
• Entry at lowest level only
• Multi-flow
• Entry at multiple levels
• Successively-inclusive
• Services available at higher levels
• Exclusive
• Services available only at particular levels

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Classical location models

• p-Median - essential services
• Minimise total population-weighted distance
  travelled to the nearest facility
• Maximal covering - limited cover services
• Maximise total population within cover
  distance/time of a facility
• The number of facilities to be located is
  specified.

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Equity objectives

• A fair distribution of services
• Minimise total absolute deviation from desirable
  service standard
• p-Median
• Distance
• Maximum cover
• Population per facility

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Hierarchical models

• p-Median
• HiMi-PMP-Eq
• HiMe-PMP-Eq
• HiS-PMP-Eq
• Max Cover
• HiMi-MCL-Eq
• HiMe-MCL-Eq
• HiS-MCL-Eq

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p-Median HiMi-PMP-Eqdecision variables
Location allocation
if demand at node i is allocated to a facility at
node j, otherwise,
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p-Median HiMi-PMP-Eqobjective
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p-Median HiMi-PMP-Eqconstraints

• subject to

Minimum distance All demand satisfied uniquely
Allocation to an open facility
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Common constraints
Within referral distance between levels Number
of facilities per level Pre-existing facilities
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Max cover HiMi-MCL-Eq Decision variables
if a level k facility is located at node
j, otherwise,
if demand at node i is allocated to a level k
facility at node j, otherwise,
used in calculating absolute values
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Max cover HiMi-MCL-EqObjective
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Max cover HiMi-MCL-Eq Max cover at any level
constraints on allocation
Demand allocated to nearest open facility at any
level Demand can be allocated at some level only
if covered at that level Can allocate demand
once only Demand must be allocated if covered by
an open facility.
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Output from HiMe-PMP-Eq, equity 0 and 1
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Output from HiMe-PMP-Eq, location of 3 low level
and 1 high level facilities.
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Making Leeds Better locating polyclinics
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Making Leeds Better - scenarios

• Candidate facility sites
• Demand proxies
• Numbers of facilities to locate
• Population covered/ average distance/ equity

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Demand modelling the Paltandih clinic
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Demand for Reproductive and Child Health clinic
in Balrampur District, U.P, India
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Known locations/populations
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Total demand for clinic (Aug 05 Feb 07)
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Cumulative percentage demand by distance

Distance from clinic (km)
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Total clinic visits
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Spatio-temporal modelling of demand
where
distance from clinic
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Spatio-temporal modelling of demand

• trust/knowledge of clinic by word of mouth,
  from
• Previous use in village
• Previous use in neighbouring village
• Proximity to clinic
• Previous provider work in village

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Parameter estimation

• Distance parameters
• Demand distance
• Awareness, influence

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Parameter estimation
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Total monthly demand - simulated
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Simulated demand confidence intervals vs actual
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In the pipeline

• Smith, Harper, Potts, Thyle. Planning
  sustainable community health schemes in rural
  areas of developing countries (Accepted for
  special issue of EJOR on OR for Better
  Management of Sustainable Development).

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• Your thoughts?