Operations research (also referred to as decision science, or management science) is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations.
DEFINITIONS
* OR is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. – Morse & Kimball
* Operations research is a scientific approach to problem solving for executive management. – H.M. Wagner
* Operations research is an aid for the executive in making this decisions by providing him with the needed quantitative information based on the scientific method of analysis. – C. Kittel
# PHASES OPERATIONS RESEARCH
# 1. Recognize the Problem
# 1. Recognize the Problem
* Decision making begins with a situation in which a problem is recognized.
* The problem may be actual or abstract, it may involve current operations or proposed expansions or contractions due to expected market shifts, it may become apparent through consumer complaints or through employee suggestions, it may be a conscious effort to improve efficiency or a response to an unexpected crisis.
* It is impossible to circumscribe the breadth of circumstances that might be appropriate for this discussion, for indeed problem situations that are amenable to objective analysis arise in every area of human activity.
#
# 2. Formulate the Problem
* At the formulation stage,
* statements of objectives, constraints on solutions, appropriate assumptions, descriptions of processes, data requirements, alternatives for action and metrics for measuring progress are introduced.
* Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. The analyst is usually not the decision maker and may not be part of the organization, so care must be taken to get agreement on the exact character of the problem to be solved from those who perceive it. There is little value to either a poor solution to a correctly formulated problem or a good solution to one that has been incorrectly formulated.
#
# 3. Construct a Model
* A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Although the analyst would hope to study the broad implications of the problem using a systems approach, a model cannot include every aspect of a situation.
* A model is always an abstraction that is, by necessity, simpler than the reality.
* Elements that are irrelevant or unimportant to the problem are to be ignored, hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem.
* The statements of the abstractions introduced in the construction of the model are called the assumptions. It is important to observe that assumptions are not necessarily statements of belief, but are descriptions of the abstractions used to arrive at a model. The appropriateness of the assumptions can be determined only by subsequent testing of the model’s validity.
* Models must be both tractable -- capable of being solved, and valid -- representative of the true situation. These dual goals are often contradictory and are not always attainable. We have intentionally represented the model with well-defined boundaries to indicate its relative simplicity.
#
# 4. Find a Solution(1)
* The next step in the process is to solve the model to obtain a solution to the problem. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model.
* Some methods can prescribe optimal solutions while other only evaluate candidates, thus requiring a trial and error approach to finding an acceptable course of action.
* It may be necessary to develop new techniques specifically tailored to the problem at hand. A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail. Such a case signals the return to the previous step for simplification or perhaps the postponement of the study if no acceptable, tractable model can be found.
# 4. Find a Solution(2)
* Of course, the solution provided by the computer is only a proposal. An analysis does not promise a solution but only guidance to the decision maker.
* Choosing a solution to implement is the responsibility of the decision maker and not the analyst. The decision maker may modify the solution to incorporate practical or intangible considerations not reflected in the model.
#
# 5. Establish the Procedure(1)
* Once a solution is accepted a procedure must be designed to retain control of the implementation effort.
* Problems are usually ongoing rather than unique. Solutions are implemented as procedures to be used repeatedly in an almost automatic fashion under perhaps changing conditions.
* Control may be achieved with a set of operating rules, a job description, laws or regulations promulgated by a government body, or computer programs that accept current data and prescribe actions.
# 5. Establish the Procedure(2)
* Once a procedure is established (and implemented), the analyst and perhaps the decision maker are ready to tackle new problems, leaving the procedure to handle the required tasks.
* But what if the situation changes?
* An unfortunate result of many analyses is a remnant procedure designed to solve a problem that no longer exists or which places restrictions on an organization that are limiting and no longer appropriate.
* Therefore, it is important to establish controls that recognize a changing situation and signal the need to modify or update the solution.
#
# 6. Implement the Solutio n
* A solution to a problem usually implies changes for some individuals in the organization. Because resistance to change is common, the implementation of solutions is perhaps the most difficult part of a problem solving exercise.
