LPP application and problem formulation

Application and Model
Formulation
Lesson- 3

Examples
• British Telecom used OR to schedule workforce for more than 40,000 field engineers. The system
was saving $150 million a year from 1997~ 2000. The workforce is projected to save $250 million.
• Sears Uses OR to create a Vehicle Routing and Scheduling System which to run its delivery and
home service fleet more efficiently -- $42 million in annual savings
• UPS use O.R. to redesign its overnight delivery network, $87 million in savings obtained from
2000 ~ 2002; Another $189 million anticipated over the following decade.
• USPS uses OR to schedule the equipment and workforce in its mail processing and distribution
centers. Estimated saving in $500 millions can be achieve.
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Case 1: Continental Airlines Survives 9/11
• Problem: Long before September 11, 2001,
Continental asked what crises plan it could use to
plan recovery from potential disasters such as
limited and massive weather delays.

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Continental Airlines (con’t)
• Strategic Objectives and Requirements are to accommodate:
• 1,400 daily flights
• 5,000 pilots
• 9,000 flight attendants
• Federal Aviation Administration
(FAA) regulations
• Union contracts

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• Model Structure: Working with CALEB
Technologies, Continental used an optimization
model to generate optimal assignments of pilots &
crews.
• The solution offers a system-wide view of the
disrupted flight schedule and all available crew
information.

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• Project Value: Millions of dollars and thousands of
hours saved for the airline and its passengers.
• After 9/11, Continental was the first airline to
resume normal operations.

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Case 2: Ford Motor Prototype Vehicle Testing
• Problem: Developing prototypes for new cars and
modified products is enormously expensive. Ford
sought to reduce costs on these unique, first-of-a-
kind creations.

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Ford Motor (con’t)
• Strategic Objectives and Requirements: Ford needs
to verify the designs of its vehicles and perform all
necessary tests.
• Historically, prototypes sit idle much of the time
waiting for various tests, so increasing their usage
would have a clear benefit.

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• Model Structure: Ford and a team from Wayne
State University developed a Prototype
Optimization Model (POM) to reduce the number
of prototype vehicles.
• The model determines an optimal set of vehicles
that can be shared and used to satisfy all testing
needs.

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• Project Value: Ford reduced annual prototype
costs by $250 million.

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Case 3: Procter & Gamble Supply Chain
• Problem: To ensure smart growth, P&G needed to
improve its supply chain, streamline work
processes, drive out non-value-added costs, and
eliminate duplication.

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P&G Supply Chain (con’t)
• Strategic Objectives and Requirements: P&G
recognized that there were potentially millions of
feasible options for its 30 product-strategy teams
to consider.
• Executives needed sound analytical support to
realize P&G’s goal within the tight, one-year
objective.

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• Model Structure: The P&G operations research department and the
University of Cincinnati created decision-making models and
software. They followed a modeling strategy of solving two easier-to-
handle subproblems:
• Distribution/location
• Product sourcing

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• Project Value: The overall Strengthening Global
Effectiveness (SGE) effort saved $200 million a year
before tax and allowed P&G to write off $1 billion
of assets and transition costs.

• The quantitative analysis approach consists of-
• defining a problem,
• developing a model,
• acquiring input data,
• developing a solution,
• analyzing the results and
• implementing the results.

Identification of
the problem(
Formulation)
Establishment
of the model
Obtain solution
for model
Testing the
model and
solution
Implementation
of the Model

Stage 1 – Identification/ Defining the problem
• A good start is half the job done
• Right Solution can not be obtained for a wrongly understood problem
• Visit doc- Headache- only medicine for headache
• Coming back – sore throat , cold??????????? No cure
• Service repair-
• My car is puncture
• Problem – low mileage – not repair??
• Correct problem lead to correct solution

• So problem identification and definition is the most difficult step, It is
essential to go beyond the symptoms of the problem and identify the
true causes.
• Experience shows that bad problem definition is main reason for
failure of management science and Operations Research groups/
Any thoughts:
It is likely that an organization will have several problems, However a
quantitative analysis group usually can not deal with all problems at a
time. What next?

• Also, when a problem is difficult to quantify, it may be necessary to
develop SPECIFIC, MEASURABLE OBJECTIVES.
• A problem might be inadequate healthcare care delivery in a hospital.
The objectives might be to increase the number of beds, reduce the
average number of days a patient spends in a hospital, increase the
physician-to-patient ratio and so on.

• Formulate the problem: This is the most important process, it is
generally lengthy and time consuming. The activities that constitute
this step are visits, observations, research, etc. With the help of such
activities, the O.R. scientist gets sufficient information and support to
proceed and is better prepared to formulate the problem.
• This process starts with understanding of the organizational climate,
its objectives and expectations. Further, the alternative courses of
action are discovered in this step.

