Question Bank Optimization Theory
a. Feasible region. b. Feasible solution. c. Optimal solution. d. Unbounded solution. e. Artificial variable.
method? 23. What do you understand by transportation problem? 24. List any three approaches used with T.P for determining the starting solution. 25. What do you mean by degeneracy in a T.P? 26. What do you mean by an unbalanced T.P? 27. How do you convert the unbalanced T.P into a balanced one? 35. What is an assignment problem? 37. State the difference between the T.P and A.P. 38. What is the objective of the traveling salesman problem? 39. How do you convert the maximization assignment problem into a minimization one? 40. What is the name of the method used in getting the optimum assignment? 41. What do you mean by integer programming problem? 42. Define a pure integer programming problem. 43. Define a mixed integer programming problem. 44. Differentiate between pure and mixed IPP. 45. What are the methods used in solving IPP 46. Explain Gomorian constraint (or) Fractional Cut constraint. 47. Where is branch and bound method used? 48. What is dynamic programming? 49. Define the terms in dynamic programming : stage, state ,state variables 50. State Bellman's principle of optimality. Numericals 1. A paper mill produces 2 grades of paper namely X and Y. Because of raw material restrictions, it cannot produce more than 400 tonnes of grade X and 300 tonnes of grade Y in a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to produce a ton of products X and Y respectively with corresponding profits of Rs.200 and Rs. 500 per ton. Formulate the above as a LPP to maximize profit and find the optimum product mix. 2. A company produces 2 types of hats. Every hat A require twice as much labour time as the second hat be. If the company produces only hat B then it can produce a total of 500 hats a day. The market limits daily sales of the hat A and hat B to 150 and 250 hats. The profits on hat A and B are Rs.8 and Rs.5 respectively. Solve graphically to get the optimal solution. 3. A company wishes to advertise its products on local radio and TV stations. Each minute of radio advertisement will cost Rs.50 and each minute of TV advertisement will cost Rs. 600. The budget of the company limits the advertisement expenditure to Rs.25000 per month. The company decides to use radio atleast twice as much as TV. Past records of the company show that each minute of TV advertisement will generate 30 times as many sales as each minute radio advertisement. Formulate the problem for optimal allocation of monthly budget to radio and TV advertisement. 4. Use graphical method to solve the following LPP Maximize Z = 2x1+4x2 subject to the constraints x1+2x2 = 5, x1+x2 = 4, x1, x2 ≥ 0 5. Use simplex method to solve the following LPP Maximize Z = 4x1+10x2 subject to the constraints 2x1+x2 ≤ 50, 2x1+5x2 ≤100, 2x1+3x2 ≤ 90, x1, x2 ≥0 6. Solve the following problem by simplex method Minimize Z = x1-3x2+2x3 subject to the constraints 3x1-x2+2x3 ≤ 7, -2x1+4x2 ≤ 12, -4x1+3x2+8x3 ≤ 10, x1, x2, x3 ≥ 0 7. Use Big M method to Maximize Z = 3x1+2x2 subject to the constraints 2x1+x2 ≤ 2, 3x1+4x2 ≥ 12, x1, x2 ≥ 0 8 Use Two Phase Simplex method to Maximize Z = 5x1-4x2+3x3 subject to the constraints 2x1+x2-6x3 = 20, 6x1+5x2+10x3 ≤ 76, 8x1-3x2+6x3 ≤ 50, x1, x2, x3 ≥ 0 9. Use Two Phase Simplex Method to Maximize Z = -4x1-3x2-9x3 . Subject to the constraints 2x1+4x2+6x3 ≥ 15, 6x1+x2+6x3 ≥ 12, x1, x2, x3 ≥ 0 10. Write the dual of the following primal LP problem. Max Z = x1+2x2+x3 Subject to 2x1+x2 –x3 ≤ 2 -2x1 + x2 -5x3 ≥ -6 4x1 + x2+x3 ≤ 6 x1, x2, x3 ≥ 0 11. Obtain an initial basic feasible solution to the following TP using Matrix minima method
12. Obtain an initial basic feasible solution to the following TP using Matrix minima method
|
Thursday, March 31, 2011
Optimization Theory (Question Bank)
Thursday, March 24, 2011
Data Mining
Data mining tools predict future trends and behaviors, allowing businesses to make proactive, knowledge-driven decisions. The automated, prospective analyses offered by data mining move beyond the analyses of past events provided by retrospective tools typical of decision support systems. Data mining tools can answer business questions that traditionally were too time consuming to resolve. They scour databases for hidden patterns, finding predictive information that experts may miss because it lies outside their expectations.