* Some say it is the most important part. Although not strictly the responsibility of the analyst, the solution process itself can be designed to smooth the way for implementation.
* The persons who are likely to be affected by the changes brought about by a solution should take part, or at least be consulted, during the various stages involving problem formulation, solution testing, and the establishment of the procedure.
# TECHNIQUES OF OR(1)
* Linear programming- It has been used to solve problems involving assignment of jobs to machines, blending, product mix, advertising media selection, least cost diet, distribution, transportation and many others.
* Dynamic programming- It has been applied to capital budgeting, selection of advertising media, cargo loading and optimal routing problems.
* Waiting line or queuing theory- It has been useful to solve problems of traffic congestion, repair and maintenance of broken-down machines, number of service facilities, scheduling and control of air-traffic, hospital operations, counter in banks and railway booking agencies.
* Inventory control / planning- These models have been used to determine economic order quantities, safety stocks, reorder levels, minimum and maximum stock level.
# TECHNIQUES OF OR(2)
* Decision theory- It has been helpful in controlling hurricuanes, water pollution, medicine, space exploration, research and development projects.
* Network analysis (PERT& CPM)- These techniques have been used in planning, scheduling and controlling construction of dams, brides, roads and highways and development & production of aircrafts, ships, computers etc.
* Simulation- It has been helpful in a wide variety of probabilistic marketing situations.
* Theory of replacement- It has been extensively employed to determine the optimum replacement interval for three types of replacement problems:
* i) Items that deteriorate with time.
* ii) Items that do not deteriorate with time but fail suddenly.
* iii) Staff replacement and recruitment.
# What is a Mathematical Model?
* The majority of practical decision problems are described in very vague terms. Therefore, a most-important step in a scientific or quantitative analysis of a problem is to formulate a model that adequately captures the essence of a problem. The result of such a formulation, or an abstraction, is called a mathematical optimization model.
* Generally speaking,
* a mathematical optimization model has the following typical components:
* a set of decision variables
* an objective function, expressed in terms of the decision variables, that is to be minimized or maximized
* a set of constraints that limit the possible values of the decision variables
# ADVANTAGES
* Provides a tool for scientific analysis.
* Provides solution for various business problems.
* Enables proper deployment of resources.
* Helps in minimizing waiting and servicing costs.
* Enables the management to decide when to buy and how much to buy?
* Assists in choosing an optimum strategy.
* Renders great help in optimum resource allocation.
* Facilitates the process of decision making.
* Management can know the reactions of the integrated business systems.
* Helps a lot in the preparation of future managers.
# LIMITATIONS
* The inherent limitations concerning mathematical expressions
* High costs are involved in the use of O.R. techniques
* O.R. does not take into consideration the intangible factors
* O.R. is only a tool of analysis and not the complete decision-making process
* Other limitations
* Bias
* Inadequate objective functions
* Internal resistance
* Competence
* Reliability of the prepared solution
# Application Fields
* Industry
* Defense
* Planning
* Agriculture
* Public utilities
Sunday, 12 June 2011
NETWORK ANALYSIS
<b>Network analysis</b>
Introduction
Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects.
PERT was developed to aid the US Navy in the planning and control of its Polaris missile program . This was a project to build a strategic weapons system, namely the first submarine launched intercontinental ballistic missile, at the time of the Cold War between the USA and Russia. Military doctrine at that time emphasised 'MAD - mutually assured destruction', namely if the other side struck first then sufficient nuclear weapons would remain to obliterate their homeland. That way peace was preserved. By the late 1950s the USA believed (or more importantly believed that the Russians believed) that American land based missiles and nuclear bombers were vulnerable to a first strike. Hence there was a strategic emphasis on completing the Polaris project as quickly as possible, cost was not an issue. However no one had ever build a submarine launched intercontinental ballistic missile before, so dealing with uncertainty was a key issue. PERT has the ability to cope with uncertain activity completion times (e.g. for a particular activity the most likely completion time is 4 weeks but it could be any time between 3 weeks and 8 weeks).
