CHAPTER ONE
INTRODUCTION TO OPERATIONS
RESEARCH AND MODELLING
Mulugeta K. (PhD)
Department of Management
1.1. Introduction to Operations Research (OR)
• Operations Research (OR) came in to existence as a
discipline during World War II:
– when there was a critical need to manage scarce
resources.
• The term “Operations research” was coined as a
result of research on military operations during this
war.
• The objective was the most effective utilization of
most limited military resources by the use of
quantitative techniques.
Cont…
OR/Management Science Defined
• OR is a scientific approach to decision making,
which seeks to determine how best to design and
operate a system, usually under conditions requiring
the allocation of scarce resources.”
-Winston
• Management science is the application of a scientific
approach to solving management problems in order
to help managers make better decisions.
-Taylor and Bernard
Cont…
• It is a scientific method of providing executive
departments with a quantitative basis for decisions
regarding the operations under their control.”
- Kimball & Morse
• In general,
• OR is a systematic application of quantitative
methods, techniques and tools to the analysis of
problems involving the operation of systems.
– A quantitative approach to decision making
Cont…
• Other names used for this discipline include:
– Management science (MS)
– OR/MS or just ORMS
– Industrial engineering (IE),
– Decision Science (DS) and Problem solving
• In OR, problems are:
– Decomposed into basic components and
– Solved via mathematical analysis.
Significance Operations Research
• Helps to balance conflicting objectives (goals or
interests) of sub units in the organization.
– where there are many alternative courses of
action available to the decision-makers.
• OR Balances the following:
# Global Optimum: the decision that is best for the
organization as a whole.
# Suboptimum decision: A decision that is best for
one or more sections of the organization
Benefits of OR
• OR helps companies to:
– Minimize Cost of Investment
– Increase Revenue or ROI
– Increase Market Share
– Manage and Reduce Risk
– Improve Quality
– Increase Throughput while Decreasing Delays
– Improves Utilization of Limited Resources
– Demonstrate Feasibility and Workability
Features of Operations Research Approach
• Features of OR approach to any decision and control
problems include:
 Inter-disciplinary approach
 Methodological Approach
 Holistic Approach/ Systems Orientate
 Objectivistic Approach
 Decision Making Approach
 Use of Computers
 Human factors
Cont…
• A system is an organization of interdependent
components that work together to accomplish the
goal of the system.
• The components may be either physical or
conceptual or both but they share a unique
relationship with each other and with the overall
objective of the system.
Cont…
• We have said that OR is a quantitative and rational
approach to decision making.
• The scientific approach to decision making requires
the use of one or more mathematical models.
• A mathematical model is a mathematical
representation of the actual situation that may be
used to make better decisions or clarify the situation.
1.2. An Introduction to Modeling in OR
• What is a model?
– A representation of an object, a system, or an idea
in some form other than that of the entity itself.
- Shannon
– A model is a limited approximation of reality.
– Models do not and cannot represent every aspect
of reality.
• The reason being the innumerable and changing
characteristics of the real life problems
Cont…
• For a model to be effective, it must:
– be representative of those aspects of reality that
are being investigated and
– have a major impact on the decision situation.
• A model is constructed to analyze and understand
the given system for the purpose of improving its
performance.
• It allows an examination of the behavioral changes
of a system w/o disturbing the on-going operations.
Types of OR Models
• There are many ways to classify models:
Based on structure
a. Physical Models: provide a physical appearance of
the real object under study either reduced in size or
scaled up.
–
Example: Scale models, prototype plants,…
b. Symbolic models: use symbols and functions to
represent variables and their relationships to
describe the properties of the system.
Cont…
Based on function or purpose
a. Descriptive models: describe some aspects of a
situation, based on observation, survey, interview
and questionnaire results or available data.
– They do not recommend anything.
b. Predictive Models: indicate “If this occurs, then that
follow”.
– They relate dependent and independent
variables and permit trying out, “what if”
questions.
Cont…
• For example:
S = a + bA +cI
• is a model that describes how the sales (S) of a
product changes in advertising expenditures (A) and
disposal personal income (I).
• Here, a, b, and c are parameters whose values must
be estimated.
• These models do not have an objective function as a
part of the model.
Cont…
c. Normative (Optimization) models: provide the
“best” or “Optimal” solution to problems subject
to certain limitations on the use of resources.
– They provide recommended courses of action.
– These models are also called prescriptive
models, because they prescribe what the
decision maker ought to do.