Most companies already collect and refine massive quantities of data. Data mining techniques can be implemented rapidly on existing software and hardware platforms to enhance the value of existing information resources, and can be integrated with new products and systems as they are brought on-line. When implemented on high performance client/server or parallel processing computers, data mining tools can analyze massive databases to deliver answers to questions such as, "Which clients are most likely to respond to my next promotional mailing, and why?"
This white paper provides an introduction to the basic technologies of data mining. Examples of profitable applications illustrate its relevance to today’s business environment as well as a basic description of how data warehouse architectures can evolve to deliver the value of data mining to end users.
What can data mining do?
Data mining is primarily used today by companies with a strong consumer focus - retail, financial, communication, and marketing organizations. It enables these companies to determine relationships among "internal" factors such as price, product positioning, or staff skills, and "external" factors such as economic indicators, competition, and customer demographics. And, it enables them to determine the impact on sales, customer satisfaction, and corporate profits. Finally, it enables them to "drill down" into summary information to view detail transactional data.
With data mining, a retailer could use point-of-sale records of customer purchases to send targeted promotions based on an individual's purchase history. By mining demographic data from comment or warranty cards, the retailer could develop products and promotions to appeal to specific customer segments.
For example, Blockbuster Entertainment mines its video rental history database to recommend rentals to individual customers. American Express can suggest products to its cardholders based on analysis of their monthly expenditures.
WalMart is pioneering massive data mining to transform its supplier relationships. WalMart captures point-of-sale transactions from over 2,900 stores in 6 countries and continuously transmits this data to its massive 7.5 terabyte Teradata data warehouse. WalMart allows more than 3,500 suppliers, to access data on their products and perform data analyses. These suppliers use this data to identify customer buying patterns at the store display level. They use this information to manage local store inventory and identify new merchandising opportunities. In 1995, WalMart computers processed over 1 million complex data queries.
The National Basketball Association (NBA) is exploring a data mining application that can be used in conjunction with image recordings of basketball games. The Advanced Scout software analyzes the movements of players to help coaches orchestrate plays and strategies. For example, an analysis of the play-by-play sheet of the game played between the New York Knicks and the Cleveland Cavaliers on January 6, 1995 reveals that when Mark Price played the Guard position, John Williams attempted four jump shots and made each one! Advanced Scout not only finds this pattern, but explains that it is interesting because it differs considerably from the average shooting percentage of 49.30% for the Cavaliers during that game.
By using the NBA universal clock, a coach can automatically bring up the video clips showing each of the jump shots attempted by Williams with Price on the floor, without needing to comb through hours of video footage. Those clips show a very successful pick-and-roll play in which Price draws the Knick's defense and then finds Williams for an open jump shot.
How does data mining work?
While large-scale information technology has been evolving separate transaction and analytical systems, data mining provides the link between the two. Data mining software analyzes relationships and patterns in stored transaction data based on open-ended user queries. Several types of analytical software are available: statistical, machine learning, and neural networks. Generally, any of four types of relationships are sought:
• Classes: Stored data is used to locate data in predetermined groups. For example, a restaurant chain could mine customer purchase data to determine when customers visit and what they typically order. This information could be used to increase traffic by having daily specials.
• Clusters: Data items are grouped according to logical relationships or consumer preferences. For example, data can be mined to identify market segments or consumer affinities.
• Associations: Data can be mined to identify associations. The beer-diaper example is an example of associative mining.
• Sequential patterns: Data is mined to anticipate behavior patterns and trends. For example, an outdoor equipment retailer could predict the likelihood of a backpack being purchased based on a consumer's purchase of sleeping bags and hiking shoes.
Data mining consists of five major elements:
• Extract, transform, and load transaction data onto the data warehouse system.
• Store and manage the data in a multidimensional database system.
• Provide data access to business analysts and information technology professionals.
• Analyze the data by application software.
• Present the data in a useful format, such as a graph or table.
Different levels of analysis are available:
• Artificial neural networks: Non-linear predictive models that learn through training and resemble biological neural networks in structure.
• Genetic algorithms: Optimization techniques that use process such as genetic combination, mutation, and natural selection in a design based on the concepts of natural evolution.