• This phase helps examine the problem at hand quantitatively
• This phase deals with issues like:
• Defining goals
• Determination of the system which will impact the problem
• Determination of the constraints which will affect solution of problem
• Determination of the assumptions
• Determination of an appropriate measure of effectiveness

Stage 2- Establishment of the Model
• In your life we have been using various models, like you may have
developed models about people’s behavior.
• Your model might be that friendship is based on reciprocity, an exchange of
favors. So, if you need a favor such as small loan, your model would suggest
that you ask a good friend.
• Architects sometimes make a physical model of a building that will
construct, Engineers develop scale models of chemical plants.
• A schematic model is a picture, drawing or a chart of reality.
• In OR we use mathematical models/quantitative models which can be
expressed in mathematical equations and inequalities and spreadsheets
and softwares can be used.

Stage 2- Establishment of the Model
• While modelling a specific problem , various symbols are used
• 1- Iconic models(imitation / physical models)
• 2- Analog(schematic Models)
• 3- Mathematic(symbolic ) models

• Develop a model: Once a problem is formulated, the next step is to
express the problem into a mathematical model that represents
systems, processes or environment in the form of equations,
relationships or formulas.
• We have to identify both the static and dynamic structural elements,
and device mathematical formulas to represent the interrelationships
among elements. The proposed model may be field tested and
modified in order to work under stated environmental constraints. A
model may also be modified if the management is not satisfied with
the answer that it gives.

To remember:
• A mathematical model is a set of mathematical relationships. In most
cases these are expressed in equations and inequalities.
• Model consists of:
• Variable: measurable quantity that may vary or is subject to change.
• (can be controllable and uncontrollable- A controllable variable is also
called decision variable- how much inventory to order)
• Parameter- is a measurable quantity that is inherent in the problem.
(eg -The cost of placing an order for more inventory items)
• So, variables are unknown and parameter are known quantities/

• All models should be developed carefully , they should be solvable,
realistic, and easy to understand and modify, and required input data
should be obtainable.
• The model developer should be careful to include the appropriate
amount of detail to eb solvable yet realistic.

After developing a model we need input data
Once we develop a model, we must obtain the data that are used in
the model(input data)
• Select appropriate data input: Garbage in and garbage out is a
famous saying. No model will work appropriately if data input is not
appropriate. The purpose of this step is to have sufficient input to
operate and test the model.
• "Data quality is the difference between a data warehouse and a data
garbage dump." - Jarrett Rosenberg
Sources of input data??

Sources of input data??
Company reports and documents, interviews, sampling, direct
measurement
Eg: A production supervisor might be able to tell you with a great
degree of accuracy

Stage 3- Obtaining solution to the model
• Solution of the model: After selecting the appropriate data input, the
next step is to find a solution. If the model is not behaving properly,
then updating and modification is considered at this stage.
• Here, we will solve equations for the best decision, sometimes we
will use trial and error method as well, in some models we may want
to try all values of the variables in the model to arrive at a best
decision, this is called complete enumeration.
• A series of steps or procedures that are repeated is called an
algorithm, named after Algorismus, an Arabic mathematician of the
ninth century.

Stage 4- Testing the Model
• Before the application of the model solution, the validity of model and
reliability of the solution should be tested( for Accuracy, completeness of
data)
• Validity of the Model can be decided by comparing its outputs with the
results of the past. If past behaviour is repeated when provided similar
inputs then the model will be valid,
• We can also consider additional data(interviews etc, and statistical tests
can be applied to see variability among data sets) to check if model is
logical and represents real situation.
• Validation of the model: A model is said to be valid if it can provide a
reliable prediction of the system’s performance. A model must be
applicable for a longer time and can be updated from time to time taking
into consideration the past, present and future aspects of the problem

Analysing the results and Sensitivity analysis
• Model is only an approximation to reality, the sensitivity of the
solution to changes in the model and input data is a very important
part of analysing the results.
• This is called sensitivity analysis or post-optimality analysis. It tells us
how much solution will change if there are changes in the model or
input data.
• If solution is sensitive to changes in input data additional testing
should be done to ensure accuracy.

• Stage 5- Implementation of the solution
• Implementation of the solution obtained from a validated model is a
reliable solution to the real-life problems.
• It is a process of incorporating the solution into the company.
• You may face manager resistance and all efforts may have no value.
• After implementation as well , it should be closely monitored. There
can be some factors which may call for modifications like changing
Economy, fluctuating demand, model enhancement requests etc.

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Mathematical Models
• Cost/benefit considerations must be made in
selecting an appropriate mathematical model.
• Frequently a less complicated (and perhaps less
precise) model is more appropriate than a more
complex and accurate one due to cost and ease of
solution considerations.

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Mathematical Models
• Relate decision variables (controllable inputs) with fixed
or variable parameters (uncontrollable inputs).
• Frequently seek to maximize or minimize some objective
function subject to constraints.
• Are said to be stochastic if any of the uncontrollable
inputs (parameters) is subject to variation (random),
otherwise are said to be deterministic.
• Generally, stochastic models are more difficult to analyze.
• The values of the decision variables that provide the
mathematically-best output are referred to as the
optimal solution for the model.