– Example: Mathematical programming models
(LP, IP, TP, AP etc)
Cont…
Based on Time Reference
a. A static model is one in which the decision variables
do not involve sequences of decisions over multiple
periods. [do not account for changes over time.]
– Example: EOQ (Inventory model)
b. A dynamic model is a model in which the decision
variables do involve sequences of decisions over
multiple periods.
– Example: Dynamic programming
Cont…
Based on degree of certainty
a. Deterministic Models:
If all the parameters,
constants and functional relationships are assumed
to be known with certainty
– Examples: Linear programming models
b. Probabilistic (Stochastic) models: Models in which at
least one parameter or decision variable is random.
– But it is possible to predict a pattern of values of
the variables by their probability distribution.
Cont…
Based on Method of solution or Quantification
a. Heuristic Models: employ some sets of rules which,
though not optimal, do facilitate solutions of
problems
b. Analytical Models: have a specific mathematical
structure and can be solved by known analytical
techniques. [Eg: Optimization models]
c. Simulation Models: have a mathematical structure
but are not solved by applying known
mathematical techniques.
Cont…
• What benefits do you think do models have?
Seven Steps to Good OR Analysis
1. Observe and Identify the Problem
– Define the problem (Is it too narrow or too broad?)
– Specify objectives
– Determine parts of the organization to be studied.
2. Understand the System
– Determine parameters affecting the problem.
– How different components of the system ınteract
wıth each other?
– Collect data to estimate values of the parameters.
Cont…
3. Formulate a Mathematical Model
• Basic components required in decision problem
model are:
–
–
–
–
–
–
Controllable (decision) Variables
Uncontrollable variable
Objective function
Constraints or Limitations
Functional relationships
Parameters
Cont…
• A general decision problem model might take the
form:
Cont…
ꙮ A model is referred to as a linear model if all
functional relationships among decision variables X1,
X2, Xn in f(x) and g(x) are of a linear form.
ꙮ But if one or more of the relationships are non –
linear, the model is said to be a non-linear model.
ꙮ If one or more of the decision variables must be
integer, then the model is an integer model.
ꙮ If all the decision variables are free to assume
fractional values, then the model is a non-integer
model.
Cont…
4. Verify the Model and Use the Model for Prediction
– Do outputs match current observatıons for
current ınputs?
– Are outputs reasonable?
– Could the model be erroneous?
5. Select a Suitable Alternative
– Given a set of alternative solutions, determine
which solution best meets the objectives.
– Inherently the most difficult step.
Cont…
6. Present the Results of the Analysis
– Present the results to the decision maker(s)
• If necessary, prepare several alternative
solutions and permit them to choose.
– Any non-approval of the study’s solution may
have stemmed from an incorrect problem
definition or failure to involve the decision
maker(s) from the start of the project.
• In such a case, return to step 1, 2, or 3.
Cont…
7. Implement and Evaluate Recommendations
• Assist in implementing the recommendations.
• Monitor and dynamically update the system as
the environment and parameters change to
ensure that recommendations enable the
organization to meet its goals.
Real Life Example: GE Capital
• GE Capital provides credit card service to 50 million
accounts with an average outstanding balance of $12
billion.
• GE Capital led by Makuch et al. (1989) developed the
PAYMENT system to reduce delinquent accounts and
the cost of collecting from delinquent accounts.
# Step 1: Its goal was to reduce the delinquent accounts
and the cost of processing them.
– To do this, GE capital needed to come up with a
method of assigning scarce labor resources to
delinquent accounts.
Cont…
# Step 2: The key to modeling delinquent accounts is
the concept of a delinquency movement matrix
(DMM).
– The DMM determines how the probability of the
payment on a delinquent account during the
current month depends on the following factors:
• size of unpaid balance
• action taken
• performance score
Cont…
• Step 3 GE developed a linear optimization model.
– The objective function was to maximize the expected
delinquent accounts collected during the next six
months.
– The decision variables represented the fraction of each
type of delinquent account.
– The constraints ensure that available resources are not
overused.
– Constraints also relate the number of each type of
delinquent account present in, say, January to the
number of delinquent accounts for each type present in
the next month.
– This dynamic aspect is crucial to the model’s success.
Cont…
# Step 4: PAYMENT was piloted on a $62 million portfolio
for a single department store.
– GE Capital managers came up with their own
strategies for allocating resources (called CHAMPION).