• Decision trees: Tree-
Reference:
http://www.anderson.ucla.edu/faculty/jason.frand/teacher/technologies/palace/datamining.htm
http://www.thearling.com/text/dmwhite/dmwhite.htm
http://www.google.com.my/imglanding?q=Data+mining&um=1&hl=en&sa=N&tbs=isch:1&tbnid=tA3K6cEcyXl3gM:&imgrefurl=http://www.datapult.com/Data_Mining.htm&imgurl=http://www.datapult.com/images/DiagramDataMining.jpg&ei=RQ2MTdj_OsvxrQeepezkDQ&zoom=1&w=620&h=526&biw=1280&bih=617
Structured Query Language (SQL) - Basic Concepts
It is a non procedural language and it is a database language.
There are 3 broad categories in SQL commands. They are namely
• Data Definition language (DDL)
• Data Manipulation Language (DML)
• Transaction Control Commands
Under each category there are many SQL commands. Let us see each in brief.
CREATE TABLE is used in creation of table(s).
SYNTAX: CREATE TABLE tablename (colname col definition, colname col definition…);
ALTER TABLE: If you want to modify a table definition we can use this command. This command is used to alter column definition in table.
SYNTAX: ALTER TABLE tablename MODIFY (Column definition);
DROP TABLE: This command is used to remove an existing table permanently from database.
SYNTAX: DROP TABLE tablename;
SYNTAX: INSERT INTO tablename VALUES (value,value,….);
SELECT: This is used to select values or data from table
SYNTAX: SELECT column name1, column name2, …. FROM tablename;
If we want to select all column values from a table then SQL command use is
DELETE: In order to delete rows from a table we use this command
SYNTAX: DELETE FROM tablename WHERE condition;
Based on the condition specified the rows gets fetched from the table and gets deleted in table. Here the WHERE clause is optional.
UPDATE: This SQL command is used to modify the values in an existing table.
SYNTAX: UPDATE tablename SET columnname = value, columnname = value,….. WHERE condition;
The rows which satisfies the WHERE condition are fetched and for these rows the column values we placed in command above in SET statement gets updated.
SYNTAX: ROLLBACK;
SAVEPOINT: This is used to identify a point in a transaction to which we can later rollback.
SYNTAX: SAVEPOINT savepoint_identifier;
COMMIT: This command is used to make all changes permanent in database and also marks the end of transaction.
SYNTAX: COMMIT;
Always it is better to commit changes to database at regular intervals since it will help loss of data or loss of work done when computer shuts due to unavoidable reasons.
Having known about the broad categories of SQL commands let us see some more SQL important terminologies.
Constraint Handling can be done in two levels namely:
• Column Level
• Table Level
Some of the Constraints used in SQL are:
The keyword NOT NULL marks a column that the particular column cannot contain null. By default column contains null unless we define the constraint NOT NULL. This is a column level constraint as it can be defined for columns only.
PRIMARY KEY
A column or a group of columns together can be defined as PRIMARY KERY. If a column or a group of columns are defined as a PRIMARY KEYS then the value of the primary key cannot appear more than once in the table. Also those columns defined as primary keys cannot have null values in it.
A table requires a key which uniquely identifies each row in the table. This is entity integrity. The key could have one column, or it could use all the columns. It should not use more columns than necessary. A key with more than one column is called a composite key.
A table may have several possible keys, the candidate keys, from which one is chosen as the primary key. If the rows of the data are not unique, it is necessary to generate an artificial primary key.
REFERENTIAL INTEGRITY
The table on which the column or a combination of columns is defined by this constraint is called the foreign key is called child table. When this constraint is defined a relation is defined between this table which has the foreign key and a table that has the primary key in relationship with this. This is called as referenced key. The table which has the primary key or in other words the referenced key is called as parent table.
Some of the functions are:
• To find the absolute value of a number we can use the SQL function ABS (number);
• To round a number to a specified number of decimal places SQL command used is
ROUND (number, number of decimal places to be rounded);
• To convert a char to a number SQL function used is TO_NUMBER (char value);
Views are created by suing CREATE VIEW command in SQL
SYNTAX: CREATE VIEW viewname AS SELECT statement
One of the important points to consider while a user uses views is that we have seen that vies are created from a base table and if suppose the base table is deleted after which if a user tries to use or access the view error will occur.