CPM was developed in the 1950's as a result of a joint effort by the DuPont Company and Remington Rand Univac. As these were commercial companies cost was an issue, unlike the Polaris project mentioned above. In CPM the emphasis is on the trade-off between the cost of the project and its overall completion time (e.g. for certain activities it may be possible to decrease their completion times by spending more money - how does this affect the overall completion time of the project?)
Introduction
Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects.
PERT was developed to aid the US Navy in the planning and control of its Polaris missile program . This was a project to build a strategic weapons system, namely the first submarine launched intercontinental ballistic missile, at the time of the Cold War between the USA and Russia. Military doctrine at that time emphasised 'MAD - mutually assured destruction', namely if the other side struck first then sufficient nuclear weapons would remain to obliterate their homeland. That way peace was preserved. By the late 1950s the USA believed (or more importantly believed that the Russians believed) that American land based missiles and nuclear bombers were vulnerable to a first strike. Hence there was a strategic emphasis on completing the Polaris project as quickly as possible, cost was not an issue. However no one had ever build a submarine launched intercontinental ballistic missile before, so dealing with uncertainty was a key issue. PERT has the ability to cope with uncertain activity completion times (e.g. for a particular activity the most likely completion time is 4 weeks but it could be any time between 3 weeks and 8 weeks).
CPM was developed in the 1950's as a result of a joint effort by the DuPont Company and Remington Rand Univac. As these were commercial companies cost was an issue, unlike the Polaris project mentioned above. In CPM the emphasis is on the trade-off between the cost of the project and its overall completion time (e.g. for certain activities it may be possible to decrease their completion times by spending more money - how does this affect the overall completion time of the project?)
CHARACTERISTICS OF A PROJECT
Characteristic of a project
A project is a temporary endeavour involving a connected sequence of
activities and a range of resources, which is designed to achieve a
specific and unique outcome and which operates within time, cost
and quality constraints and which is often used to introduce change.
qA unique, one-time operational activity or effort
qRequires the completion of a large number of interrelated activities
qEstablished to achieve specific objective
qResources, such as time and/or money, are limited
qTypically has its own management structure
qNeed leadership
Initiation phase
The initiation phase is the beginning of the project. In this phase, the idea for the project is explored and elaborated. The goal of this phase is to examine the feasibility of the project. In addition, decisions are made concerning who is to carry out the project, which party (or parties) will be involved and whether the project has an adequate base of support among those who are involved.
In this phase, the current or prospective project leader writes a proposal, which contains a description of the above-mentioned matters. Examples of this type of project proposal include business plans and grant applications. The prospective sponsors of the project evaluate the proposal and, upon approval, provide the necessary financing. The project officially begins at the time of approval.
Questions to be answered in the initiation phase include the following:
* Why this project?
* Is it feasible?
* Who are possible partners in this project?
* What should the results be?
* What are the boundaries of this project (what is outside the scope of the project)?
Definition phase
After the project plan (which was developed in the initiation phase) has been approved, the project enters the second phase: the definition phase. In this phase, the requirements that are associated with a project result are specified as clearly as possible. This involves identifying the expectations that all of the involved parties have with regard to the project result. How many files are to be archived? Should the metadata conform to the Data Documentation Initiative format, or will the Dublin Core (DC) format suffice? May files be deposited in their original format, or will only those that conform to the �Preferred Standards� be accepted? Must the depositor of a dataset ensure that it has been processed adequately in the archive, or is this the responsibility of the archivist? Which guarantees will be made on the results of the project? The list of questions goes on and on.