Models in OR( Different classification
schemes)
• Based on degree of abstraction, functions of models, time horizon of
model, structure of the model, nature of environment, extent of generality
• Degree of abstraction-
• - Mathematical models- give us equations, give us nos. so that we can
understand a situation
• - Language models-like explaining you about the match that I saw
yesterday- like scores, very costly overs, hattrick,
• - Concrete models- solid models that you can see, very much evident, like a
flyover, a metro station etc
As we name it we can find nature of the model

• Based on functions-
• Descriptive models
• Predictive models
• Normative models
• Based on time horizon
• - Static Models
• - Dynamic Models
• Based on structure- Iconic models, Analog models, Symbolic Models

• Iconic models- Icon?? Icons on desktop, seen icons on mobiles- those icons
representative, when we see that picture, we can corelate like weather
application , photo gallery, news etc, calculator, music
• Scale down models, 3 D models, static and rigid, limited in scope, not allow to
modify, no what ifs?
• Analog models/ schematics- representation in pictorial form, flow charts symbols-
2 D models
In cars there are n no of wires- schematics tell me functions of wire
Laying wires in building Electrician will draw schematic diagram,( switchboards,
sockets, generators etc.), charts- bar graphs etc
Both of the above are visual but analog models can be changed
Symbolic and mathematical models- Simplex, Assignment, Transportation, Monte
Carlo, PERT CPM

• Nature of environment
• Deterministic models- like EOQ model
• Probabilistic models- Exponential smoothing in demand forecasting –
not too much sure
• Extent of generality-
• General models
• Specific models

• Career Scope of Operation Research: Employment Areas
• With a degree in Operation Research or its related field, candidates
can enter many employment areas. These leading job destinations
can carve your career and provide you with a high-end growth
ahead. To help you understand the scope of operation research, let’s
elaborate some of the top-notch job-sectors that you can explore.
• Defence Services
• Agriculture
• Industrial Sector
• Healthcare
• Logistics and Supply Chain Management
• Marketing Management

• Defence Services
• There are several departments in the defence services like
administrations, training, supply etc. which involves in-depth
knowledge of operations. To perform warfare tasks in the Army,
Navy, Air Force with promptness, there is always a constant
demand for candidates with a degree in operation research.
Thus, in the defence services, there is a wide scope of
operation research as candidates get the opportunity to work in
a dynamic environment and under higher roles facilitating the
formulation of policies and strategies.

• Agriculture
• Being brought up in a country like India where agriculture is a colossal part
of the economy, we often think that this domain is only for farmers or rather
scientists. But, with the dire need to ensure optimum utilization of
resources, there is a greater scope of operation research in this field. With
sky-rocketing population, operation research can ensure optimization in
agriculture and potential graduates in this field can avail the opportunities
to work as research assistants under this domain.
• Industrial Sector
• In the advent of globalization, the industrial sector is experiencing an
upheaval across the globe. To frame and handle the ever-rising demands
of the organizations, candidates with brainstorming abilities are selected
for various profiles in operation research. You can also opt for a
specialised role like an Operational Research Analyst, who is expected to
tackle the upcoming discrepancies in a business.

Scope of Operational Research: Job
Profiles
• In the above-mentioned sectors, there is a multitude of career profiles available for those wanting to kickstart their
career in operation research. Below we have brought you some of the key job roles which depict the varied scope of
operation research:
• Operations Analyst
• Research Analyst
• Business Analyst
• Operation Research Analyst
• Project Manager
• Data Analyst
• Consultant
• System Analyst
• Senior Analyst
• Operations Officer
• Project Analyst
• Quality Assurance Analyst

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Deterministic vs. Stochastic Models
Deterministic models
assume all data are known with certainty
Stochastic models
explicitly represent uncertain data via
random variables or stochastic processes.
Deterministic models involve optimization
Stochastic models
characterize / estimate system performance.

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Operations Research Models
Deterministic Models Stochastic Models
• Linear Programming • Discrete-Time Markov Chains
• Network Optimization • Continuous-Time Markov Chains
• Integer Programming • Queuing Theory (waiting lines)
• Nonlinear Programming • Decision Analysis
• Inventory Models Game Theory
Inventory models
Simulation

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Model Development
• Models are representations of real objects or situations.
• Three forms of models are iconic, analog, and
mathematical.
• Iconic models are physical replicas (scalar representations) of
real objects.
• Analog models are physical in form, but do not physically
resemble the object being modeled.
• Mathematical models represent real world problems through a
system of mathematical formulas and expressions based on key
assumptions, estimates, or statistical analyses.

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Advantages of Models
• Generally, experimenting with models (compared to experimenting
with the real situation):
• requires less time
• is less expensive
• involves less risk

LPP application and problem formulation

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