SYNTAX: CREATE synonym name FOR username.tablename;
There are many more SQL commands and terminologies in SQL but the above gives only an overview of the basics of SQL.
Refence:
http://www.exforsys.com/tutorials/programming-concepts/sql-basic-concepts.html
http://db.grussell.org/sql1.html
TRANSACTION PROCESSING SYSTEM (TPS)
Transaction Processing Systems were the exclusive domain of mainframe computers. Typical examples of such systems would be Airline Reservation Systems, Banking Systems, or the Accounting System of almost any large company. Because of this, Transaction Processing Systems are mostly unknown to the world of personal computers.
But all of this is about to change drastically, and it's all because of the Internet. Today, many small companies, non-commercial organizations, and even private individuals are discovering applications that can benefit from a Transaction Processing System.
The main problems addressed by Transaction Processing Systems are:
- the need to handle hundreds, even thousands of simultaneous Users
- the need to allow many Users to work on the same set of data, with immediate updating
- the need to handle errors in a safe and consistent manner
Transaction processing systems provide three functional areas:
System runtime functions
Transaction processing systems provide an execution environment that ensures the integrity, availability, and security of data. It also ensures fast response time and high transaction throughput.
System administration functions
Transaction processing systems provide administrative support that lets users configure, monitor, and manage their transaction systems.
Application development functions
Transaction processing systems provide functions for use in custom business applications, including functions to access data, to perform intercomputer communications, and to design and manage the user interface.
The services of a transaction processing system runtime environment include the following:
- Scheduling and load balancing. Controlling the rate and order in which tasks are processed to give higher-priority tasks the best response times and to adapt to the availability of application servers and other system resources.
- Managing system resources. Maintaining a pool of operating system resources to be used for transaction processing, loading application programs, and acquiring and releasing storage.
- Monitoring. Monitoring the progress of tasks, suspending those waiting for input, adjusting task priorities, and resolving problems.
- Managing data. Obtaining required data needed by tasks, coordinating resource managers (such as file servers and database managers), locking data for update, and logging changes.
- Managing communications. Monitoring communications with users and between servers and other systems, starting communications sessions as needed, managing data handling and conversion, and routing data to the right destination.
- Time management. Managing transaction processing in relation to the passage of time, starting tasks at predefined times, logging the date and time of events onto disk, and regularly controlling part of the business system to provide degrees of automation.
Services for systems administration and application development are described in subsequent sections.
Operations Research (O.R.)
In the last lecture, madam has mention about operating research (OR). So this time i would like to learn together with you all what actually the operating research are and what is the functions of using operating research.
Operations research (O.R.) is the discipline of applying advanced analytical methods to help make better decisions. OR will use the mathematical modeling to analyze complex situations, operations research gives executives the power to make more effective decisions and build more productive systems based on:
- More complete data
- Consideration of all available options
- Careful predictions of outcomes and estimates of risk
- The latest decision tools and technique
To achieve these results, O.R. professionals draw upon the latest analytical technologies, including:
- Simulation==>Giving you the ability to try out approaches and test ideas for improvement
- Optimization==>Narrowing the choices to the very best when there are virtually innumerable feasible options and comparing them is difficult
- Probability and Statistics==> Helping to measure risk, mine data to find valuable connections and insights, test conclusions, and make reliable forecasts
There are several advantages when we are using OR to analyze:
- Better Control: The management of large organizations recognize that it is a difficult and costly affair to provide continuous executive supervision to every routine work. An O.R. approach may provide the executive with an analytical and quantitative basis to identify the problem area. The most frequently adopted applications in this category deal with production scheduling and inventory replenishment.
- Better Systems: Often, an O.R. approach is initiated to analyze a particular problem of decision making such as best location for factories, whether to open a new warehouse, etc. It also helps in selecting economical means of transportation, jobs sequencing, production scheduling, replacement of old machinery, etc.
- Better Decisions: O.R. models help in improved decision making and reduce the risk of making erroneous decisions. O.R. approach gives the executive an improved insight into how he makes his decisions.
- Dependence on an Electronic Computer: O.R. techniques try to find out an optimal solution taking into account all the factors. In the modern society, these factors are enormous and expressing them in quantity and establishing relationships among these require voluminous calculations that can only be handled by computers.
- Non-Quantifiable Factors: O.R. techniques provide a solution only when all the elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified find no place in O.R. models.
