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OPERATIONS
RESEASRCH
ā€œthe science of betterā€
Dr. Mounica C
Guide: Dr Babitha Rajan
Contents
1. Introduction
2. History
3. Operations research (OR) in the field of health
4. Terminologies
5. How does OR differ from other types of Research?
6. Features of operations research
7. Operations Research process
8. Scientific methods in operations research
9. Applications of operations research
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Contents Contā€¦
10. Benefits of OR
11. Techniques in operations research
12. Challenges of OR
13. Critical Review of OR in Public Health
14. How to measure the success of OR?
15. Conclusion
16. References
17. Exercise on OR
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Introduction
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ā€¢ One of the popular managerial decision science tools
ā€¢ Application of quantitative mathematical methods & logic to
find solutions to managerial problems
ā€¢ Concerned with means of dealing with:
o Resource constraints
o Assignment and maximisation of values &
o Appraisal of alternatives in an uncertain, dynamic
environment
History ā€˜war babyā€™
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ā€¢ The Battle of Britain- 1940 (World War II)
ā€¢ Gave effective assistance in missions - deploying radar,
searching for enemy submarines, and getting supplies
In India
ā€¢ OR came into existence in 1949-OR unit was established at
Regional Research Laboratory, Hyderabad
ā€¢ Prof. R.S.Verma - Defence Science Laboratory
ā€¢ Prof. Mahalanobis - used OR in national planning
OR in the field of health
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ā€¢ Provides decision-makers with information to enable them to
improve performance of their programs
ā€¢ Helps to identify solutions to problems that limit program
quality, efficiency and effectiveness, or to determine which
alternative service delivery strategy would yield the best
outcomes
ā€¢ ā€œthe science of betterā€
OR in the field of health Contā€¦
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ā€¢ Seeks to improve number and quality of services and
program outcomes by optimizing program inputs (e.g.,
personnel, supplies) and processes (e.g., training, supervision,
and promotion of services)
ā€¢ Determine cost-effective and sustainable ways to build
service delivery capacity
Terminologies
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Operation: Set of activities ā€“ for desired outcome
Research
WHO (2003) defines OR as
ā€œthe use of systematic research techniques for program
decision-making to achieve a specific outcomeā€
Terminologies Contā€¦
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A global meeting held in Geneva in 2008 resulted in a
consensus definition of OR in context of public health as
ā€œAny research producing practically usable knowledge
(evidence, findings, information, etc) which can improve
program implementation (e.g. effectiveness, efficiency,
quality, access, scale up, sustainability) regardless of the type
of research (design, methodology, approach) falls within the
boundaries of ORā€
How does OR differ from other
types of Research?
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Basic
Reserach
Not
implement
ed in to
practice
Focusing
on an
individual
Routinely
collected
data can
be used
Deals
general
health
issues
Research
under
controlled
conditions
May be
only
researcher
/s involved
How does OR differ from other
types of Research?
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OR
Examines a
system
Systematic
data
collection
Treating
the system
in its real
environme
ntCollaboration
b/w
researchers &
program
managers
Deals with
specific
health
issues
Successful
when results
implemented
Features of OR
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Decision making
Scientific approach
Objective
Inter-disciplinary team approach
Digital computer
The OR Process
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Defining the problem
Developing a model
Acquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
Scientific methods in OR: Phases
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ā€¢ Identification of problem
ā€¢ Selection of appropriate goal
ā€¢ Measurement
ā€¢ Formulation of model
Judgement
phase
ā€¢ Observation & Data collection
ā€¢ Formulation of hypothesis
ā€¢ Experimentation
ā€¢ Analysis
ā€¢ Generalisation
Research
phase
ā€¢ Recommendations for decision
Action
phase
Applications of OR
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OR
Finance,
Budgeting
&
Investment
Marketing
Physical
distribution
Purchasing,
Procurement
&
Exploration
Personnel
Production
Research
&
Developme
nt
Applications in hospital management
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ā€¢ Allocation problems
ā€¢ Replacement problems
ā€¢ Sequencing problems
ā€¢ Placing jobs or activities in certain order
ā€¢ Finding optimal route
ā€¢ Inventory problems
ā€¢ Quantum of holding or storing resources in the inventory
ā€¢ Queuing problems
ā€¢ Waiting line problems for service utilisation
ā€¢ Searching information for decision making
Benefits of OR
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Ability to deal in a
quantitative manner
with conditions of
uncertainty
Use of objective
methods to sort out in
complex situations
Capacity to illustrate
the likely outcomes of
alternative courses
Assist managers in
understanding many
inter-related factors
Provision of various
logical approaches to
make decisions
Ability to handle
masses of data with
help of computer
Management Techniques/ Methods in OR
A. Statistical techniques
1. Time trends & forecasting
2. Decision theory & tree
B. Activity analysis
1. Time motion studies
2. Work sampling & activity
analysis
3. Queuing theory
4. Gantt chart & work schedule
C. Mathematical techniques
1. Simulation study/models
2. System analysis
3. Linear programming
4. Inventory control
5. Network analysis - PERT &
CPM
D. Financial techniques
1. Monitoring expenditure
2. Cost accounting & analysis
3. DALY
4. Cost benefit analysis
5. Cost effectiveness analysis
6. Zero base budgeting
7. Input output analysis
8. Outcome budget
E. Miscellaneous
1. Management by exception
2. Situational analysis
3. Current state assessment
4. SWOT analysis
5. Log frame analysis
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Time trends & forecasting
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ā€¢ Data gathered on a given characteristic over a period of time
at regular intervals
ā€¢ Predictions can be made about expected occurrence, by using
mathematical methods
ā€¢ If incidence of a disease exceeds expectation by certain limits,
epidemic can be anticipated, detected at the earliest and
appropriate steps taken for control
Time trends & forecasting Contā€¦
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ā€¢ Forecasting is defined as the science of predicting for future
ā€¢ Forecasting the demand for supplies of materials like
vaccine, drugs etc, can also be similarly anticipated and a state
of preparedness maintained
Situation 1
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As a medical officer in-charge of the hospital you have
observed that in the past 3 years, many measles cases are
coming to your hospital in the months of January till April
ā€¢ Method applied: Time trends
Calculate the measles vaccine requirements for one month,
given the population being catered to is 36,000,
CBR=22/1000population and IMR=9/1000 live births
ā€¢ Method applied: Forecasting
Decision theory & Decision tree
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ā€¢ Decision theory is the body of analytical tools, including logic
& mathematical models, using probability theory &
diagrammatic representation for use in decision making
ā€¢ Decision tree is a diagram which depicts key interactions
among decisions & associated chance events
ā€¢ The most rational decision can be taken in terms of resource
& the effectiveness
Decision tree for micro invasive cancer of the cervix showing selected
probabilities and possible utility calculations Available from URL:
http://ars.els-cdn.com/content/image/1-s2.0-S0140673601057099-gr1.jpg
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Decision analysis
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ā€¢ Process of making choices from among several alternatives
ā€¢ Includes many procedures, methods, and tools for identifying,
clearly representing, and formally assessing important
aspects of a decision
ā€¢ Helps in prescribing a recommended course of action by
applying the maximum expected utility action
Time motion studies
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ā€¢ Consists of observing & timing by using stopwatches the
physical work & movements carried out by a worker
ā€¢ The movements carried out in performance of a task are then
broken into segments, analyzed & redesigned so that task can
be accomplished more efficiently
Situation 2
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Sisters in the ward always complained that the ward boys
were not available at the time of emergency.