Design phase
The list of requirements that is developed in the definition phase can be used to make design choices. In the design phase, one or more designs are developed, with which the project result can apparently be achieved. Depending on the subject of the project, the products of the design phase can include dioramas, sketches, flow charts, site trees, HTML screen designs, prototypes, photo impressions and UML schemas. The project supervisors use these designs to choose the definitive design that will be produced in the project. This is followed by the development phase. As in the definition phase, once the design has been chosen, it cannot be changed in a later stage of the project.
Development phase
During the development phase, everything that will be needed to implement the project is arranged. Potential suppliers or subcontractors are brought in, a schedule is made, materials and tools are ordered, instructions are given to the personnel and so forth. The development phase is complete when implementation is ready to start. All matters must be clear for the parties that will carry out the implementation.
In some projects, particularly smaller ones, a formal development phase is probably not necessary. The important point is that it must be clear what must be done in the implementation phase, by whom and when.
Implementation phase
The project takes shape during the implementation phase. This phase involves the construction of the actual project result. Programmers are occupied with encoding, designers are involved in developing graphic material, contractors are building, the actual reorganisation takes place. It is during this phase that the project becomes visible to outsiders, to whom it may appear that the project has just begun. The implementation phase is the �doing� phase, and it is important to maintain the momentum.
In one project, it had escaped the project team�s attention that one of the most important team members was expecting to become a father at any moment and would thereafter be completely unavailable for about a month. When the time came, an external specialist was brought in to take over his work, in order to keep the team from grinding to a halt. Although the team was able to proceed, the external expertise put a considerable dent in the budget.
Follow-up phase
Although it is extremely important, the follow-up phase is often neglected. During this phase, everything is arranged that is necessary to bring the project to a successful completion. Examples of activities in the follow-up phase include writing handbooks, providing instruction and training for users, setting up a help desk, maintaining the result, evaluating the project itself, writing the project report, holding a party to celebrate the result that has been achieved, transferring to the directors and dismantling the project team.
The central question in the follow-up phase concerns when and where the project ends. Project leaders often joke among themselves that the first ninety per cent of a project proceeds quickly and that the final ten per cent can take years. The boundaries of the project should be considered in the beginning of a project, so that the project can be closed in the follow-up phase, once it has reached these boundaries.
It is sometimes unclear for those concerned whether the project result is to be a prototype or a working product. This is particularly common in innovative projects in which the outcome is not certain. Customers may expect to receive a product, while the project team assumes that it is building a prototype. Such situations are particularly likely to manifest themselves in the follow-up phase. Consider the case of a software project to test a very new concept.
A project is a temporary endeavour involving a connected sequence of
activities and a range of resources, which is designed to achieve a
specific and unique outcome and which operates within time, cost
and quality constraints and which is often used to introduce change.
qA unique, one-time operational activity or effort
qRequires the completion of a large number of interrelated activities
qEstablished to achieve specific objective
qResources, such as time and/or money, are limited
qTypically has its own management structure
qNeed leadership
Initiation phase
The initiation phase is the beginning of the project. In this phase, the idea for the project is explored and elaborated. The goal of this phase is to examine the feasibility of the project. In addition, decisions are made concerning who is to carry out the project, which party (or parties) will be involved and whether the project has an adequate base of support among those who are involved.
In this phase, the current or prospective project leader writes a proposal, which contains a description of the above-mentioned matters. Examples of this type of project proposal include business plans and grant applications. The prospective sponsors of the project evaluate the proposal and, upon approval, provide the necessary financing. The project officially begins at the time of approval.
Questions to be answered in the initiation phase include the following:
* Why this project?
* Is it feasible?
* Who are possible partners in this project?
* What should the results be?
* What are the boundaries of this project (what is outside the scope of the project)?
Definition phase
After the project plan (which was developed in the initiation phase) has been approved, the project enters the second phase: the definition phase. In this phase, the requirements that are associated with a project result are specified as clearly as possible. This involves identifying the expectations that all of the involved parties have with regard to the project result. How many files are to be archived? Should the metadata conform to the Data Documentation Initiative format, or will the Dublin Core (DC) format suffice? May files be deposited in their original format, or will only those that conform to the �Preferred Standards� be accepted? Must the depositor of a dataset ensure that it has been processed adequately in the archive, or is this the responsibility of the archivist? Which guarantees will be made on the results of the project? The list of questions goes on and on.