- Distance between Manager and Operations Researcher: O.R. being specialist's job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Thus, there is a gap between the two.
- Money and Time Costs: When the basic data are subjected to frequent changes, incorporating them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after sometime.
- Implementation: Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behavior.
1. Finance, Budgeting and Investments
- Credit policy analysis.
- Cash flow analysis.
- Dividend policies.
- Investment portfolios.
2. Marketing
- Product selection, timing, etc.
- Advertising media, budget allocation.
- Number of salesman required.
- Selection of product mix.
3. Purchasing, Procurement and Exploration
- Optimal buying and reordering.
- Replacement policies
4. Production Management
- Location and size of warehouses, factories, retail outlets, etc.
- Distribution policy.
- Loading and unloading facilities for trucks, etc.
- Production scheduling.
- Optimum product mix.
- Project scheduling and allocation of resources.
5. Personnel Management
- Selection of suitable personnel.
- Recruitment of employees.
- Assignment of jobs.
- Skills balancing.
6. Research and Development
- Project selection.
- Control of R&D projects.
- Reliability and alternative design.
Sources retrieved from:
http://www.scienceofbetter.org/what/index.htm
http://www.universalteacherpublications.com/univ/ebooks/or/Ch1/advlim.htm
Knowledge workers
They analyze information and apply expertise in a variety of areas to solve problems, generate ideas, or create new products and services. Examples of knowledge workers include professionals, scientists, educators, and information system designers. Knowledge work is characterized by the use of information, by unique work situations, and by creativity and autonomy. Knowledge workers make decisions rather than physical items and work with ideas rather than with objects. Their work focuses on mental rather than muscle power and is characterized by non-repetitive tasks.
In competitive working environment, employees have the freedom to choose their work methods and work in the environments in which they function best. Treating knowledge workers as the new bosses means that management operates as a facilitator rather than as a controller of work. This gives knowledge workers the autonomy they need to complete their work as they see fit. Employers make work attractive and rewarding by providing growth opportunities, such as those that are associated with ongoing training and development, special assignments, and rotation of jobs and job responsibilities. In such ways, employers attempt to address the knowledge worker shortage.
Author: William W. Prince
Retrieved from http://www.referenceforbusiness.com/management/Int-Loc/Knowledge-Workers.html
This article tell the stories of "How to think like knowledge worker?"
http://unpan1.un.org/intradoc/groups/public/documents/unpan/unpan031277.pdf
"Are All Employees Knowledge Workers?"
http://blogs.hbr.org/bigshift/2010/04/are-all-employees-knowledge-wo.html
"Knowledge Workers and Knowledge Work"
SPSS Software
Nowadays, competitive in the market become more intense. To make sure your firm can gain more competitive advantage in the future you will need to doing a forecasting. So, organizations in virtually every industry around the globe are realizing the benefits of using data to align their current actions with their future objectives. By incorporating predictive analytic s into their daily operations, these organizations have gained control over the decisions they make every day, so that they can successfully meet their business goals. Then, SPSS is a suitable software that is able to help you.
Actually, SPSS and Microsoft Excel is same. But why i suggest that SPSS to you? Even Microsoft Excel also can be use to analyze, manipulate, provide visual comparison data and so on but it's still have something missing compare with SPSS software. By the help of the function on SPSS, it would able to enhance the function of Excel. The following example is focus on IBM SPSS.
For decades, analysts have relied on IBM SPSS Statistics to help them guide decision-making through data analysis. IBM SPSS Advantage for Excel 2007 provides selected IBM SPSS Statistics techniques, plus the ability to access, manage and analyze enormous amounts of data.
This means you can discover information in your data even if you don’t have a detailed knowledge of statistics. IBM SPSS Advantage for Microsoft Excel includes 10 procedures specifically chosen to enable business users to use advanced data preparation and analysis tools within Excel. In particular, it features procedures for conducting recency, frequency and monetary value (RFM) analysis. Wizards guide you through the steps to help you manage and explore data, find value in your large datasets and perform analysis.
- Conduct RFM analysis
- Easily identify groups
- Find unusual data
- Prepare and transform data
- Save Excel tables to native IBM SPSS data files
Information retrieved from:
http://www.spss.com/software/statistics/
http://ittraining.iu.edu/ematerials/samples/SPSBAv8.0.0.TRUNC.pdf
http://www.youtube.com