Activities of the ward boy included shifting the patients to
x-ray/ USG department; helping during dressing; handing
over blood & urine samples to lab; collecting reports,
miscellaneousā€¦.
ā€¢ Method applied: Time motion studies
Situation 3
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In the hospital at reception counter patients arrive at an
interval of 5 minutes & reception desk takes 2 minutes for
servicing each patient. Under these conditions:
How long on an average a patient does wait in the queuing
system?
If the management is of the view that it can allow a waiting
time up to 5 minutes only, how much does the flow of
patients be to justify for opening a second counter in the
reception desk?
ā€¢ Technique applied: Queuing theory
Queuing theory
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ā€¢ Concepts and parameters used in queuing theory
o Waiting time cost & service cost
o Mean arrival time of customers - ļ¬
o Mean service rate - ļ­
ā€¢ In the above scenario: Arrival pattern
o Mean inter arrival time=(1/ mean arrival time)=(1/ļ¬)=5 mn
o Mean arrival rate per minute = (1/5) = 0.2 patients
o Mean arrival rate per hour = 0.2 x 60 = 12 patients per hour
Queuing theory Contā€¦
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ā€¢ Service pattern
o Mean service time per patient = (1/ Mean service rate) =
(1/ļ­) = 2 minutes
o Patients served per minute = (1/2) = 0.5
o Patients served per hour = 0.5 x 60= 30 patients
ā€¢ Average waiting time of a patient in the queue E(w) = {ļ¬/ ļ­
(ļ­-ļ¬)}= 12/30 (30-12)= 1/45 =0.22 hour or 1.33 minutes
ā€¢ To open a second counter- how much should be the patient
inflow?
Queuing theory Contā€¦
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ā€¢ Mean arrival rate of patients E (w) = {ļ¬ā€™/ ļ­ (ļ­-ļ¬ā€™)}where ļ¬ā€™ -
expected arrival rate
E(w)=average waiting time of a patient in queue=5 min or
(1/12) hr, (1/12) = {ļ¬ā€™/ 30 (30-ļ¬ā€™)}
So ļ¬ā€™ = arrival rate per hour = 21.43, nearly 3/min
ā€¢ Hence mean arrival rate should go up to 21 from present 12
or nearly one patient for every 3 minutes, in contrast to one
patient for every 5 minutes, to justify for the setting up of
second counter
Linear Programming
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ā€¢ For use with a common management problem ā€“ the allocation
of resources in an optimum manner
ā€¢ Mathematical or graphical technique - used to determine best
use of scarce resources to accomplish a defined objective
ā€¢ Used when problems have these characteristics:
o mix
o needs an optimum solution
o Constraints
o linear relationship
Situation 4
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Is it possible to predict number of nursing personnel of each
type needed for each nursing unit based on information
concerning the number and degree of illness of each patient?
ā€¢ Method applied: Linear Programming
ā€¢ This can be done immediately before each shift reports for
duty by computerized program matched against current
patient illness characteristics, and assignments of nursing
personnel can thus be made on a predicted patient care need
for next shift rather than just on number of patients on each
unit, or merely based on number of beds in each unit
Network Analysis
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ā€¢ Method of presentation of composite activities - diagrammatic
form recording their interdependence of an operation - total
view of situation from start to finish
ā€¢ Depicts interdependency of activities, by splitting up the total
project into activities & assists in estimation of time for each
activity & enables in target achievement
ā€¢ Enable better planning & evaluation of proposed schedule
of activities
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Network Analysis
Critical Path Method (CPM)
Time required for completion of
activity is estimated
This estimation does not involve any
statistical methodology
Program Evaluation &
Review Technique (PERT)
Assumes 3 time estimates for each
activity in terms of optimistic,
pessimistic & most likely time for
completion of activity
Calculated using these 3 times
through statistical average approach
ā€¢ Enables stricter control on completion of activity in time besides
enabling in estimation of men, money & material for completion
of program in scheduled time
ā€¢ Depending on the situations, it also helps in modification of time
required for activities
Steps involved in drawing a network
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List all activities to be performed with well defined end point
Schedule events in sequential order ā€“ merge/ burst events
Assess performance time for each event
Put events in sequential chain taking interdependence of events
Converted into graphic line from start to finish along with time
Each chain will have total time of completion - All chains
together form NETWORK
Chain with maximum required time is THE CRITICAL PATH
Situation 5
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How to set up a laboratory in a hospital?