Design phase
The list of requirements that is developed in the definition phase can be used to make design choices. In the design phase, one or more designs are developed, with which the project result can apparently be achieved. Depending on the subject of the project, the products of the design phase can include dioramas, sketches, flow charts, site trees, HTML screen designs, prototypes, photo impressions and UML schemas. The project supervisors use these designs to choose the definitive design that will be produced in the project. This is followed by the development phase. As in the definition phase, once the design has been chosen, it cannot be changed in a later stage of the project.
Development phase
During the development phase, everything that will be needed to implement the project is arranged. Potential suppliers or subcontractors are brought in, a schedule is made, materials and tools are ordered, instructions are given to the personnel and so forth. The development phase is complete when implementation is ready to start. All matters must be clear for the parties that will carry out the implementation.
In some projects, particularly smaller ones, a formal development phase is probably not necessary. The important point is that it must be clear what must be done in the implementation phase, by whom and when.
Implementation phase
The project takes shape during the implementation phase. This phase involves the construction of the actual project result. Programmers are occupied with encoding, designers are involved in developing graphic material, contractors are building, the actual reorganisation takes place. It is during this phase that the project becomes visible to outsiders, to whom it may appear that the project has just begun. The implementation phase is the �doing� phase, and it is important to maintain the momentum.
In one project, it had escaped the project team�s attention that one of the most important team members was expecting to become a father at any moment and would thereafter be completely unavailable for about a month. When the time came, an external specialist was brought in to take over his work, in order to keep the team from grinding to a halt. Although the team was able to proceed, the external expertise put a considerable dent in the budget.
Follow-up phase
Although it is extremely important, the follow-up phase is often neglected. During this phase, everything is arranged that is necessary to bring the project to a successful completion. Examples of activities in the follow-up phase include writing handbooks, providing instruction and training for users, setting up a help desk, maintaining the result, evaluating the project itself, writing the project report, holding a party to celebrate the result that has been achieved, transferring to the directors and dismantling the project team.
The central question in the follow-up phase concerns when and where the project ends. Project leaders often joke among themselves that the first ninety per cent of a project proceeds quickly and that the final ten per cent can take years. The boundaries of the project should be considered in the beginning of a project, so that the project can be closed in the follow-up phase, once it has reached these boundaries.
It is sometimes unclear for those concerned whether the project result is to be a prototype or a working product. This is particularly common in innovative projects in which the outcome is not certain. Customers may expect to receive a product, while the project team assumes that it is building a prototype. Such situations are particularly likely to manifest themselves in the follow-up phase. Consider the case of a software project to test a very new concept.
inventoy control
The objectives of inventory management can be explained in detail as under:
(i) To ensure that the supply of raw material & finished goods will remain continuous so that production process is not halted and demands of customers are duly met.
(ii) To minimise carrying cost of inventory.
(iii) To keep investment in inventory at optimem level.
(iv) To reduce the losses of theft, obsolescence & wastage etc.
(v) To make arrangement for sale of slow moving items.
(vi) To minimise inventory ordering costs.
The ABC analysis is a business term used to define an inventory categorization technique often used in materials management. It is also known as Selective Inventory Control.
The ABC analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost, [1] while also providing a mechanism for identifying different categories of stock that will require different management and controls.[2]
The ABC analysis suggests that inventories of an organization are not of equal value. [3] Thus, the inventory is grouped into three categories (A, B, and C) in order of their estimated importance.
'A' items are very important for an organization. Because of the high value of these ‘A’ items, frequently value analysis are required. In addition to that, an organization needs to choose an appropriate order pattern (e.g. ‘Just- in- time’) to avoid excess capacity.
