DMS 311: OPERATIONS RESEARCH FOR MANAGEMENT 1
1. Introduction
Operations Research (OR) started just before World War II in Britain with the
establishment of teams of scientists to study the strategic and tactical problems involved in
military operations. The objective was to find the most effective utilization of limited military
resources by the use of quantitative techniques. Following the war, numerous peacetime
applications emerged, leading to the use of OR in many industries and occupations. OR is the
study of mathematical models for complex organizational systems. OR is focused on the
application of information technology for informed decision-making. OR represents the study
of optimal resource allocation. The goal of OR is to provide rational bases for decision
making by seeking to understand and structure complex situations, and to utilize this
understanding to predict system behavior and improve system performance. Much of the
actual work is conducted by using analytical and numerical techniques to develop and
manipulate mathematical models of organizational systems that are composed of people,
machines, and procedures.
Definition of OR: It is the representation of real-world systems by mathematical models
together with the use of quantitative methods for solving such models, with a view to
optimizing.
2. Terminologies in OR
The British/Europeans refer to "operational research", the Americans to "operations research"
- but both are often shortened to just "OR" (which is the term we will use).
Another term which is used for OR is "management science" ("MS"). The Americans
sometimes combine the terms OR and MS together and say "OR/MS" or "ORMS". Yet other
terms sometimes used are "industrial engineering" ("IE") and "decision science" ("DS") and
“problem solving”. In recent years there has been a move towards a standardisation upon a
single term for the field, namely the term "OR".
System: A functionally related group of elements, especially:
➢ The human body regarded as a functional physiological unit.
➢ An organism as a whole, especially with regard to its vital processes or functions.
➢ A group of physiologically or anatomically complementary organs or parts: the
nervous system; the skeletal system.
➢ A group of interacting mechanical or electrical components.
➢ A network of structures and channels, as for communication, travel, or distribution.
➢ A network of related computer software, hardware, and data transmission devices.
Model: A schematic description of a system, theory, or phenomenon that accounts for its
known or inferred properties and may be used for further study of its characteristics.
Optimization is a branch of OR which uses mathematical techniques such as linear and
nonlinear programming to derive values for system variables that will optimize performance.
A mathematical model consists of:
Decision variables, which are the unknowns to be determined by the solution to the model.
Constraints to represent the physical limitations of the system.
An objective function
Max. z = 3x + 2y
1
, Subject to 2x + y <= 100
x + y < = 80
x <= 40
x, y > = 0 (Sign restriction)
An optimal solution to the model is the identification of a set of variable values which are
feasible (satisfy all the constraints) and which lead to the optimal value of the objective
function.
An optimization model seeks to find values of the decision variables that optimize (maximize
or minimize) an objective function among the set of all values for the decision variables that
satisfy the given constraints.
Linear Programming
Typically, a single objective function, representing either a profit to be maximized or a cost
to be minimized, and a set of constraints that restrict the decision variables. The objective
function and constraints all are linear functions of the decision variables.
3. Origins of Operations Research
Since the advent of the industrial revolution, the world has seen a remarkable growth in the
size and complexity of organizations. The artisans’ small shops of an earlier era have evolved
into the billion-dollar corporations of today. An integral part of this revolutionary change has
been a tremendous increase in the division of labour and segmentation of management
responsibilities in these organizations. The results have been spectacular.
However, along with its blessings, this increasing specialization has created new problems,
problems that are still occurring in many organizations. One problem is a tendency for the
many components of an organization to grow into relatively autonomous empires with their
own goals and value systems, thereby losing sight of how their activities and objectives mesh
with those of the overall organization. What is best for one component frequently is
detrimental to another, so the components may end up working at cross purposes.
A related problem is that as the complexity and specialization in an organization increase, it
becomes more and more difficult to allocate the available resources to the various activities in
a way that is most effective for the organization as a whole. These kinds of problems and the
need to find a better way to solve them provided the environment for the emergence of OR.
The roots of OR can be traced back many decades, when early attempts were made to use a
scientific approach in the management of organizations. However, the beginning of the
activity called operations research has generally been attributed to the military services early
in World War II. Because of the war effort, there was an urgent need to allocate scarce
resources to the various military operations and to the activities within each operation in an
effective manner. Therefore, the British and then the U.S. military management called upon a
large number of scientists to apply a scientific approach to dealing with this and other
strategic and tactical problems. In effect, they were asked to do research on (military)
operations. These teams of scientists were the first OR teams. By developing effective
methods of using the new tool of radar, these teams were instrumental in winning the Air
Battle of Britain. Through their research on how to better manage convoy and antisubmarine
operations, they also played a major role in winning the Battle of the North Atlantic. Similar
efforts assisted the Island Campaign in the Pacific.