ā€¢ Method applied: Network analysis
ā€¢ CPM & PERT
Respective chains can be drawn as:
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ā€¢ A: Placing orders for equipment & furniture
ā€¢ D: Supply of equipment & furniture
ā€¢ G: Installation of for equipment &
laboratory
Chain 1
Related to
equipment
ā€¢ B: Procurement of chemicals & reagents
ā€¢ E: Stacking of chemicals & reagents
ā€¢ H: Preparation of protocols for
investigations
Chain 2
Related to
chemicals
& reagents
ā€¢ C: Advertise for personnel
ā€¢ F: Recruitment of personnel
ā€¢ I: Training of personal
Chain 3
Related to
staff
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Ev
ent
Acti
vity
Description activity Predecesso
r activity
T(e)
(day)
1 A Placing orders for equipment &
furniture
- 3
1 B Procurement of chemicals &
reagents
- 5
1 C Advertise for personnel - 4
2 D Supply of equipment & furniture A 2
3 E Stacking of chemicals & reagents B 3
4 F Recruitment of personnel C 9
5 G Installation of for equipment &
laboratory
D,E 8
6 H Preparation of protocols for
investigations
B 7
7 I Training of personal G,H 9
Network Analysis
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Critical path, slack time, non critical path, bottleneck/ critical activities,
EST, EFT, LFT, LST, floats
Network Analysis
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CPM
ā€¢ Advantages:
ā€¢ Ascertaining time schedule
ā€¢ Makes detailed planning
possible
ā€¢ Identifies most critical
elements
ā€¢ Limitations:
ā€¢ May not be a true
assumption in practice
ā€¢ Does not incorporate
statistical analysis
PERT
ā€¢ Advantages:
ā€¢ Ability to plan best possible
use of resources
ā€¢ Presses for right action, at
right point, & at right time
ā€¢ Limitations:
ā€¢ Difficulty in way of time
estimates
ā€¢ Does not consider resources
required at various stages
ā€¢ Frequent updating &
revising calculations-costly
affairs
Inventory Control
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ā€¢ ā€œUsable but idle resource having an economic valueā€
ā€¢ ā€˜Paretoā€™s lawā€™ - forms the basis
ā€¢ Ultimate aim in healthcare setting - to ensure that adequate
and optimal essential items are properly stored, controlled,
are easily retrievable and distributed to points of uses so
that patient care does not suffer due to lack of these
essential medical supplies
Various selective inventory control measures
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ā€¢ ABC: Based on annual total cost of items
ā€¢ VED: Based on criticality and importance of consumables,
items are classified as Vital (V), Essential (E) & Desirable (D)
ā€¢ HML: Based on cost of individual item as High cost (H),
Medium cost (M) and Low cost (L)
ā€¢ SDE: Based on ease of availability of items - classified as
Scarce (S), Difficult to obtain (D) and Easy to obtain (E)
Various selective inventory control measures
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ā€¢ GOLF: Based on source of supply & include Governmental
sources (G), Ordinary (O), Local (L) & Foreign (F)
ā€¢ FSN: Based on rate of issue from the stores into Fast- moving
(F), Slow moving (S) & Nonmoving (N) items
ā€¢ SOS: Based on Seasonal (S) & Off-seasonal (OS) availability
ā€¢ XYZ: Based on value of stocks of items held
Situation 6
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Have to indent essential drugs.
How much to indent?
How frequently to indent?
ā€¢ Method applied: Inventory control
ā€¢ In a hospital setting, combination of ABC analysis (based on
annual cost) and VED analysis (based on criticality of item)
is to be adopted
ā€¢ Category I: Contain all the vital and costly items
ā€¢ Category II: Items that are essential but are less costly
ā€¢ Category III: Items that are desirable
Gantt chart
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ā€¢ Horizontal bar chart developed as a production control tool
in 1917 by Henry L. Gantt
ā€¢ Provides a graphical illustration of a schedule that helps to
plan, coordinate, and track specific tasks in a project
ā€¢ Useful tool for analyzing and planning complex projects
ā€¢ Help to monitor whether the project is on schedule
ā€¢ Assess how long a project should take, determine resources
needed, & lay out order in which tasks need to be carried out
Situation 7
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Consider constructing a hospital in your district
ā€¢ Method applied: Gantt chart
List of activities in
hospital construction project
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Acti
vity
Description Predece
sors
Duration
(weeks)
A Select administrative and medical staff - 12
B Select site and do site survey - 9
C Select equipment A 10
D Prepare final construction plans B 10
E Bring utilities to the site B 24
F Interview applicants & fill positions in
nursing support staff, maintenance
A 10
G Purchase & take delivery of equipment C 35
H Construct the hospital D 40
I Develop an information system A 15
J Install the equipment E, G, H 4
Gantt chart for
hospital construction project
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SWOT Analysis
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ā€¢ Strengths (S), Weaknesses (W), Opportunities (O) &Threats
(T) are identified in context of proposed program
ā€¢ S&W - Permanent phenomena that exist within organization
ā€¢ O&T - Temporary, often fleeting, phenomena that exist in
external environment
S: Powerful
attributes, which it
may possess
W: Actual or
potential liabilities &
weak points
O: Circumstances
conducive to its
flourishing &
growth further
T: Aspects which
may hinder its
growth &
development
Situation 8
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Proposed programme for prevention & control of HIV in our
country
ā€¢ Method applied: SWOT Analysis
S: Organizational &
constitutional philosophy
& political will of the
country
W: Common social
tendency not to encourage
talking about sexual health
O: Funds for developing
health educational
material & strongly in
favor of educating public
& high risk groups
T: Some recent resistance
and objection from parents
against sex education of
children
Financial Techniques
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Cost Accounting/Cost Analysis ā€“ tool for measuring the cost of
health services.
ā€¢ Ex: Unit cost of items like drug consumption/day/patient
ā€¢ Costing also helps to assess the efficiency & effectiveness of
functions
Cost Benefit Analysis - evaluation method for comparing the
monetary value of all resources consumed (costs) in providing
a program or intervention with the monetary value of the
outcome (benefit) from the program or intervention
Financial Techniques Cont...
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Cost effectiveness analysis - To determine which program
accomplishes given objective at least cost. Effectiveness is
measured in terms of non-monetary units that describe desired
objective (Lives saved/ disability days avoided/ cases treated)
Zero based budgeting (ZBB) - ā€œPlanning & budgeting process
which requires each manager to justify entire budget in detail
from ā€˜scratchā€™ (ā€˜zero baseā€™) thereby making it responsibility of
each manager to justify why he should spend any money at all
during budget periodā€
Challenges of OR
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ā€¢ Operate in absence of detailed, systematic research plan, with
clear linkages to programme priorities
ā€¢ Implementing research studies in absence of a carefully conducted
situation analysis prevents from achieving their desired goals
ā€¢ Appropriate external sources of support ā€“ financial, technical and
research mentoring ā€“ must be in place at all stages of planning and
implementation of research. Such resources are insufficient or
absent at some or all stages
ā€¢ Training in OR methodology is required for both service providers
and academics
Critical Review of OR
in Public Health
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ā€¢ Gaining importance in public health programs and
interventions increasingly both nationally and internationally
ā€¢ Guide program implementation to achieve best results
ā€¢ Modulates inputs & processes involved & strive to produce
optimal gains in achieving targets & goals
ā€¢ Identifies problems; often program managers encompass in
operation of public health goods and test the feasible
solutions for them
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Approaches for OR in Public Health
Secondary data analysis Primary level research
Types of OR studies as defined by the Population Council
Exploratory study Field intervention
Monitoring &
Evaluation
Economic analysis
How to measure the success of OR?