– Store’s accounts were randomly assigned to the
CHAMPION and PAYMENT strategies.
– PAYMENT used more live calls and “no action”.
– PAYMENT showed a 5-7% improvement over
CHAMPION.
# Step 5: For each type of account PAYMENT tells the credit
managers the fraction that should receive each type of
contact.
Cont…
# Steps 6 and 7: PAYMENT was next applied to the 18
million accounts of the $4.6 billion Montgomery
Ward store portfolio.
– Comparing accounts to the previous year,
PAYMENT increased collections by $1.6 million
per month.
– Overall, GE Capital estimated PAYMENT increased
collections by $37 million per year and used
fewer resources than previous strategies.
Some other Successful Applications of OR
Company
Year
Problem
Designing buffers into production
line
Techniques Used
Annual Savings
Hewlett Packard
1998
Queuing models
$280 million
Taco Bell
1998
Employee scheduling
IP, Forecasting, Simulation
$13 million
Proctor & Gamble
1997
Redesign production & distributon
system
Transportation models
$200 million
Delta Airlines
1994
Assigning planes to routes
Integer Programming
$100 million
AT&T
1993
Call center design
Queuing models,
Simulation
$750 million
Yellow Freight Systems,
Inc.
1992
Design trucking network
Network models,
Forecasting, Simulation
$17.3 million
San Francisco Police
Dept.
1989
Patrol Scheduling
Linear Programming
$11 million
Bethlehem Steel
1989
Design an Ingot Mold Stripper
Integer Programming
$8 million
North American Van
Lines
1988
Assigning loads to drivers
Network modeling
$2.5 million
Citgo Petroleum
1987
Refinery operations & distribution
Linear Programming,
Forecasting
$70 million
United Airlines
1986
Scheduling reservation personnel
LP, Queuing, Forecasting
$6 million
Dairyman's Creamery
1985
Optimal production levels
Linear Programming
$48,000
Phillips Petroleum
1983
Equipment replacement
Network modeling
$90,000
[Some] Application Areas of OR
 Transportation and Travel
• OR techniques are used by airlines and rail companies to
offer varying fares and make higher revenues by filling more
seats at different prices - an OR technique known as Yield
Management. All airlines depend on the effective use of OR
techniques to make them operate at a profit.
Financial Services
• Used to address issues such as portfolio and risk
management, planning and analysis of customer service.
They are widely employed in Credit Risk Management—to
find optimum balance of risk and revenue.
Cont…
Retailing
• In supermarkets, data from store loyalty card schemes is
analyzed by OR groups to advise on merchandising policies &
profitability improvement. OR methods are also used to
decide when and where new store developments should be
made.
Health
• Hospital managers use OR to make decisions such as
determining the optimal utilization of operating rooms and
personnel, assessing the risks posed by patients with various
medical conditions, and deciding necessary levels of
perishable medicine in stock.
Cont…
 Government
• OR is a key contributor in modernizing government services
and making them more efficient. Some OR applications
include modeling the impact of performance related
paying for employees, evaluating government call-centers,
projecting the size of the prison population, and national
defense…..
 Production Systems
• Such problems may arise in settings that include, but are
not limited to, manufacturing, telecommunications,
health-care delivery, facility location, layout, and staffing
Common Operations Research Models
1. Allocation Models: Optimization models
•
•
Helps to solve both:
Linear programming problems, and
Non-linear programming problems
Allocation models include
– Linear programming
– Integer programming
– Goal programming
– Stochastic programming
– Transportation problems
– Assignment problems
Cont…
2. Probabilistic Models
–
–
Decision Analysis models
Queuing Theory
3. Inventory Model
–
–
EOQ
EPQ
4. Network Models
–
–
CPM
PERT
5. Competitive (Game Theory) Model
6. Simulation Models
Algorisms and OR Software Packages
• Popular tools/ modeling systems, approaches and
software packages include:
–
–
–
–
–
–
Excel Solver
LINDO/LINGO
MATLAB
OR Tutor
CPLEX
MPL
Recommended OR Journals
• The following academic journals contain many useful
articles that reflect state of the art applications of OR.
1. Operations Research
2. Management Science
3. European Journal of Operational Research
4. Journal of the Operational Research Society
5. Mathematical Programming
6. Networks
7. Naval Research Logistics
8. Interfaces
• The first seven of the above are mainly theoretical whilst the
eighth (Interfaces) concentrates upon case studies.
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