When the war ended, the success of OR in the war effort spurred interest in applying OR
outside the military as well. As the industrial boom following the war was running its course,
the problems caused by the increasing complexity and specialization in organizations was
again coming to the forefront. It was becoming apparent to a growing number of people,
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1. Introduction
Operations Research (OR) started just before World War II in Britain with the
establishment of teams of scientists to study the strategic and tactical problems involved in
military operations. The objective was to find the most effective utilization of limited military
resources by the use of quantitative techniques. Following the war, numerous peacetime
applications emerged, leading to the use of OR in many industries and occupations. OR is the
study of mathematical models for complex organizational systems. OR is focused on the
application of information technology for informed decision-making. OR represents the study
of optimal resource allocation. The goal of OR is to provide rational bases for decision
making by seeking to understand and structure complex situations, and to utilize this
understanding to predict system behavior and improve system performance. Much of the
actual work is conducted by using analytical and numerical techniques to develop and
manipulate mathematical models of organizational systems that are composed of people,
machines, and procedures.
Definition of OR: It is the representation of real-world systems by mathematical models
together with the use of quantitative methods for solving such models, with a view to
optimizing.
2. Terminologies in OR
The British/Europeans refer to "operational research", the Americans to "operations research"
- but both are often shortened to just "OR" (which is the term we will use).
Another term which is used for OR is "management science" ("MS"). The Americans
sometimes combine the terms OR and MS together and say "OR/MS" or "ORMS". Yet other
terms sometimes used are "industrial engineering" ("IE") and "decision science" ("DS") and
“problem solving”. In recent years there has been a move towards a standardisation upon a
single term for the field, namely the term "OR".
System: A functionally related group of elements, especially:
➢ The human body regarded as a functional physiological unit.
➢ An organism as a whole, especially with regard to its vital processes or functions.
➢ A group of physiologically or anatomically complementary organs or parts: the
nervous system; the skeletal system.
➢ A group of interacting mechanical or electrical components.
➢ A network of structures and channels, as for communication, travel, or distribution.
➢ A network of related computer software, hardware, and data transmission devices.
Model: A schematic description of a system, theory, or phenomenon that accounts for its
known or inferred properties and may be used for further study of its characteristics.
Optimization is a branch of OR which uses mathematical techniques such as linear and
nonlinear programming to derive values for system variables that will optimize performance.
A mathematical model consists of:
Decision variables, which are the unknowns to be determined by the solution to the model.
Constraints to represent the physical limitations of the system.
An objective function
Max. z = 3x + 2y
1
, Subject to 2x + y <= 100
x + y < = 80
x <= 40
x, y > = 0 (Sign restriction)
An optimal solution to the model is the identification of a set of variable values which are
feasible (satisfy all the constraints) and which lead to the optimal value of the objective
function.
An optimization model seeks to find values of the decision variables that optimize (maximize
or minimize) an objective function among the set of all values for the decision variables that
satisfy the given constraints.
Linear Programming
Typically, a single objective function, representing either a profit to be maximized or a cost
to be minimized, and a set of constraints that restrict the decision variables. The objective
function and constraints all are linear functions of the decision variables.
3. Origins of Operations Research
Since the advent of the industrial revolution, the world has seen a remarkable growth in the
size and complexity of organizations. The artisans’ small shops of an earlier era have evolved
into the billion-dollar corporations of today. An integral part of this revolutionary change has
been a tremendous increase in the division of labour and segmentation of management
responsibilities in these organizations. The results have been spectacular.
However, along with its blessings, this increasing specialization has created new problems,
problems that are still occurring in many organizations. One problem is a tendency for the
many components of an organization to grow into relatively autonomous empires with their
own goals and value systems, thereby losing sight of how their activities and objectives mesh
with those of the overall organization. What is best for one component frequently is
detrimental to another, so the components may end up working at cross purposes.
A related problem is that as the complexity and specialization in an organization increase, it
becomes more and more difficult to allocate the available resources to the various activities in
a way that is most effective for the organization as a whole. These kinds of problems and the
need to find a better way to solve them provided the environment for the emergence of OR.
The roots of OR can be traced back many decades, when early attempts were made to use a
scientific approach in the management of organizations. However, the beginning of the
activity called operations research has generally been attributed to the military services early
in World War II. Because of the war effort, there was an urgent need to allocate scarce
resources to the various military operations and to the activities within each operation in an
effective manner. Therefore, the British and then the U.S. military management called upon a
large number of scientists to apply a scientific approach to dealing with this and other
strategic and tactical problems. In effect, they were asked to do research on (military)
operations. These teams of scientists were the first OR teams. By developing effective
methods of using the new tool of radar, these teams were instrumental in winning the Air
Battle of Britain. Through their research on how to better manage convoy and antisubmarine
operations, they also played a major role in winning the Battle of the North Atlantic. Similar
efforts assisted the Island Campaign in the Pacific.
When the war ended, the success of OR in the war effort spurred interest in applying OR
outside the military as well. As the industrial boom following the war was running its course,
the problems caused by the increasing complexity and specialization in organizations was
again coming to the forefront. It was becoming apparent to a growing number of people,
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