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ā€¢ Results & new knowledge must also lead to action, which will
lead to changes in clinical or laboratory practice &
management & if possible, also to changes in policy
ā€¢ All OR & new knowledge created by research should lead to
& be measured by:
o Publications
o Capacity development of service providers & academic
researchers
o Changes in practice and/or policy
Conclusion
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ā€¢ To survive & lead todayā€™s highly competitive & demand
driven market, pressure is on management to make
economical decisions
ā€¢ One of essential managerial skills is ability to allocate &
utilize resources appropriately in the efforts of achieving
optimal performance efficiently
ā€¢ Translating outcomes of research into practice will lead to a
better health system in terms of 4 Aā€™s ā€“ accessibility,
availability, affordability and acceptability bridging
prevailing inequities & disparities
References
8/10/2018 Operations research
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1. WHO. Grunde F, Reinke WA. Health practice research and
formalised managerial methods. [serial online] Geneva: WHO;
1973. Available from URL:
http://apps.who.int/iris/bitstream/10665/40852/2/WHO_PHP_51_r
us.pdf
2. Sathe PV. Epidemiology and management for health care for all.
4th ed. Mumbai: Vora publications; 2009. p.173-190.
3. Vani C. Operation research. Seminar notes. Department of
community medicine.
4. Chetana T. Operation research.Seminar notes. Department of
community medicine.
5. Rao.NSN. Operation research techniques in health care
management. Unpublished material
6. Organization & management of hospitals. PGDHHM-03. New
Delhi: Akashdepp publishers;2009.
References Cont...
8/10/2018 Operations research
59
7. Agarwal S, Subramanian K R, Kapoor S. Operations research -
contemporary role in managerial decision making. IJRRAS [serial
online] 2010 May [cited 2017 Jan 2] Available from URL:
http://www.arpapress.com/Volumes/Vol3Issue2/IJRRAS_3_210.pdf
8. WHO. Foreit J, Schmid G. Guide to operational research in
programs supported by the global fund. [serial online] Geneva:
WHO. [cited 2016 Dec 26] Available from URL:
http://www.who.int/hiv/pub/operational/or_guide_gf.pdf
9. Swarup K, Gupta PK, Mohan M. Operations research. 13th ed New
Delhi: Sultan Chand & sons educational publishers; 2007.
10. Gantt chart. [serial online] [cited 2016 Dec 23] Available from
URL:http://www.improhealth.org/fileadmin/Documents/Improvem
ent_Tools/Gantt_Chart.pdf
References Cont...
8/10/2018 Operations research
60
11. WHO. Application of system analysis to health management.
Technical Report Series 596. [serial online] Geneva: WHO. [cited
2017 Jan 3] Available from URL:
http://whqlibdoc.who.int/trs/WHO_TRS_596.pdf
12. Bhalwar R, Vaidya R, Tilak R, Gupta R, Kunte R. Text book of
public health and community medicine. Pune: Department of
Community Medicine Armed Forces Medical College; 2009.
13. W. Durfee and T. Chase (2003), Brief tutorial on Gantt charts,
University of Minnesota
14. Malhotra S, Zodpey SP. Operations research in public health.
Indian Journal of Public Health July-September 2010; 54 (3): 145-
15
15. Korenromp E, Komatsu R, Katz I, Katz I, Xueref S, Low-Beer D.
Operational research on HIV/AIDS, tuberculosis and malaria
control in Global Fund-supported programmes: Round 1-6 grants.
In: Proceedings of the 5th European conference on tropical
medicine and international health, Amsterdam, 24ā€“28 May 2007
References Cont...
8/10/2018 Operations research
61
16. HIV testing, treatment and prevention: generic tools for operational
research. Geneva: World Health Organization; 2009. 11.
17. The framework for operations and implementation research in
health and disease control programmes. Geneva: World Health
Organization; 2008. 20.
18. Trochim WM, Cabrera DA, Milstein B, Gallagher RS, Leischow
SJ. Practical challenges of systems thinking and modeling in public
health. Am J Public Health 2006; 96: 538-46 48.
19. Zachariah R, Harries AD, Ishikawa N, Rieder HL, Bissell K,
Laserson K, et al., et al. Operational research in low-income
countries: what, why, and how? Lancet Infect Dis 2009; 9: 711-7
20. Geoff Royston. Meeting global health challenges through
operational research and management science. Bulletin of the
World Health Organization 2011;89: 683-688.
21. Rama Murthy P. Operations research. 2nd edition. New Delhi: New
Age International Publishers; 2007.
References Cont...
8/10/2018 Operations research
62
22. Rais A, Viana A. Operations Research in Healthcare: a survey.
Intl Trans in Op Res. Jan 2010; 18: 1ā€“31.
23. Boldy, D. Operational Research Applied to Health Services.
New York: St. Martinā€™s Press; 1981.
24. Brandeau, M., Sainfort, F., Pierskalla, W. Operations
Research and Health Care. A Handbook of Methods and
Applications. Kluwerā€™s International Series, Dordrecht; 2004.
25. Linda V. Using Operations Research to Reduce Delays for
Healthcare. Tutorials in Operations Research, 2008 INFORM.
26. Guide To Operational Research In Programs Supported By
The Global Fund. WHO.