'B' items are important, but of course less important, than ‘A’ items and more important than ‘C’ items. Therefore ‘B’ items are intergroup items.
'C' items are marginally important. [4]
[edit] ABC analysis categories
* ‘A’ items – 20% of the items accounts for 70% of the annual consumption value of the items.
* ‘B’ items - 30% of the items accounts for 25% of the annual consumption value of the items.
* ‘C’ items - 50% of the items accounts for 5% of the annual consumption value of the items.[5]
ABC Analysis is similar to the Pareto principle in that the 'A' items will typically account for a large proportion of the overall value but a small percentage of the overall volume of inventory.[6]
Another recommended breakdown of ABC classes[7]:
1. "A" approximately 10% of items or 66.6% of value
2. "B" approximately 20% of items or 23.3% of value
3. "C" approximately 70% of items or 10.1% of value
STEPS IN ABC ANALYSIS
* The steps in computing ABC analysis are:
* a Determine the annual usage in units for each item for the past one-year.
* b. Multiply the annual usage quantity with the average unit price of each item to calculate the annual usage in US$ for each item.
* c. Item with highest dollar usage annually is ranked first. Then the next lower annual usage item is listed till the lowest item is listed in the last.
* d. Table 1 shows ranks of the items according to the annual usage in US$. for 10 items.
* e. Arrange the items in the inventory by cumulative annual usage (dollars) and by cumulative percentage. Categorize the items in A, B , and C categories.
(i) To ensure that the supply of raw material & finished goods will remain continuous so that production process is not halted and demands of customers are duly met.
(ii) To minimise carrying cost of inventory.
(iii) To keep investment in inventory at optimem level.
(iv) To reduce the losses of theft, obsolescence & wastage etc.
(v) To make arrangement for sale of slow moving items.
(vi) To minimise inventory ordering costs.
The ABC analysis is a business term used to define an inventory categorization technique often used in materials management. It is also known as Selective Inventory Control.
The ABC analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost, [1] while also providing a mechanism for identifying different categories of stock that will require different management and controls.[2]
The ABC analysis suggests that inventories of an organization are not of equal value. [3] Thus, the inventory is grouped into three categories (A, B, and C) in order of their estimated importance.
'A' items are very important for an organization. Because of the high value of these ‘A’ items, frequently value analysis are required. In addition to that, an organization needs to choose an appropriate order pattern (e.g. ‘Just- in- time’) to avoid excess capacity.
'B' items are important, but of course less important, than ‘A’ items and more important than ‘C’ items. Therefore ‘B’ items are intergroup items.
'C' items are marginally important. [4]
[edit] ABC analysis categories
* ‘A’ items – 20% of the items accounts for 70% of the annual consumption value of the items.
* ‘B’ items - 30% of the items accounts for 25% of the annual consumption value of the items.
* ‘C’ items - 50% of the items accounts for 5% of the annual consumption value of the items.[5]
ABC Analysis is similar to the Pareto principle in that the 'A' items will typically account for a large proportion of the overall value but a small percentage of the overall volume of inventory.[6]
Another recommended breakdown of ABC classes[7]:
1. "A" approximately 10% of items or 66.6% of value
2. "B" approximately 20% of items or 23.3% of value
3. "C" approximately 70% of items or 10.1% of value
STEPS IN ABC ANALYSIS
* The steps in computing ABC analysis are:
* a Determine the annual usage in units for each item for the past one-year.
* b. Multiply the annual usage quantity with the average unit price of each item to calculate the annual usage in US$ for each item.
* c. Item with highest dollar usage annually is ranked first. Then the next lower annual usage item is listed till the lowest item is listed in the last.
* d. Table 1 shows ranks of the items according to the annual usage in US$. for 10 items.
* e. Arrange the items in the inventory by cumulative annual usage (dollars) and by cumulative percentage. Categorize the items in A, B , and C categories.
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