Exercise: MR Campaign
8/10/2018 Operations research 63
Activity Activity Description Immediate
Predecessor
Te
A Establishment of surveillance --- 2W
B Local epidemiological information --- 2W
C Knowledge of public perceptions --- 2W
D To obtain funds for cold chain --- 4W
E Identification of staff A 3W
F Development of training materials B 4W
G Training staff E, F 3W
H Development of health education material C,B 4W
I Public acceptance H 2W
J Establishment of cold chain D 3W
K Availability of vaccine J 2W
Ending Vaccination programme on G,I,K ---
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Operation research

  • 1. OPERATIONS RESEASRCH ā€œthe science of betterā€ Dr. Mounica C Guide: Dr Babitha Rajan
  • 2. Contents 1. Introduction 2. History 3. Operations research (OR) in the field of health 4. Terminologies 5. How does OR differ from other types of Research? 6. Features of operations research 7. Operations Research process 8. Scientific methods in operations research 9. Applications of operations research 8/10/2018 Operations research 2
  • 3. Contents Contā€¦ 10. Benefits of OR 11. Techniques in operations research 12. Challenges of OR 13. Critical Review of OR in Public Health 14. How to measure the success of OR? 15. Conclusion 16. References 17. Exercise on OR 8/10/2018 Operations research 3
  • 4. Introduction 8/10/2018 Operations research 4 ā€¢ One of the popular managerial decision science tools ā€¢ Application of quantitative mathematical methods & logic to find solutions to managerial problems ā€¢ Concerned with means of dealing with: o Resource constraints o Assignment and maximisation of values & o Appraisal of alternatives in an uncertain, dynamic environment
  • 5. History ā€˜war babyā€™ 8/10/2018 Operations research 5 ā€¢ The Battle of Britain- 1940 (World War II) ā€¢ Gave effective assistance in missions - deploying radar, searching for enemy submarines, and getting supplies In India ā€¢ OR came into existence in 1949-OR unit was established at Regional Research Laboratory, Hyderabad ā€¢ Prof. R.S.Verma - Defence Science Laboratory ā€¢ Prof. Mahalanobis - used OR in national planning
  • 6. OR in the field of health 8/10/2018 Operations research 6 ā€¢ Provides decision-makers with information to enable them to improve performance of their programs ā€¢ Helps to identify solutions to problems that limit program quality, efficiency and effectiveness, or to determine which alternative service delivery strategy would yield the best outcomes ā€¢ ā€œthe science of betterā€
  • 7. OR in the field of health Contā€¦ 8/10/2018 Operations research 7 ā€¢ Seeks to improve number and quality of services and program outcomes by optimizing program inputs (e.g., personnel, supplies) and processes (e.g., training, supervision, and promotion of services) ā€¢ Determine cost-effective and sustainable ways to build service delivery capacity
  • 8. Terminologies 8/10/2018 Operations research 8 Operation: Set of activities ā€“ for desired outcome Research WHO (2003) defines OR as ā€œthe use of systematic research techniques for program decision-making to achieve a specific outcomeā€
  • 9. Terminologies Contā€¦ 8/10/2018 Operations research 9 A global meeting held in Geneva in 2008 resulted in a consensus definition of OR in context of public health as ā€œAny research producing practically usable knowledge (evidence, findings, information, etc) which can improve program implementation (e.g. effectiveness, efficiency, quality, access, scale up, sustainability) regardless of the type of research (design, methodology, approach) falls within the boundaries of ORā€
  • 10. How does OR differ from other types of Research? 8/10/2018 Operations research 10 Basic Reserach Not implement ed in to practice Focusing on an individual Routinely collected data can be used Deals general health issues Research under controlled conditions May be only researcher /s involved
  • 11. How does OR differ from other types of Research? 8/10/2018 Operations research 11 OR Examines a system Systematic data collection Treating the system in its real environme ntCollaboration b/w researchers & program managers Deals with specific health issues Successful when results implemented
  • 12. Features of OR 8/10/2018 Operations research 12 Decision making Scientific approach Objective Inter-disciplinary team approach Digital computer
  • 13. The OR Process 8/10/2018 Operations research 13 Defining the problem Developing a model Acquiring input data Developing a solution Testing the solution Analyzing the results Implementing the results
  • 14. Scientific methods in OR: Phases 8/10/2018 Operations research 14 ā€¢ Identification of problem ā€¢ Selection of appropriate goal ā€¢ Measurement ā€¢ Formulation of model Judgement phase ā€¢ Observation & Data collection ā€¢ Formulation of hypothesis ā€¢ Experimentation ā€¢ Analysis ā€¢ Generalisation Research phase ā€¢ Recommendations for decision Action phase
  • 15. Applications of OR 8/10/2018 Operations research 15 OR Finance, Budgeting & Investment Marketing Physical distribution Purchasing, Procurement & Exploration Personnel Production Research & Developme nt
  • 16. Applications in hospital management 8/10/2018 Operations research 16 ā€¢ Allocation problems ā€¢ Replacement problems ā€¢ Sequencing problems ā€¢ Placing jobs or activities in certain order ā€¢ Finding optimal route ā€¢ Inventory problems ā€¢ Quantum of holding or storing resources in the inventory ā€¢ Queuing problems ā€¢ Waiting line problems for service utilisation ā€¢ Searching information for decision making
  • 17. Benefits of OR 8/10/2018 Operations research 17 Ability to deal in a quantitative manner with conditions of uncertainty Use of objective methods to sort out in complex situations Capacity to illustrate the likely outcomes of alternative courses Assist managers in understanding many inter-related factors Provision of various logical approaches to make decisions Ability to handle masses of data with help of computer
  • 18. Management Techniques/ Methods in OR A. Statistical techniques 1. Time trends & forecasting 2. Decision theory & tree B. Activity analysis 1. Time motion studies 2. Work sampling & activity analysis 3. Queuing theory 4. Gantt chart & work schedule C. Mathematical techniques 1. Simulation study/models 2. System analysis 3. Linear programming 4. Inventory control 5. Network analysis - PERT & CPM D. Financial techniques 1. Monitoring expenditure 2. Cost accounting & analysis 3. DALY 4. Cost benefit analysis 5. Cost effectiveness analysis 6. Zero base budgeting 7. Input output analysis 8. Outcome budget E. Miscellaneous 1. Management by exception 2. Situational analysis 3. Current state assessment 4. SWOT analysis 5. Log frame analysis 8/10/2018 Operations research 18
  • 19. Time trends & forecasting 8/10/2018 Operations research 19 ā€¢ Data gathered on a given characteristic over a period of time at regular intervals ā€¢ Predictions can be made about expected occurrence, by using mathematical methods ā€¢ If incidence of a disease exceeds expectation by certain limits, epidemic can be anticipated, detected at the earliest and appropriate steps taken for control
  • 20. Time trends & forecasting Contā€¦ 8/10/2018 Operations research 20 ā€¢ Forecasting is defined as the science of predicting for future ā€¢ Forecasting the demand for supplies of materials like vaccine, drugs etc, can also be similarly anticipated and a state of preparedness maintained
  • 21. Situation 1 8/10/2018 Operations research 21 As a medical officer in-charge of the hospital you have observed that in the past 3 years, many measles cases are coming to your hospital in the months of January till April ā€¢ Method applied: Time trends Calculate the measles vaccine requirements for one month, given the population being catered to is 36,000, CBR=22/1000population and IMR=9/1000 live births ā€¢ Method applied: Forecasting
  • 22. Decision theory & Decision tree 8/10/2018 Operations research 2 ā€¢ Decision theory is the body of analytical tools, including logic & mathematical models, using probability theory & diagrammatic representation for use in decision making ā€¢ Decision tree is a diagram which depicts key interactions among decisions & associated chance events ā€¢ The most rational decision can be taken in terms of resource & the effectiveness
  • 23. Decision tree for micro invasive cancer of the cervix showing selected probabilities and possible utility calculations Available from URL: http://ars.els-cdn.com/content/image/1-s2.0-S0140673601057099-gr1.jpg 8/10/2018 Operations research 23
  • 24. Decision analysis 8/10/2018 Operations research 24 ā€¢ Process of making choices from among several alternatives ā€¢ Includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing important aspects of a decision ā€¢ Helps in prescribing a recommended course of action by applying the maximum expected utility action
  • 25. Time motion studies 8/10/2018 Operations research 25 ā€¢ Consists of observing & timing by using stopwatches the physical work & movements carried out by a worker ā€¢ The movements carried out in performance of a task are then broken into segments, analyzed & redesigned so that task can be accomplished more efficiently
  • 26. Situation 2 8/10/2018 Operations research 26 Sisters in the ward always complained that the ward boys were not available at the time of emergency. Activities of the ward boy included shifting the patients to x-ray/ USG department; helping during dressing; handing over blood & urine samples to lab; collecting reports, miscellaneousā€¦. ā€¢ Method applied: Time motion studies
  • 27. Situation 3 8/10/2018 Operations research 27 In the hospital at reception counter patients arrive at an interval of 5 minutes & reception desk takes 2 minutes for servicing each patient. Under these conditions: How long on an average a patient does wait in the queuing system? If the management is of the view that it can allow a waiting time up to 5 minutes only, how much does the flow of patients be to justify for opening a second counter in the reception desk? ā€¢ Technique applied: Queuing theory
  • 28. Queuing theory 8/10/2018 Operations research 28 ā€¢ Concepts and parameters used in queuing theory o Waiting time cost & service cost o Mean arrival time of customers - ļ¬ o Mean service rate - ļ­ ā€¢ In the above scenario: Arrival pattern o Mean inter arrival time=(1/ mean arrival time)=(1/ļ¬)=5 mn o Mean arrival rate per minute = (1/5) = 0.2 patients o Mean arrival rate per hour = 0.2 x 60 = 12 patients per hour
  • 29. Queuing theory Contā€¦ 8/10/2018 Operations research 2 ā€¢ Service pattern o Mean service time per patient = (1/ Mean service rate) = (1/ļ­) = 2 minutes o Patients served per minute = (1/2) = 0.5 o Patients served per hour = 0.5 x 60= 30 patients ā€¢ Average waiting time of a patient in the queue E(w) = {ļ¬/ ļ­ (ļ­-ļ¬)}= 12/30 (30-12)= 1/45 =0.22 hour or 1.33 minutes ā€¢ To open a second counter- how much should be the patient inflow?
  • 30. Queuing theory Contā€¦ 8/10/2018 Operations research 30 ā€¢ Mean arrival rate of patients E (w) = {ļ¬ā€™/ ļ­ (ļ­-ļ¬ā€™)}where ļ¬ā€™ - expected arrival rate E(w)=average waiting time of a patient in queue=5 min or (1/12) hr, (1/12) = {ļ¬ā€™/ 30 (30-ļ¬ā€™)} So ļ¬ā€™ = arrival rate per hour = 21.43, nearly 3/min ā€¢ Hence mean arrival rate should go up to 21 from present 12 or nearly one patient for every 3 minutes, in contrast to one patient for every 5 minutes, to justify for the setting up of second counter
  • 31. Linear Programming 8/10/2018 Operations research 31 ā€¢ For use with a common management problem ā€“ the allocation of resources in an optimum manner ā€¢ Mathematical or graphical technique - used to determine best use of scarce resources to accomplish a defined objective ā€¢ Used when problems have these characteristics: o mix o needs an optimum solution o Constraints o linear relationship
  • 32. Situation 4 8/10/2018 Operations research 32 Is it possible to predict number of nursing personnel of each type needed for each nursing unit based on information concerning the number and degree of illness of each patient? ā€¢ Method applied: Linear Programming ā€¢ This can be done immediately before each shift reports for duty by computerized program matched against current patient illness characteristics, and assignments of nursing personnel can thus be made on a predicted patient care need for next shift rather than just on number of patients on each unit, or merely based on number of beds in each unit
  • 33. Network Analysis 8/10/2018 Operations research 33 ā€¢ Method of presentation of composite activities - diagrammatic form recording their interdependence of an operation - total view of situation from start to finish ā€¢ Depicts interdependency of activities, by splitting up the total project into activities & assists in estimation of time for each activity & enables in target achievement ā€¢ Enable better planning & evaluation of proposed schedule of activities
  • 34. 8/10/2018 Operations research 34 Network Analysis Critical Path Method (CPM) Time required for completion of activity is estimated This estimation does not involve any statistical methodology Program Evaluation & Review Technique (PERT) Assumes 3 time estimates for each activity in terms of optimistic, pessimistic & most likely time for completion of activity Calculated using these 3 times through statistical average approach ā€¢ Enables stricter control on completion of activity in time besides enabling in estimation of men, money & material for completion of program in scheduled time ā€¢ Depending on the situations, it also helps in modification of time required for activities
  • 35. Steps involved in drawing a network 8/10/2018 Operations research 35 List all activities to be performed with well defined end point Schedule events in sequential order ā€“ merge/ burst events Assess performance time for each event Put events in sequential chain taking interdependence of events Converted into graphic line from start to finish along with time Each chain will have total time of completion - All chains together form NETWORK Chain with maximum required time is THE CRITICAL PATH
  • 36. Situation 5 8/10/2018 Operations research 36 How to set up a laboratory in a hospital? ā€¢ Method applied: Network analysis ā€¢ CPM & PERT
  • 37. Respective chains can be drawn as: 8/10/2018 Operations research 37 ā€¢ A: Placing orders for equipment & furniture ā€¢ D: Supply of equipment & furniture ā€¢ G: Installation of for equipment & laboratory Chain 1 Related to equipment ā€¢ B: Procurement of chemicals & reagents ā€¢ E: Stacking of chemicals & reagents ā€¢ H: Preparation of protocols for investigations Chain 2 Related to chemicals & reagents ā€¢ C: Advertise for personnel ā€¢ F: Recruitment of personnel ā€¢ I: Training of personal Chain 3 Related to staff
  • 38. 8/10/2018 Operations research 38 Ev ent Acti vity Description activity Predecesso r activity T(e) (day) 1 A Placing orders for equipment & furniture - 3 1 B Procurement of chemicals & reagents - 5 1 C Advertise for personnel - 4 2 D Supply of equipment & furniture A 2 3 E Stacking of chemicals & reagents B 3 4 F Recruitment of personnel C 9 5 G Installation of for equipment & laboratory D,E 8 6 H Preparation of protocols for investigations B 7 7 I Training of personal G,H 9
  • 39. Network Analysis 8/10/2018 Operations research 39 Critical path, slack time, non critical path, bottleneck/ critical activities, EST, EFT, LFT, LST, floats
  • 40. Network Analysis 8/10/2018 Operations research 40 CPM ā€¢ Advantages: ā€¢ Ascertaining time schedule ā€¢ Makes detailed planning possible ā€¢ Identifies most critical elements ā€¢ Limitations: ā€¢ May not be a true assumption in practice ā€¢ Does not incorporate statistical analysis PERT ā€¢ Advantages: ā€¢ Ability to plan best possible use of resources ā€¢ Presses for right action, at right point, & at right time ā€¢ Limitations: ā€¢ Difficulty in way of time estimates ā€¢ Does not consider resources required at various stages ā€¢ Frequent updating & revising calculations-costly affairs
  • 41. Inventory Control 8/10/2018 Operations research 41 ā€¢ ā€œUsable but idle resource having an economic valueā€ ā€¢ ā€˜Paretoā€™s lawā€™ - forms the basis ā€¢ Ultimate aim in healthcare setting - to ensure that adequate and optimal essential items are properly stored, controlled, are easily retrievable and distributed to points of uses so that patient care does not suffer due to lack of these essential medical supplies
  • 42. Various selective inventory control measures 8/10/2018 Operations research 42 ā€¢ ABC: Based on annual total cost of items ā€¢ VED: Based on criticality and importance of consumables, items are classified as Vital (V), Essential (E) & Desirable (D) ā€¢ HML: Based on cost of individual item as High cost (H), Medium cost (M) and Low cost (L) ā€¢ SDE: Based on ease of availability of items - classified as Scarce (S), Difficult to obtain (D) and Easy to obtain (E)
  • 43. Various selective inventory control measures 8/10/2018 Operations research 43 ā€¢ GOLF: Based on source of supply & include Governmental sources (G), Ordinary (O), Local (L) & Foreign (F) ā€¢ FSN: Based on rate of issue from the stores into Fast- moving (F), Slow moving (S) & Nonmoving (N) items ā€¢ SOS: Based on Seasonal (S) & Off-seasonal (OS) availability ā€¢ XYZ: Based on value of stocks of items held
  • 44. Situation 6 8/10/2018 Operations research 44 Have to indent essential drugs. How much to indent? How frequently to indent? ā€¢ Method applied: Inventory control ā€¢ In a hospital setting, combination of ABC analysis (based on annual cost) and VED analysis (based on criticality of item) is to be adopted ā€¢ Category I: Contain all the vital and costly items ā€¢ Category II: Items that are essential but are less costly ā€¢ Category III: Items that are desirable
  • 45. Gantt chart 8/10/2018 Operations research 45 ā€¢ Horizontal bar chart developed as a production control tool in 1917 by Henry L. Gantt ā€¢ Provides a graphical illustration of a schedule that helps to plan, coordinate, and track specific tasks in a project ā€¢ Useful tool for analyzing and planning complex projects ā€¢ Help to monitor whether the project is on schedule ā€¢ Assess how long a project should take, determine resources needed, & lay out order in which tasks need to be carried out
  • 46. Situation 7 8/10/2018 Operations research 46 Consider constructing a hospital in your district ā€¢ Method applied: Gantt chart
  • 47. List of activities in hospital construction project 8/10/2018 Operations research 47 Acti vity Description Predece sors Duration (weeks) A Select administrative and medical staff - 12 B Select site and do site survey - 9 C Select equipment A 10 D Prepare final construction plans B 10 E Bring utilities to the site B 24 F Interview applicants & fill positions in nursing support staff, maintenance A 10 G Purchase & take delivery of equipment C 35 H Construct the hospital D 40 I Develop an information system A 15 J Install the equipment E, G, H 4
  • 48. Gantt chart for hospital construction project 8/10/2018 Operations research 48
  • 49. SWOT Analysis 8/10/2018 Operations research 49 ā€¢ Strengths (S), Weaknesses (W), Opportunities (O) &Threats (T) are identified in context of proposed program ā€¢ S&W - Permanent phenomena that exist within organization ā€¢ O&T - Temporary, often fleeting, phenomena that exist in external environment S: Powerful attributes, which it may possess W: Actual or potential liabilities & weak points O: Circumstances conducive to its flourishing & growth further T: Aspects which may hinder its growth & development
  • 50. Situation 8 8/10/2018 Operations research 50 Proposed programme for prevention & control of HIV in our country ā€¢ Method applied: SWOT Analysis S: Organizational & constitutional philosophy & political will of the country W: Common social tendency not to encourage talking about sexual health O: Funds for developing health educational material & strongly in favor of educating public & high risk groups T: Some recent resistance and objection from parents against sex education of children
  • 51. Financial Techniques 8/10/2018 Operations research 51 Cost Accounting/Cost Analysis ā€“ tool for measuring the cost of health services. ā€¢ Ex: Unit cost of items like drug consumption/day/patient ā€¢ Costing also helps to assess the efficiency & effectiveness of functions Cost Benefit Analysis - evaluation method for comparing the monetary value of all resources consumed (costs) in providing a program or intervention with the monetary value of the outcome (benefit) from the program or intervention
  • 52. Financial Techniques Cont... 8/10/2018 Operations research 52 Cost effectiveness analysis - To determine which program accomplishes given objective at least cost. Effectiveness is measured in terms of non-monetary units that describe desired objective (Lives saved/ disability days avoided/ cases treated) Zero based budgeting (ZBB) - ā€œPlanning & budgeting process which requires each manager to justify entire budget in detail from ā€˜scratchā€™ (ā€˜zero baseā€™) thereby making it responsibility of each manager to justify why he should spend any money at all during budget periodā€
  • 53. Challenges of OR 8/10/2018 Operations research 53 ā€¢ Operate in absence of detailed, systematic research plan, with clear linkages to programme priorities ā€¢ Implementing research studies in absence of a carefully conducted situation analysis prevents from achieving their desired goals ā€¢ Appropriate external sources of support ā€“ financial, technical and research mentoring ā€“ must be in place at all stages of planning and implementation of research. Such resources are insufficient or absent at some or all stages ā€¢ Training in OR methodology is required for both service providers and academics
  • 54. Critical Review of OR in Public Health 8/10/2018 Operations research 54 ā€¢ Gaining importance in public health programs and interventions increasingly both nationally and internationally ā€¢ Guide program implementation to achieve best results ā€¢ Modulates inputs & processes involved & strive to produce optimal gains in achieving targets & goals ā€¢ Identifies problems; often program managers encompass in operation of public health goods and test the feasible solutions for them
  • 55. 8/10/2018 Operations research 55 Approaches for OR in Public Health Secondary data analysis Primary level research Types of OR studies as defined by the Population Council Exploratory study Field intervention Monitoring & Evaluation Economic analysis
  • 56. How to measure the success of OR? 8/10/2018 Operations research 56 ā€¢ Results & new knowledge must also lead to action, which will lead to changes in clinical or laboratory practice & management & if possible, also to changes in policy ā€¢ All OR & new knowledge created by research should lead to & be measured by: o Publications o Capacity development of service providers & academic researchers o Changes in practice and/or policy
  • 57. Conclusion 8/10/2018 Operations research 57 ā€¢ To survive & lead todayā€™s highly competitive & demand driven market, pressure is on management to make economical decisions ā€¢ One of essential managerial skills is ability to allocate & utilize resources appropriately in the efforts of achieving optimal performance efficiently ā€¢ Translating outcomes of research into practice will lead to a better health system in terms of 4 Aā€™s ā€“ accessibility, availability, affordability and acceptability bridging prevailing inequities & disparities
  • 58. References 8/10/2018 Operations research 58 1. WHO. Grunde F, Reinke WA. Health practice research and formalised managerial methods. [serial online] Geneva: WHO; 1973. Available from URL: http://apps.who.int/iris/bitstream/10665/40852/2/WHO_PHP_51_r us.pdf 2. Sathe PV. Epidemiology and management for health care for all. 4th ed. Mumbai: Vora publications; 2009. p.173-190. 3. Vani C. Operation research. Seminar notes. Department of community medicine. 4. Chetana T. Operation research.Seminar notes. Department of community medicine. 5. Rao.NSN. Operation research techniques in health care management. Unpublished material 6. Organization & management of hospitals. PGDHHM-03. New Delhi: Akashdepp publishers;2009.
  • 59. References Cont... 8/10/2018 Operations research 59 7. Agarwal S, Subramanian K R, Kapoor S. Operations research - contemporary role in managerial decision making. IJRRAS [serial online] 2010 May [cited 2017 Jan 2] Available from URL: http://www.arpapress.com/Volumes/Vol3Issue2/IJRRAS_3_210.pdf 8. WHO. Foreit J, Schmid G. Guide to operational research in programs supported by the global fund. [serial online] Geneva: WHO. [cited 2016 Dec 26] Available from URL: http://www.who.int/hiv/pub/operational/or_guide_gf.pdf 9. Swarup K, Gupta PK, Mohan M. Operations research. 13th ed New Delhi: Sultan Chand & sons educational publishers; 2007. 10. Gantt chart. [serial online] [cited 2016 Dec 23] Available from URL:http://www.improhealth.org/fileadmin/Documents/Improvem ent_Tools/Gantt_Chart.pdf
  • 60. References Cont... 8/10/2018 Operations research 60 11. WHO. Application of system analysis to health management. Technical Report Series 596. [serial online] Geneva: WHO. [cited 2017 Jan 3] Available from URL: http://whqlibdoc.who.int/trs/WHO_TRS_596.pdf 12. Bhalwar R, Vaidya R, Tilak R, Gupta R, Kunte R. Text book of public health and community medicine. Pune: Department of Community Medicine Armed Forces Medical College; 2009. 13. W. Durfee and T. Chase (2003), Brief tutorial on Gantt charts, University of Minnesota 14. Malhotra S, Zodpey SP. Operations research in public health. Indian Journal of Public Health July-September 2010; 54 (3): 145- 15 15. Korenromp E, Komatsu R, Katz I, Katz I, Xueref S, Low-Beer D. Operational research on HIV/AIDS, tuberculosis and malaria control in Global Fund-supported programmes: Round 1-6 grants. In: Proceedings of the 5th European conference on tropical medicine and international health, Amsterdam, 24ā€“28 May 2007
  • 61. References Cont... 8/10/2018 Operations research 61 16. HIV testing, treatment and prevention: generic tools for operational research. Geneva: World Health Organization; 2009. 11. 17. The framework for operations and implementation research in health and disease control programmes. Geneva: World Health Organization; 2008. 20. 18. Trochim WM, Cabrera DA, Milstein B, Gallagher RS, Leischow SJ. Practical challenges of systems thinking and modeling in public health. Am J Public Health 2006; 96: 538-46 48. 19. Zachariah R, Harries AD, Ishikawa N, Rieder HL, Bissell K, Laserson K, et al., et al. Operational research in low-income countries: what, why, and how? Lancet Infect Dis 2009; 9: 711-7 20. Geoff Royston. Meeting global health challenges through operational research and management science. Bulletin of the World Health Organization 2011;89: 683-688. 21. Rama Murthy P. Operations research. 2nd edition. New Delhi: New Age International Publishers; 2007.
  • 62. References Cont... 8/10/2018 Operations research 62 22. Rais A, Viana A. Operations Research in Healthcare: a survey. Intl Trans in Op Res. Jan 2010; 18: 1ā€“31. 23. Boldy, D. Operational Research Applied to Health Services. New York: St. Martinā€™s Press; 1981. 24. Brandeau, M., Sainfort, F., Pierskalla, W. Operations Research and Health Care. A Handbook of Methods and Applications. Kluwerā€™s International Series, Dordrecht; 2004. 25. Linda V. Using Operations Research to Reduce Delays for Healthcare. Tutorials in Operations Research, 2008 INFORM. 26. Guide To Operational Research In Programs Supported By The Global Fund. WHO.
  • 63. Exercise: MR Campaign 8/10/2018 Operations research 63 Activity Activity Description Immediate Predecessor Te A Establishment of surveillance --- 2W B Local epidemiological information --- 2W C Knowledge of public perceptions --- 2W D To obtain funds for cold chain --- 4W E Identification of staff A 3W F Development of training materials B 4W G Training staff E, F 3W H Development of health education material C,B 4W I Public acceptance H 2W J Establishment of cold chain D 3W K Availability of vaccine J 2W Ending Vaccination programme on G,I,K ---